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L. Whitten}, + Date-Added = {2019-04-12 14:52:42 +0200}, + Date-Modified = {2019-04-12 14:53:34 +0200}, + Doi = {10.1063/1.1679012}, + Journal = {J. Chem. Phys.}, + Pages = {4496}, + Title = {Coulombic potential energy integrals and approximations}, + Volume = {58}, + Year = {1973}} + +@article{BarLoo-JCP-17, + Author = {Barca, Giuseppe MJ and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2019-04-11 14:20:15 +0200}, + Date-Modified = {2019-04-11 14:20:29 +0200}, + File = {/Users/loos/Zotero/storage/DCFUMHWZ/56.pdf}, + Journal = {J. Chem. Phys.}, + Number = {2}, + Pages = {024103}, + Shorttitle = {Three-and Four-Electron Integrals Involving {{Gaussian}} Geminals}, + Title = {Three-and Four-Electron Integrals Involving {{Gaussian}} Geminals: {{Fundamental}} Integrals, Upper Bounds, and Recurrence Relations}, + Volume = {147}, + Year = {2017}} + +@article{FelPet-JCP-09, + Author = {D. Feller and K. A. Peterson}, + Date-Added = {2019-04-07 20:41:03 +0200}, + Date-Modified = {2019-04-07 20:41:44 +0200}, + Doi = {10.1063/1.478747}, + Journal = {J. Chem. Phys.}, + Pages = {8384}, + Title = {Re-examination of atomization energies for the Gaussian-2 set of molecules}, + Volume = {110}, + Year = {1999}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.478747}} + +@article{FelPetDix-JCP-08, + Author = {D. Feller and K. A. Peterson and D. A. Dixon}, + Date-Added = {2019-04-07 20:39:13 +0200}, + Date-Modified = {2019-04-07 20:40:12 +0200}, + Doi = {10.1063/1.3008061}, + Journal = {J. Chem. Phys.}, + Pages = {204105}, + Title = {A survey of factors contributing to accurate theoretical predictions of atomization energies and molecular structures}, + Volume = {129}, + Year = {2008}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3008061}} + +@article{FelPetHil-JCP-11, + Author = {D. Feller and K. A. Peterson and J. G Hill}, + Date-Added = {2019-04-07 20:37:05 +0200}, + Date-Modified = {2019-04-07 20:38:11 +0200}, + Journal = {J. Chem. Phys.}, + Keywords = {10.1063/1.3613639}, + Pages = {044102}, + Title = {On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies}, + Volume = {135}, + Year = {2011}} + +@article{FelPet-JCP-13, + Author = {D. Feller and K. A. Peterson}, + Date-Added = {2019-04-07 20:35:12 +0200}, + Date-Modified = {2019-04-07 20:36:01 +0200}, + Doi = {10.1063/1.4819125}, + Journal = {J. Chem. Phys.}, + Pages = {084110}, + Title = {An expanded calibration study of the explicitly correlated CCSD(T)-F12b method using large basis set standard CCSD(T) atomization energies}, + Volume = {139}, + Year = {2013}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4819125}} + +@article{Gro-JCP-09, + Author = {J. C. Grossman}, + Date-Added = {2019-04-07 20:32:32 +0200}, + Date-Modified = {2019-04-07 20:33:29 +0200}, + Doi = {10.1063/1.1487829}, + Journal = {J. Chem. Phys.}, + Pages = {1434}, + Title = {Benchmark quantum Monte Carlo calculations}, + Volume = {117}, + Year = {2002}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1487829}} + +@article{KesSylKohTewMar-JCP-18, + Author = {M. K. Kesharwani and N. Sylvetsky and A. Kohn and D. P. Tew and Jan M. L. Martin}, + Date-Added = {2019-04-07 20:30:12 +0200}, + Date-Modified = {2019-04-07 20:36:23 +0200}, + Doi = {10.1063/1.5048665}, + Journal = {J. Chem. Phys.}, + Pages = {154109}, + Title = {Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies}, + Volume = {149}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5048665}} + +@article{NemTowNee-JCP-10, + Author = {Nemec, Norbert and Towler, Michael D. and Needs, R. J.}, + Date-Added = {2019-04-07 20:28:31 +0200}, + Date-Modified = {2019-04-07 20:28:40 +0200}, + Doi = {10.1063/1.3288054}, + Issn = {1089-7690}, + Journal = {J. Chem. Phys.}, + Month = {Jan}, + Number = {3}, + Pages = {034111}, + Publisher = {AIP Publishing}, + Title = {Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules}, + Url = {http://dx.doi.org/10.1063/1.3288054}, + Volume = {132}, + Year = {2010}, + Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3288054}} + +@article{Hylleraas30, + Author = {E. A. Hylleraas}, + Date-Added = {2019-04-07 14:28:20 +0200}, + Date-Modified = {2019-04-07 14:28:20 +0200}, + Journal = {Z. Phys.}, + Pages = {209}, + Volume = {65}, + Year = {1930}} + +@article{Hyl-ZP-29, + Author = {E. A. Hylleraas}, + Date-Added = {2019-04-07 14:28:17 +0200}, + Date-Modified = {2019-04-07 14:29:49 +0200}, + Journal = {Z. Phys.}, + Pages = {347}, + Title = {Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium}, + Volume = {54}, + Year = {1929}} + +@article{IrmGru-arXiv-2019, + Author = {A. Irmler and A. Gruneis}, + Date-Added = {2019-04-07 14:23:32 +0200}, + Date-Modified = {2019-04-07 14:24:07 +0200}, + Journal = {arXiv}, + Title = {Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory}, + Volume = {1903.05559}, + Year = {2019}} + +@article{IrmHumGru-arXiv-2019, + Author = {A. Irmler and F. Hummel and A. Gruneis}, + Date-Added = {2019-04-07 14:22:15 +0200}, + Date-Modified = {2019-04-07 14:23:22 +0200}, + Journal = {arXiv}, + Title = {On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories}, + Volume = {1903.05458}, + Year = {2019}} + +@article{BooCleAlaTew-JCP-2012, + Author = {G. H. Booth and D. Cleland and A. Alavi and D. P. Tew}, + Date-Added = {2019-04-07 14:20:11 +0200}, + Date-Modified = {2019-04-07 14:21:08 +0200}, + Doi = {10.1063/1.4762445}, + Journal = {J. Chem. Phys.}, + Pages = {164112}, + Title = {An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo}, + Volume = {137}, + Year = {2012}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4762445}} + +@article{TorVal-JCP-09, + Author = {M. Torheyden and E. F. Valeev}, + Date-Added = {2019-04-07 14:18:42 +0200}, + Date-Modified = {2019-04-07 14:19:34 +0200}, + Doi = {10.1063/1.3254836}, + Journal = {J. Chem. Phys.}, + Pages = {171103}, + Title = {Universal perturbative explicitly correlated basis set incompleteness correction}, + Volume = {131}, + Year = {2009}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3254836}} + +@article{KonVal-JCP-11, + Author = {L. Kong and E. F. Valeev}, + Date-Added = {2019-04-07 14:15:52 +0200}, + Date-Modified = {2019-04-07 14:40:18 +0200}, + Doi = {10.1063/1.3664729}, + Journal = {J. Chem. Phys.}, + Pages = {214105}, + Title = {{{SF-[2]$_\text{R12}$}}: A spin-adapted explicitly correlated method applicable to arbitrary electronic states}, + Volume = {135}, + Year = {2011}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3664729}} + +@article{KonVal-JCP-10, + Author = {L. Kong and E. F. Valeev}, + Date-Added = {2019-04-07 14:14:33 +0200}, + Date-Modified = {2019-04-07 14:16:10 +0200}, + Doi = {10.1063/1.3499600}, + Journal = {J. Chem. Phys.}, + Pages = {174126}, + Title = {Perturbative correction for the basis set incompleteness error of complete-active- space self-consistent field}, + Volume = {133}, + Year = {2010}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3499600}} + +@misc{g09, + Author = {M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria and M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and B. Mennucci and G. A. Petersson and H. Nakatsuji and M. Caricato and X. Li and H. P. Hratchian and A. F. Izmaylov and J. Bloino and G. Zheng and J. L. 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Theory Comput.}, + Pages = {1395}, + Title = {Deterministic construction of nodal surfaces within quantum Monte Carlo: the case of FeS}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b01250}} + +@article{QP2, + Author = {Y. Garniron and K. Gasperich and T. Applencourt and A. Benali and A. Fert{\'e} and J. Paquier and B. Pradines and R. Assaraf and P. Reinhardt and J. Toulouse and P. Barbaresco and N. Renon and G. David and J. P. Malrieu and M. V{\'e}ril and M. Caffarel and P. F. Loos and E. Giner and A. Scemama}, + Date-Added = {2019-04-07 13:54:16 +0200}, + Date-Modified = {2019-04-07 13:54:21 +0200}, + Journal = {J. Chem. Theory Comput.}, + Title = {Quantum Package 2.0: a open-source determinant-driven suite of programs}, + Volume = {submitted}, + Year = {2019}} + +@article{PerRuzTaoStaScuCso-JCP-05, + Author = {J. P. Perdew and A. Ruzsinszky and J. Tao and V. N. Staroverov and G. E. Scuseria and G. I. 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Rev.}, + Pages = {75}, + Title = {Explicitly Correlated R12/F12 Methods for Electronic Structure}, + Volume = {112}, + Year = {2012}} + +@article{HatKloKohTew-CR-12, + Author = {C. Hattig and W. Klopper and A. Kohn and D. P. Tew}, + Date-Added = {2019-04-03 21:43:00 +0200}, + Date-Modified = {2019-04-07 14:36:11 +0200}, + Journal = {Chem. Rev.}, + Pages = {4}, + Title = {Explicitly Correlated Electrons in Molecules}, + Volume = {112}, + Year = {2012}} + +@article{KloBacTewHat-PRA-10, + Author = {W. Klopper and R. A. Bachorz and D. P. Tew and C. Hattig}, + Date-Added = {2019-04-03 21:43:00 +0200}, + Date-Modified = {2019-04-03 21:43:29 +0200}, + Journal = {Phys. Rev. A}, + Pages = {022503}, + Volume = {81}, + Year = {2010}} + +@article{TewKlo-JCP-05, + Author = {D. P. Tew and W. Klopper}, + Date-Added = {2019-04-03 21:43:00 +0200}, + Date-Modified = {2019-04-03 21:43:18 +0200}, + Journal = {J. Chem. 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Nachtigall}, + Journal = {Theor. Chem. Acc.}, + Pages = {135}, + Volume = {99}, + Year = {1998}} + +@article{BouBenMayCaf-JCP-09, + Author = {T. Bouab\c{c}a and N. Ben Amor and D. Maynau and M. Caffarel}, + Journal = {J. Chem. Phys.}, + Pages = {114107}, + Volume = {130}, + Year = {2009}} + +@article{BouBraCaf-JCP-10, + Author = {T. Bouab\c{c}a and B. Bra\"ida and M. Caffarel}, + Journal = {J. Chem. Phys.}, + Pages = {044111}, + Title = {Multi-Jastrow trial wavefunctions for electronic structure calculations with quantum Monte Carlo}, + Volume = {133}, + Year = {2010}} + +@article{BouChiLegDucBlaJac-JCTC-14, + Author = {{P. Boulanger, S. Chibani, B. Le Guennic, I. Duchemin, X. Blase, and D. Jacquemin}}, + Journal = {J. Chem. Theory Comput.}, + Pages = {4548}, + Volume = {10}, + Year = {2014}} + +@article{BouJacDucBla-JCTC-14, + Author = {P. Boulanger and D. Jacquemin and I. Duchemin and X. Blase}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1212}, + Volume = {10}, + Year = {2014}} + +@article{BowSugAld-PRB-94, + Author = {C. Bowen and G. Sugiyama and B. J. Alder}, + Journal = {Phys. Rev. B}, + Pages = {14838}, + Volume = {{50}}, + Year = {1996}} + +@article{BoyCou-JPB-73, + Author = {R. J. Boyd and C. A. Coulson}, + Journal = {J. Phys. B}, + Pages = {782}, + Volume = {6}, + Year = {1973}} + +@article{BoySarUga-JPB-88, + Author = {R. J. Boyd and C. Sarasola and J. M. Ugalde}, + Journal = {J. Phys. B}, + Pages = {2555}, + Volume = {21}, + Year = {1988}} + +@article{BraHib-02, + Author = {B. Braida and L. Thogersen and W. Wu and P. C. Hiberty}, + Journal = {J. Am. Chem. Soc.}, + Pages = {11781}, + Volume = {124}, + Year = {2002}} + +@article{BraHib-04, + Author = {B. Braida and P. C. Hiberty}, + Journal = {J. Am. Chem. Soc.}, + Pages = {14890}, + Volume = {126}, + Year = {2004}} + +@article{BraHib-08, + Author = {B. Braida and P. C. Hiberty}, + Journal = {J. Phys. Chem. A}, + Pages = {13045}, + Volume = {112}, + Year = {2008}} + +@article{BraTouCafUmr-JCP-11, + Author = {B. Bra\"ida and J. Toulouse and M. Caffarel and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {084108}, + Title = {Quantum Monte Carlo with Jastrow-valence-bond wave functions}, + Volume = {134}, + Year = {2011}} + +@misc{BraTouCafUmr-JJJ-XX-note2, + Note = {In our BOVB wave functions, we use different sets of orbital coefficients, but a single set of basis exponents shared by all orbital sets.}} + +@misc{BraTouCafUmr-JJJ-XX-note3, + Note = {Bouab\c{c}a {\it et al.}~\cite{BouBraCaf-JCP-10} have introduced a wave function with several Jastrow factors attached to individual molecular orbitals. With such a wave function, the correlation effects can be treated differently in atomic and binding regions. In the case of the FH molecule, no atomic core Jastrow was used and two different valence Jastrow factors (one for the lone pairs paying a role in the bond and the other one for the $\sigma$-bond) were introduced. The resulting binding energy was essentially exact within error bars. Combining the various VB wave functions discussed in this work with this multi-Jastrow approach is presently under investigation.}} + +@misc{BraTouCafUmr-JJJ-XX-note, + Note = {In the condensed-matter community, ``stricly localized orbitals'' often refers to orbitals that vanish exactly at some finite distance. In the present work, ``stricly localized orbitals'' is employed in the sense usually used in the quantum chemistry community, i.e. orbitals expanded on Gaussian or Slater basis functions centered on a single atom. Thus, these orbitals vanish exactly only at infinite distance.}} + +@article{BreAda-JCP-11, + Author = {E. Br\'emond and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {024106}, + Volume = {135}, + Year = {2011}} + +@article{BreBou-PRB-96, + Author = {J. L. Bretonnet and M. Boulahbak}, + Journal = {Phys. Rev. B}, + Pages = {6859}, + Volume = {{53}}, + Year = {1996}} + +@incollection{BreCepRey-INC-01, + Author = {D. Bressanini and D. M. Ceperley and P. Reynolds}, + Booktitle = {Recent Advances in Quantum Monte Carlo Methods, II}, + Editor = {S. Rothstein}, + Publisher = {World Scientific}, + Title = {What do we know about wave function nodes?}, + Year = {2001}} + +@article{BreMelMor-PRA-98, + Author = {D. Bressanini and M. Mella and G. Morosi}, + Journal = {Phys. Rev. A}, + Pages = {1678}, + Volume = {57}, + Year = {1998}} + +@article{BreMorTar-JCP-05, + Author = {D. Bressanini and G. Morosi and S. Tarasco}, + Journal = {J. Chem. Phys.}, + Pages = {204109}, + Volume = {123}, + Year = {2005}} + +@article{BroDevLem-PRB-80, + Author = {F. Brosens and J. T. Devreese and L. F. Lemmens}, + Journal = {Phys. Rev. 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Phys.}, + Pages = {044301}, + Volume = {147}, + Year = {2017}} + +@phdthesis{Bru-THESIS-05, + Author = {F. Bruneval}, + School = {Ecole Polytechnique}, + Year = {2005}} + +@article{BuiBae-MP-02, + Author = {M. A. Buijse and E. J. Baerends}, + Journal = {Mol. Phys.}, + Pages = {401}, + Volume = {100}, + Year = {2002}} + +@article{BurCruLam-JCP-98, + Author = {K. Burke and F. G. Cruz and K.-C. Lam}, + Journal = {J. Chem. Phys}, + Pages = {8161}, + Volume = {109}, + Year = {1998}} + +@article{BurErnPer-CPL-97, + Author = {K. Burke and M. Ernzerhof and J. P. Perdew}, + Journal = {Chem. Phys. Lett.}, + Pages = {115}, + Volume = {265}, + Year = {1997}} + +@article{BurFilDol-JCP-07, + Author = {M. Burkatzki and C. Filippi and M. Dolg}, + Journal = {J. Chem. Phys.}, + Pages = {234105}, + Volume = {126}, + Year = {2007}} + +@article{Bur-JCP-12, + Author = {K. Burke}, + Journal = {J. Chem. Phys.}, + Pages = {150901}, + Title = {{Perspective on density functional theory}}, + Volume = {136}, + Year = {2012}} + +@article{BurPerErn-JCP-98, + Author = {K. Burke and J. P. Perdew and M. Ernzerhof}, + Journal = {J. Chem. Phys}, + Pages = {3760}, + Volume = {109}, + Year = {1998}} + +@article{BurPer-IJQC-95, + Author = {K. Burke and J. P. Perdew}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {199}, + Volume = {{56}}, + Year = {1995}} + +@article{BurPerLan-PRL-94, + Author = {K. Burke and J. P. Perdew and D. C. Langreth}, + Journal = {Phys. Rev. Lett.}, + Pages = {1283}, + Volume = {73}, + Year = {1994}} + +@article{BurPerLev-PRA-96, + Author = {K. Burke and J. P. Perdew and M. Levy}, + Journal = {Phys. Rev. A}, + Pages = {R2915}, + Volume = {53}, + Year = {1996}} + +@inbook{BurPerWan-INC-98, + Address = {NY}, + Author = {Kieron Burke and John P. Perdew and Y. Wang}, + Booktitle = {Electronic Density Functional Theory: Recent Progress and New Directions}, + Date-Modified = {2013-02-12 00:16:04 +0000}, + Editor = {J. F. Dobson and G. Vignale and M. P. Das}, + Organization = {Plenum}, + Pages = {81}, + Pub-Num = {34}, + Publisher = {Plenum}, + Title = {Derivation of a generalized gradient approximation: The PW91 density functional}, + Url = {http://link.springer.com/chapter/10.1007%2F978-1-4899-0316-7_7}, + Year = {1997}, + Bdsk-Url-1 = {http://link.springer.com/chapter/10.1007%2F978-1-4899-0316-7_7}} + +@article{BygAllMan-JCP-12, + Author = {P. J. Bygrave and N. L. Allan and F. R. Manby}, + Journal = {J. Chem. Phys.}, + Pages = {164102}, + Volume = {137}, + Year = {2012}} + +@article{BylKle-PRB-90, + Author = {D. M. Bylander and L. Kleinman}, + Journal = {Phys. Rev. B}, + Pages = {7868}, + Volume = {41}, + Year = {1990}} + +@article{ByrCotMon-JCP-11, + Author = {{J. N. Byrd, R. C\^ot\'e, and J. A. Montgomery, Jr}}, + Journal = {J. Chem. Phys.}, + Pages = {244307}, + Volume = {135}, + Year = {2011}} + +@article{BytRue-JCP-05, + Author = {L. Bytautas and K. Ruedenberg}, + Journal = {J. Chem. Phys.}, + Pages = {154110}, + Volume = {122}, + Year = {2005}} + +@misc{BytRue-JCP-05-note, + Note = {Note that this estimate of the exact well depth differs from the one used in Ref.~\onlinecite{UmrTouFilSorHeg-JJJ-XX} where we used instead the scalar-relativistic, valence-corrected estimate of Ref.~\onlinecite{BytRue-JCP-05} since calculations were performed with a relativistic pseudopotential.}} + +@article{CadWah-ADNDT-74, + Author = {P. E. Cade and A. C. Wahl}, + Journal = {At. Data Nucl. Data Tables}, + Pages = {340}, + Volume = {13}, + Year = {1974}} + +@article{Caf-ActNum-98, + Author = {R. E. Caflisch}, + Journal = {Acta Numerica}, + Pages = {1}, + Title = {{Monte Carlo and quasi-Monte Carlo methods}}, + Volume = {1998}, + Year = {1998}} + +@article{CafCla-JCP-88, + Author = {M. Caffarel and P. Claverie}, + Doi = {10.1063/1.454228}, + Journal = {J. Chem. Phys.}, + Keywords = {QUANTUM STATISTICAL MECHANICS; MONTE CARLO METHOD; FERMIONS; FEYNMAN PATH INTEGRAL; SCHROEDINGER EQUATION}, + Number = {2}, + Pages = {1100-1109}, + Publisher = {AIP}, + Title = {{Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman--Kac formula. II. Applications to simple systems}}, + Volume = {88}, + Year = {1988}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.454228}} + +@article{CaiRei-JCP-00, + Author = {Z.-L. Cai and J. R. Reimers}, + Journal = {J. Chem. Phys.}, + Pages = {527}, + Volume = {112}, + Year = {2000}} + +@article{CaiZanKitKocKreScr-PRA-05, + Author = {J. Caillat and J. Zanghellini and M. Kitzler and O. Koch and W. Kreuzer and A. Scrinzi}, + Journal = {Phys. Rev. A}, + Pages = {012712}, + Volume = {71}, + Year = {2005}} + +@article{CalSor-PRB-98, + Author = {{M. Calandra Buonaura and S. Sorella}}, + Journal = {Phys. Rev. B}, + Pages = {11446}, + Title = {{Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers}}, + Volume = {57}, + Year = {1998}} + +@article{CanBoyTha-JCP-93, + Author = {N. M. Cann and R. J. Boyd and A. J. Thakkar}, + Journal = {J. Chem. Phys.}, + Pages = {7132}, + Volume = {98}, + Year = {1993}} + +@article{CanMou-NL-14, + Author = {Eric Canc\`es and Nahia Mourad}, + Journal = {Nonlinearity}, + Number = {9}, + Pages = {1999}, + Title = {A mathematical perspective on density functional perturbation theory}, + Volume = {27}, + Year = {2014}} + +@article{CanPer-JCP-08, + Author = {E. Canc\`es and K. Pernal}, + Journal = {J. Chem. Phys.}, + Pages = {134108}, + Title = {{Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations}}, + Volume = {128}, + Year = {2008}} + +@article{CapNalPar-JCP-82, + Author = {Joseph F. Capitani and Roman F. Nalewajski and Robert G. 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Chem.}, + Pages = {287}, + Title = {Progress in Time-Dependent Density-Functional Theory}, + Volume = {63}, + Year = {2012}} + +@incollection{CasHui-TCC-15, + Author = {M. E. Casida and M. Huix-Rotllant}, + Booktitle = {Density-Functional Methods for Excited States}, + Doi = {10.1007/128_2015_632}, + Editor = {N. Ferr\'e and M. Filatov and M. Huix-Rotllant}, + Publisher = {Springer}, + Series = {Topics in Current Chemistry}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1007/128_2015_632}} + +@incollection{Cas-INC-95, + Address = {Singapore}, + Author = {M. E. Casida}, + Booktitle = {Recent Advances in Density Functional Methods, Part I}, + Editor = {D. P. Chong}, + Pages = {155}, + Publisher = {World Scientific}, + Year = {1995}} + +@article{CasJamCasSal-JCP-98, + Author = {M. E. Casida and C. Jamorski and K. C. Casida and D. R. Salahub}, + Journal = {J. Chem. Phys.}, + Pages = {4439}, + Volume = {108}, + Year = {1998}} + +@article{Cas-JCP-05, + Author = {M. E. 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Cundari}, + Pages = {91-165}, + Publisher = {Wiley, Hoboken}, + Title = {Excited states from time-dependent density functional theory}, + Year = {2009}} + +@article{EllGolCanMai-CP-11, + Author = {P. Elliot and S. Goldson and C. Canahui and N. T. Maitra}, + Journal = {Chem. Phys.}, + Pages = {110}, + Title = {{Perspectives on double-excitations in TDDFT}}, + Volume = {391}, + Year = {2011}} + +@article{Ell-JPB-77, + Author = {D. E. Ellis}, + Journal = {J. Phys. B,}, + Volume = {10}, + Year = {1977}} + +@article{ElsHobFraSuhKax-JCP-01, + Author = {M. Elstner and P. Hobza and T. Frauenheim and S. Suhai and E. Kaxiras}, + Journal = {J. Chem. Phys.}, + Pages = {5149}, + Volume = {114}, + Year = {2001}} + +@article{EmaGarRamLopFerMeiPal-JCC-03, + Author = {{I. Ema, J. M. Garc\'ia de la Vega, G. Ram\'irez, R. L\'opez, J. Fern\'andez Rico, H. Meissner and J. Paldus}}, + Journal = {J. Comput. Chem.}, + Pages = {859}, + Volume = {24}, + Year = {2003}} + +@article{EmaGarRamLopFerMeiPal-JCC-03_fr, + Author = {{I. Ema, J. M. Garc\'ia de la Vega, G. Ram\'irez, R. L\'opez, J. Fern\'andez Rico, H. Meissner et J. Paldus}}, + Journal = {J. Comput. Chem.}, + Pages = {859}, + Volume = {24}, + Year = {2003}} + +@article{EngBon-IJMPB-01, + Author = {E. Engel and A. F. Bonetti}, + Journal = {Int. J. Mod. Phys. B}, + Pages = {1703}, + Volume = {15}, + Year = {2001}} + +@article{EngDre-JCC-99, + Author = {E. Engel and R. M. Dreizler}, + Journal = {J. Comput. Chem.}, + Pages = {31}, + Volume = {20}, + Year = {1999}} + +@incollection{EngDre-TCC-96, + Address = {Berlin}, + Author = {E. Engel and R. M. Drezler}, + Booktitle = {Density-Functional Theory II, Topics in Current Chemistry Vol. 181}, + Editor = {R. F. Nalewajski}, + Pages = {1}, + Publisher = {Springer}, + Year = {1996}} + +@article{EngHocDre-PRA-00, + Author = {E. Engel and A. H\"ock and R. M. Dreizler}, + Journal = {Phys. Rev. A}, + Pages = {032502}, + Volume = {61}, + Year = {2000}} + +@incollection{Eng-INC-02, + Author = {E. Engel}, + Booktitle = {Relativistic Electronic Structure Theory, Part 1: Fundamentals}, + Editor = {P. Schwerdtfeger}, + Pages = {523-621}, + Publisher = {Elsevier}, + Series = {Theoretical and Computational Chemistry, Vol. 11}, + Year = {2002}} + +@incollection{Eng-INC-03, + Address = {Berlin}, + Author = {E. Engel}, + Booktitle = {A Primer in Density Functional Theory}, + Editor = {C. Fiolhais and F. Nogueira and M. A. L. Marques}, + Pages = {56-122}, + Publisher = {Springer}, + Series = {Vol. 620 of Lecture Notes in Physics}, + Year = {2003}} + +@article{EngJiaFac-PRA-05, + Author = {{E. Engel, H. Jiang, and A. Facco Bonetti}}, + Journal = {Phys. Rev. A}, + Pages = {052503}, + Volume = {72}, + Year = {2005}} + +@article{EngKelDre-PRA-96, + Author = {{E. Engel, S. Keller, and R. M. Dreizler}}, + Journal = {Phys. Rev. A}, + Pages = {1367}, + Volume = {53}, + Year = {1996}} + +@article{EngKelFacMulDre-PRA-95, + Author = {{E. Engel, S. Keller, A. Facco Bonetti, H. M\"uller, and R. M. Dreizler}}, + Journal = {Phys. Rev. A}, + Pages = {2750}, + Volume = {52}, + Year = {1995}} + +@incollection{EngMulSpeDre-INC-95, + Address = {New York}, + Author = {E. Engel and H. M\"uller and C. Speicher and R. M. Dreizler}, + Booktitle = {Density Functional Theory, Vol. 337 of NATO ASI Series B}, + Editor = {E. K. U. Gross and R. M. Dreizler}, + Pages = {65}, + Publisher = {Plenum}, + Year = {1995}} + +@article{Eng-PRA-95, + Author = {E. Engel}, + Journal = {Phys. Rev. A}, + Pages = {1159}, + Volume = {{51}}, + Year = {1995}} + +@article{EngVos-PRB-93, + Author = {E. Engel and S. H. Vosko}, + Journal = {Phys. Rev. B}, + Pages = {13164}, + Volume = {{47}}, + Year = {1993}} + +@article{ErhBleGor-PRL-16, + Author = {J. Erhard and P. Bleiziffer and A. G\"orling}, + Journal = {Phys. Rev. Lett.}, + Pages = {143002}, + Volume = {117}, + Year = {2016}} + +@article{ErnBurPer-JCP-96, + Author = {M. Ernzerhof and K. Burke and J. P. Perdew}, + Journal = {J. Chem. Phys.}, + Pages = {2798}, + Volume = {105}, + Year = {1996}} + +@article{Ern-CPL-96, + Author = {M. Ernzerhof}, + Journal = {Chem. Phys. Lett.}, + Pages = {499}, + Volume = {263}, + Year = {1996}} + +@article{ErnPerBur-IJQC-97, + Author = {M. Ernzerhof and J. P. Perdew and K. Burke}, + Journal = {Int. J. Quantum Chem.}, + Pages = {285}, + Volume = {64}, + Year = {1997}} + +@incollection{ErnPerBur-INC-96, + Address = {Berlin}, + Author = {M. Ernzerhof and J. P. Perdew, and K. Burke}, + Booktitle = {Density Functional Theory}, + Editor = {R. Nalewajski}, + Publisher = {Springer-Verlag}, + Year = {1996}} + +@article{ErnPer-JCP-98, + Author = {M. Ernzerhof and J. P. Perdew}, + Journal = {J. Chem. Phys.}, + Pages = {3313}, + Volume = {{109}}, + Year = {1998}} + +@article{ErnScu-JCP-99a, + Author = {M. Ernzerhof and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {5029}, + Volume = {110}, + Year = {1999}} + +@article{EshBatFur-TCA-12, + Affiliation = {Department of Chemistry, University of California, 1102 Natural Sciences II, Irvine, CA 92697-2025, USA}, + Author = {Eshuis, Henk and Bates, Jefferson and Furche, Filipp}, + Issue = {1}, + Journal = {Theor. Chem. Acc.}, + Keyword = {Chemistry and Materials Science}, + Optnote = {10.1007/s00214-011-1084-8}, + Opturl = {http://dx.doi.org/10.1007/s00214-011-1084-8}, + Pages = {1084}, + Publisher = {Springer Berlin / Heidelberg}, + Title = {Electron correlation methods based on the random phase approximation}, + Volume = {131}, + Year = {2012}} + +@article{EshFur-JCP-12, + Author = {H. Eshuis and F. Furche}, + Journal = {J. Chem. Phys.}, + Pages = {084105}, + Volume = {136}, + Year = {2012}} + +@article{EshFur-JPCL-11, + Author = {H. Eshuis and F. Furche}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {983}, + Volume = {2}, + Year = {2011}} + +@article{EshYarFur-JCP-10, + Author = {Henk Eshuis and Julian Yarkony and Filipp Furche}, + Journal = {J. Chem. Phys.}, + Pages = {234114}, + Volume = {132}, + Year = {2010}} + +@article{EvaShuTul-JPCA-13, + Author = {F. A. Evangelista and P. Shushkov and J. C. Tully}, + Journal = {J. Phys. Chem. A}, + Pages = {7378}, + Volume = {117}, + Year = {2013}} + +@article{Ewa-AP-21, + Author = {P. P. Ewald}, + Journal = {Ann. Phys.}, + Pages = {253}, + Volume = {{64}}, + Year = {1921}} + +@misc{exp_2nd_excited_state, + Note = {Le r{\'e}sultat exp{\'e}rimental dans l'article de Alijah et Duxbury (1.411 eV) a {\'e}t{\'e} corrig{\'e} pour enlever l'{\'e}nergie de point z{\'e}ro en utilisant les calculs FCI/TZ2P de Sherrill et al. (0.004 eV).}} + +@article{FabBouDucAttBla-JCP-13, + Author = {C. Faber and P. Boulanger and I. Duchemin and C. Attaccalite and X. Blase}, + Journal = {J. Chem. Phys.}, + Pages = {194308}, + Volume = {139}, + Year = {2013}} + +@article{FabDel-JCP-07, + Author = {{E. Fabiano and F. Della Sala}}, + Journal = {J. Chem. Phys.}, + Pages = {214102}, + Volume = {126}, + Year = {2007}} + +@article{FabDel-TCA-12, + Author = {{E. Fabiano and F. Della Sala}}, + Journal = {Theor. Chem. Acc.}, + Pages = {1278}, + Volume = {131}, + Year = {2012}} + +@article{FabDucDeuBla-PRB-12, + Author = {C. Faber and I. Duchemin and T. Deutsch and X. Blase}, + Journal = {Phys. Rev. B}, + Pages = {155315}, + Volume = {86}, + Year = {2012}} + +@article{FacEngSchDre-PRL-01, + Author = {{A. Facco Bonetti, E. Engel, R. N. Schmid, and R. M. Dreizler}}, + Journal = {Phys. Rev. Lett.}, + Pages = {2241}, + Volume = {86}, + Year = {2001}} + +@article{FacEngSchDre-PRL-03, + Author = {{A. Facco Bonetti, E. Engel, R. N. Schmid, and R. M. Dreizler}}, + Journal = {Phys. Rev. Lett.}, + Pages = {219302}, + Volume = {90}, + Year = {2003}} + +@incollection{Fah-INC-99, + Address = {Dordrecht}, + Author = {S. Fahy}, + Booktitle = {Quantum Monte Carlo Methods in Physics and Chemistry}, + Editor = {M. P. Nightingale and C. J. Umrigar}, + Pages = {101}, + Publisher = {Kluwer}, + Series = {NATO ASI Ser. C 525}, + Year = {1999}} + +@article{FarHeiEngRob-PRB-93, + Author = {B. Farid and V. Heine and G. E. Engel and I. J. Robertson}, + Journal = {Phys. Rev. B}, + Pages = {11602}, + Volume = {{48}}, + Year = {1993}} + +@article{FasCorSanTru-JPCA-99, + Author = {P. L. Fast and J. Corchado and M. L. Sanchez and D. G. Truhlar}, + Journal = {J. Phys. Chem. A}, + Pages = {3139}, + Volume = {103}, + Year = {1999}} + +@article{FasSanTru-JCP-99, + Author = {P. L. Fast and M. L. S\'anchez and D. G. Truhlar}, + Journal = {J. Chem. Phys.}, + Pages = {2921}, + Volume = {111}, + Year = {1999}} + +@article{Fel-JCC-96, + Author = {D. Feller}, + Journal = {J. Comput. Chem.}, + Pages = {1571}, + Volume = {17}, + Year = {1996}} + +@article{Fel-JCP-13, + Author = {D. Feller}, + Journal = {J. Chem. Phys.}, + Pages = {074103}, + Volume = {138}, + Year = {2013}} + +@article{Fel-JCP-92, + Author = {D. Feller}, + Journal = {J. Chem. Phys.}, + Pages = {6104}, + Volume = {96}, + Year = {1992}} + +@article{Fel-JCP-93, + Author = {D. Feller}, + Journal = {J. Chem. Phys.}, + Pages = {7059}, + Volume = {98}, + Year = {1993}} + +@article{FelPetHil-JCP-10, + Author = {D. Feller and K. A. Peterson and J. G. Hill}, + Journal = {J. Chem. Phys.}, + Pages = {184102}, + Volume = {133}, + Year = {2010}} + +@article{FerAss-JCP-02, + Author = {N. Ferr\'e and X. Assfeld}, + Journal = {J. Chem. Phys.}, + Pages = {4119}, + Volume = {117}, + Year = {2002}} + +@article{FerBalLop-JCTC-15, + Author = {R. G. Fernando and M. C. Balhoff and K. Lopata}, + Journal = {J. Chem. Theory Comput.}, + Pages = {646}, + Volume = {11}, + Year = {2015}} + +@article{FerLopAguEmaRam-IJQC-01, + Author = {{J. Fern\'andez Rico, R. L\'opez, A. Aguado, I. Ema, and G. Ram\'irez}}, + Journal = {Int. J. Quantum Chem.}, + Pages = {148}, + Volume = {81}, + Year = {2001}} + +@article{Fer-PR-57, + Author = {R. A. Ferrell}, + Journal = {Phys. Rev.}, + Pages = {450}, + Volume = {{107}}, + Year = {1957}} + +@article{FerRamLopFer-CCCC-88, + Author = {{J. Fern\'andez Rico, G. Ram\'irez, R. L\'opez and J. I. Fern\'andez-Alonso}}, + Journal = {Collection Czechoslovak Chem. Commun.}, + Pages = {2250}, + Volume = {{53}}, + Year = {1988}} + +@book{FetWal-BOOK-03, + Author = {A. L. Fetter and J. D. Walecka}, + Publisher = {Dover}, + Title = {Quantum Theory of Many-Particle Systems}, + Year = {2003}} + +@article{FilAssMor-JCP-16, + Author = {C. Filippi, R. Assaraf and S. Moroni}, + Journal = {J. Chem. Phys.}, + Pages = {194105}, + Title = {{Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo}}, + Volume = {144}, + Year = {2016}} + +@article{FilFah-JCP-00, + Author = {Claudia Filippi and Stephen Fahy}, + Journal = {J. Chem. Phys.}, + Pages = {3523}, + Volume = {112}, + Year = {2000}} + +@incollection{FilGonUmr-INC-96, + Address = {Amsterdam}, + Author = {Claudia Filippi and Xavier Gonze and C. J. Umrigar}, + Booktitle = {Recent Developments of Modern Density Functional Theory}, + Editor = {J. M. Seminario}, + Pages = {295-326}, + Publisher = {Elsevier}, + Title = {Generalized gradient approximations to density functional theory: comparison with exact results}, + Year = {1996}} + +@misc{Fil-PRIV-XX, + Author = {C. Filippi}, + Note = {private communication}} + +@article{FilSha-CPL-00, + Author = {Michael Filatov and Sason Shaik}, + Journal = {Chem. Phys. Lett.}, + Pages = {409}, + Volume = {332}, + Year = {1999}} + +@article{FilSha-CPL-99, + Author = {M. Filatov and S. Shaik}, + Journal = {Chem. Phys. Lett.}, + Pages = {429}, + Title = {{A spin-restricted ensemble-referenced Kohn-Sham method and its application to diradicaloid situations}}, + Volume = {304}, + Year = {1999}} + +@article{FilSha-JPCA-00, + Author = {Michael Filatov and Sason Shaik}, + Journal = {J. Phys. Chem. A}, + Pages = {6628}, + Volume = {104}, + Year = {2000}} + +@article{FilSha-JPCA-99, + Author = {Michael Filatov and Sason Shaik}, + Journal = {J. Phys. Chem. A}, + Pages = {8885}, + Volume = {103}, + Year = {1999}} + +@article{FilShaWoeGriPey-CPL-00, + Author = {Michael Filatov and Sason Shaik and M. Woeller and S. Grimme and S.D. Peyerimhoff}, + Journal = {Chem. Phys. Lett.}, + Pages = {135}, + Volume = {316}, + Year = {2000}} + +@misc{FilTouUmr-JJJ-XX, + Author = {Claudia Filippi and Julien Toulouse and C. J. Umrigar}, + Title = {in preparation}} + +@article{FilUmrGon-JCP-97, + Author = {C. Filippi and C. J. Umrigar and X. Gonze}, + Journal = {J. Chem. Phys.}, + Pages = {9994}, + Title = {{Excitation energies from density functional perturbation theory}}, + Volume = {107}, + Year = {1997}} + +@article{FilUmrGon-PRA-96, + Author = {C. Filippi and C. J. Umrigar and X. Gonze}, + Journal = {Phys. Rev. A}, + Pages = {4810}, + Volume = {54}, + Year = {1996}} + +@article{FilUmr-JCP-96, + Author = {C. Filippi and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {213}, + Title = {Multiconfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules}, + Volume = {{105}}, + Year = {1996}} + +@article{Fil-WIR-14, + Author = {M. Filatov}, + Journal = {WIREs Comput. Mol. Sci.}, + Pages = {146}, + Title = {{Spin-restricted ensemble-referenced Kohn-Sham method: basic principles and application to strongly correlated ground and excited states of molecules}}, + Volume = {5}, + Year = {2015}} + +@article{FilZacBud-JCTC-09, + Author = {C. Filippi and M. Zaccheddu and F. Buda}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2074}, + Title = {Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods?}, + Volume = {5}, + Year = {2009}} + +@article{FilZacBud-JJJ-XX, + Author = {Claudia Filippi and Maurizio Zaccheddu and Francesco Buda}, + Note = {unpublished}} + +@incollection{FlaCafSav-INC-97, + Address = {Singapore}, + Author = {H.-J. Flad and M. Caffarel and A. Savin}, + Booktitle = {Recent advances in quantum Monte Carlo methods}, + Editor = {W. A. Lester}, + Pages = {73}, + Publisher = {World Scientific}, + Title = {Quantum Monte Carlo calculations with multi-reference trial wave functions}, + Year = {1997}} + +@misc{Fla-PRIV-XX, + Author = {H. J. Flad}, + Title = {private communication}} + +@article{FlaSav-JCP-95, + Author = {H.-J. Flad and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {691}, + Volume = {103}, + Year = {1995}} + +@article{FlaSavPre-JCP-92, + Author = {H.-J. Flad and A. Savin and H. Preuss}, + Journal = {J. Chem. Phys.}, + Pages = {459}, + Volume = {97}, + Year = {1992}} + +@article{FlaSavScuNicPre-CPL-94, + Author = {H.-J. Flad and A. Savin and M. Schultheiss and A. Nicklass and H. Preuss}, + Journal = {Chem. Phys. Lett.}, + Pages = {274}, + Volume = {222}, + Year = {1994}} + +@article{FloGda-JCP-05, + Author = {J. R. Flores and R. J. Gdanitz}, + Journal = {J. Chem. Phys.}, + Pages = {144316}, + Volume = {123}, + Year = {2005}} + +@article{Foc-ZP-30, + Author = {V. Fock}, + Journal = {Z. Phys.}, + Pages = {855}, + Volume = {63}, + Year = {1930}} + +@article{FouMitNeeRaj-RMP-01, + Author = {W. M. C. Foulkes and L. Mitas and R. J. Needs and G. Rajagopal}, + Journal = {Rev. Mod. Phys.}, + Pages = {33}, + Title = {{Quantum Monte Carlo simulations of solids}}, + Volume = {{73}}, + Year = {2001}} + +@article{FraDurMes-JCP-97, + Author = {X. Fradera and M. Duran and J. Mestres}, + Journal = {J. Chem. Phys.}, + Pages = {3576}, + Volume = {107}, + Year = {1997}} + +@article{FraFilAmo-JCTC-12, + Author = {F. Fracchia and C. Filippi and C. Amovilli}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1943}, + Title = {Size-extensive wave functions for quantum Monte Carlo: A linear scaling generalized valence bond approach}, + Volume = {8}, + Year = {2012}} + +@misc{FraLupTou-JJJ-XX, + Author = {O. Franck and E. Luppi and J. Toulouse}, + Note = {unpublished}} + +@article{FraMusLupTou-JCP-15, + Author = {O. Franck and B. Mussard and E. Luppi and J. Toulouse}, + Journal = {J. Chem. Phys.}, + Pages = {074107}, + Title = {Basis convergence of range-separated density-functional theory}, + Volume = {142}, + Year = {2015}} + +@misc{FraMusLupTou-JJJ-XX, + Author = {O. Franck and B. Mussard and E. Luppi and J. Toulouse}, + Note = {Basis convergence of range-separated density-functional theory, arXiv:1412.2613, to appear in J. Chem. Phys.}} + +@misc{FraMusLupTou-JJJ-XX-note1, + Note = {Note that the partial-wave expansion of any {\it odd} power of $r_{12}$ contains an infinite number of terms. In contrast, the partial-wave expansion of any {\it even} power of $r_{12}$ terminates at a finite $\ell$.}} + +@misc{FraMusLupTou-JJJ-XX-note2, + Note = {For a discussion of angular and radial correlation and the shape of the correlation hole in the He atom with the long-range interaction, see Ref.~\onlinecite{PolColLeiStoWerSav-IJQC-03}.}} + +@misc{FraMusLupTou-JJJ-XX-note3, + Note = {For $\mu=1$ the difference between the long-range MP2 correlation energies for $X=5$ and $X=6$ is still as small as about 0.2 mhartree.}} + +@misc{FraMusLupTou-JJJ-XX-note4, + Note = {For $r_1=r_2$, $f\lr_\ell >0$ for $\ell=0$ and $f\lr_\ell <0$ for $\ell \geq 1$.}} + +@article{FreHuxMor-PRA-84, + Author = {{D. E. Freund, B. D. Huxtable, and J. D. Morgan III}}, + Journal = {Phys. Rev. A}, + Pages = {980}, + Volume = {29}, + Year = {1984}} + +@article{FreLev-JCP-82, + Author = {Karl F. Freed and Mel Levy}, + Journal = {The Journal of Chemical Physics}, + Keywords = {ALGORITHMS; ELECTRON DENSITY; FUNCTIONALS; SERIES EXPANSION; WAVE FUNCTIONS; GROUND STATES}, + Number = {1}, + Pages = {396-398}, + Publisher = {AIP}, + Title = {Direct first principles algorithm for the universal electron density functional}, + Url = {http://link.aip.org/link/?JCP/77/396/1}, + Volume = {77}, + Year = {1982}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/77/396/1}} + +@article{Fre-PRB-77, + Author = {D. L. Freeman}, + Journal = {Phys. Rev. B}, + Pages = {5512}, + Volume = {{15}}, + Year = {1977}} + +@article{FroCimJen-PRA-10, + Author = {Fromager, Emmanuel and Cimiraglia, Renzo and Jensen, Hans J\o{}rgen Aa.}, + Doi = {10.1103/PhysRevA.81.024502}, + Issue = {2}, + Journal = {Phys. Rev. A}, + Month = {Feb}, + Numpages = {4}, + Pages = {024502}, + Publisher = {American Physical Society}, + Title = {Merging multireference perturbation and density-functional theories by means of range separation: Potential curves for ${\mathrm{Be}}_{2}$, ${\mathrm{Mg}}_{2}$, and ${\mathrm{Ca}}_{2}$}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.81.024502}} + +@article{Fro-JCP-11, + Author = {E. Fromager}, + Journal = {J. Chem. Phys.}, + Pages = {244106}, + Volume = {135}, + Year = {2011}} + +@article{FroJen-JCP-11, + Author = {E. Fromager and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {034116}, + Volume = {135}, + Year = {2011}} + +@article{FroJen-PRA-08, + Author = {E. Fromager and H. J. Aa. Jensen}, + Journal = {Phys. Rev. A}, + Pages = {022504}, + Volume = {78}, + Year = {2008}} + +@misc{FroKneJen-ARX-12, + Author = {Emmanuel Fromager and Stefan Knecht and H. J. Aa. Jensen}, + Note = {\url{http://fr.arxiv.org/abs/1211.4829v1}}} + +@article{FroKneJen-JCP-13, + Author = {E. Fromager and S. Knecht and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {084101}, + Title = {{Multi-configuration time-dependent density-functional theory based on range separation}}, + Volume = {138}, + Year = {2013}} + +@article{FroReaWahWahJen-JCP-09, + Author = {E. Fromager and F. R\'eal and P. W{\aa}hlin and U. Wahlgren and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {054107}, + Volume = {131}, + Year = {2009}} + +@article{FroTouJen-JCP-07, + Author = {E. Fromager and J. Toulouse and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {074111}, + Title = {On the universality of the long-/short-range separation in multiconfigurational density-functional theory}, + Volume = {126}, + Year = {2007}} + +@article{FucGon-PRB-02, + Author = {M. Fuchs and X. Gonze}, + Journal = {Phys. Rev. B}, + Pages = {235109}, + Volume = {65}, + Year = {2002}} + +@article{FucNiqGonBur-JCP-05, + Abstract = {We show that density functional theory within the RPA (random phase + approximation for the exchange-correlation energy) provides a correct + description of bond dissociation in H2 in a spin-restricted Kohn-<96>Sham + formalism, i.e., without artificial symmetry breaking. We present + accurate adiabatic connection curves both at equilibrium and beyond + the Coulson-Fisher point. The strong curvature at large bond length + implies important static (left-<96>right) correlation, justifying modern + hybrid functional constructions but also demonstrating their limitations. + Although exact at infinite separation and accurate near the equilibrium + bond length, the RPA dissociation curve displays unphysical repulsion + at larger but finite bond lengths. Going beyond the RPA by including + the exact exchange kernel (RPA + X), we find a similar repulsion. + We argue that this deficiency is due to the absence of double excitations + in adiabatic linear response theory. Further analyzing the H2 dissociation + limit we show that the RPA + X is not size consistent, in contrast + to the RPA.}, + Author = {Fuchs, M. and Niquet, Y. M. and Gonze, X. and Burke, K.}, + Doi = {10.1063/1.1858371}, + Journal = {J. Chem. Phys.}, + Pages = {094116}, + Title = {Describing static correlation in bond dissociation by Kohn-Sham density functional theory}, + Volume = {122}, + Year = {2005}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1858371}} + +@article{FukIwaSaw-PR-64, + Author = {N. Fukuda and F. Iwamoto and K. Sawada}, + Journal = {Phys. Rev.}, + Pages = {A932}, + Volume = {135}, + Year = {1964}} + +@book{Ful-BOOK-93, + Address = {Berlin}, + Author = {P. Fulde}, + Publisher = {Springer}, + Title = {Electron Correlations in Molecules and Solids}, + Year = {1993}} + +@article{Fur-JCP-01, + Author = {F. Furche}, + Journal = {J. Chem. Phys.}, + Pages = {5982}, + Volume = {114}, + Year = {2001}} + +@article{Fur-JCP-08, + Author = {F. Furche}, + Journal = {J. Chem. Phys.}, + Pages = {114105}, + Volume = {129}, + Year = {2008}} + +@article{FurPer-JCP-06, + Author = {F. Furche and J. P. Perdew}, + Journal = {J. Chem. Phys.}, + Pages = {044103}, + Volume = {124}, + Year = {2006}} + +@article{Fur-PRA-04, + Author = {Filipp Furche}, + Eid = {022514}, + Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, + Keywords = {density functional theory; HF calculations; boson systems; electron pairs; ground states; Schrodinger equation}, + Number = {2}, + Numpages = {10}, + Pages = {022514}, + Publisher = {APS}, + Title = {Towards a practical pair density-functional theory for many-electron systems}, + Url = {http://link.aps.org/abstract/PRA/v70/e022514}, + Volume = {70}, + Year = {2004}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v70/e022514}} + +@article{Fur-PRB-01, + Author = {F. Furche}, + Journal = {Phys. Rev. B}, + Pages = {195120}, + Volume = {64}, + Year = {2001}} + +@incollection{FurRap-INC-05, + Address = {Amsterdam}, + Author = {F. Furche and D. Rappoport}, + Booktitle = {Computational Photochemistry}, + Editor = {M. Olivucci}, + Pages = {93-128}, + Publisher = {Elsevier}, + Series = {Theoretical and Computational Chemistry, Vol. 16}, + Title = {Density functional methods for excited states: equilibrium structure and electronic spectra}, + Year = {2005}} + +@article{FurVoo-JCP-05, + Author = {F. Furche and T. Van Voorhis}, + Journal = {J. Chem. Phys.}, + Pages = {164106}, + Title = {Fluctuation-dissipation theorem density-functional theory}, + Volume = {122}, + Year = {2005}} + +@article{GagTruLiCarHoyBa-ACR-17, + Author = {{L. Gagliardi, D. G. Truhlar, G. Li Manni, R. K. Carlson, C. E. Hoyer, and J. Lucas Bao}}, + Journal = {Acc. Chem. Res.}, + Pages = {66}, + Volume = {50}, + Year = {2017}} + +@book{Gal-BOOK-02, + Author = {G. A. Gallup}, + Publisher = {Cambridge University Press}, + Title = {Valence Bond Methods: Theory and applications}, + Year = {2002}} + +@article{GalBueSar-CPL-03a, + Author = {F. J. G\'alvez and E. Buend\'ia and A. Sarsa}, + Journal = {Chem. Phys. 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Bartlett}, + Eid = {022512}, + Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, + Keywords = {quantum chemistry; electron correlations; wave functions}, + Number = {2}, + Numpages = {12}, + Pages = {022512}, + Publisher = {APS}, + Title = {Short-range corrections to the correlation hole}, + Url = {http://link.aps.org/abstract/PRA/v70/e022512}, + Volume = {70}, + Year = {2004}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v70/e022512}} + +@article{HenIzmScuSav-JCP-07, + Author = {T. M. Henderson and A. F. Izmaylov and G. E. Scuseria and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {221103}, + Volume = {127}, + Year = {2007}} + +@article{HenIzmScuSav-JCTC-08, + Author = {T. M. Henderson and A. F. Izmaylov and G. E. Scuseria and A. Savin}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1254}, + Volume = {4}, + Year = {2008}} + +@article{HenScu-MP-10, + Author = {T. M. Henderson and G. E. Scuseria}, + Journal = {Mol. 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Phys.}, + Pages = {054102}, + Volume = {127}, + Year = {2007}} + +@article{HesJan-CPL-03, + Author = {A. He{\ss}elmann and G. Jansen}, + Journal = {Chem. Phys. Lett.}, + Pages = {778}, + Volume = {367}, + Year = {2003}} + +@article{HesJanSch-JCP-05, + Author = {A. He{\ss}elmann and G. Jansen and M. Sch\"utz}, + Journal = {J. Chem. Phys.}, + Pages = {014103}, + Volume = {122}, + Year = {2005}} + +@article{Hes-JCP-11, + Author = {A. He{\ss}elmann}, + Journal = {J. Chem. Phys.}, + Pages = {204107}, + Volume = {134}, + Year = {2011}} + +@article{Hes-PCCP-06, + Author = {A. He{\ss}elmann}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {563}, + Volume = {8}, + Year = {2006}} + +@article{HetSchStoWer-JCP-00, + Author = {G. Hetzer and M. Sch\"utz and H. Stoll and H.-J. Werner}, + Journal = {J. Chem. Phys.}, + Pages = {9443}, + Volume = {113}, + Year = {2000}} + +@article{HeyPerScuMar-JCP-05, + Author = {J. Heyd and J. E. Peralta and G. E. Scuseria and R. L. Martin}, + Journal = {J. Chem. 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Phys.}, + Pages = {3834}, + Volume = {{88}}, + Year = {1988}} + +@article{JenJor-JCP-84, + Author = {H. J. Aa. Jensen and P. J{\o}rgensen}, + Journal = {J. Chem. Phys.}, + Pages = {1204}, + Volume = {{80}}, + Year = {1984}} + +@article{JiaEng-JCP-07, + Author = {Hong Jiang and Eberhard Engel}, + Doi = {10.1063/1.2795707}, + Journal = {J. Chem. Phys.}, + Keywords = {density functional theory; eigenvalues and eigenfunctions; ground states; ionisation potential; orbital calculations; perturbation theory; potential energy functions}, + Pages = {184108}, + Title = {Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms}, + Volume = {127}, + Year = {2007}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.2795707}} + +@article{JieNorSer-JCP-05, + Author = {A. Jiemchooroj and P. Norman and Bo E. Sernelius}, + Journal = {J. Chem. Phys.}, + Pages = {124312}, + Volume = {123}, + Year = {2005}} + +@article{JieNorSer-JCP-06, + Author = {A. Jiemchooroj and P. Norman and Bo E. Sernelius}, + Journal = {J. Chem. Phys.}, + Pages = {124306}, + Volume = {125}, + Year = {2006}} + +@article{JohBec-JCP-05b, + Author = {E. R. Johnson and A. D. Becke}, + Journal = {J. Chem. Phys.}, + Pages = {024101}, + Volume = {123}, + Year = {2005}} + +@article{JohMorCohYan-JCP-08, + Author = {E. R. Johnson and P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {204112}, + Volume = {129}, + Year = {2008}} + +@article{JonGun-RMP-89, + Author = {R. O. Jones and O. Gunnarsson}, + Journal = {Rev. Mod. Phys.}, + Pages = {689}, + Volume = {{61}}, + Year = {1989}} + +@article{jones:325, + Author = {R. O. Jones}, + Journal = {The Journal of Chemical Physics}, + Keywords = {OZONE; SULFUR DIOXIDE; GROUND STATES; EXCITED STATES; ELECTRONIC STRUCTURE; CONFIGURATION INTERACTION; DISSOCIATION ENERGY; ATMOSPHERIC CHEMISTRY}, + Number = {1}, + Pages = {325-332}, + Publisher = {AIP}, + Title = {Energy surfaces of low-lying states of O[sub 3] and SO[sub 2]}, + Url = {http://link.aip.org/link/?JCP/82/325/1}, + Volume = {82}, + Year = {1985}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/82/325/1}} + +@article{JorSim-JCP-83, + Author = {P. J{\o}rgensen and J. Simons}, + Journal = {J. Chem. Phys.}, + Pages = {334}, + Volume = {79}, + Year = {1983}} + +@article{JouSri-JCP-98, + Author = {Daniel P. Joubert and G. P. Strivastava}, + Journal = {J. Chem. Phys.}, + Pages = {5212}, + Volume = {109}, + Year = {1998}} + +@article{JurSpoCerHob-PCCP-06, + Author = {P. Jure{\v c}ka and J. {\v S}poner and J. {\v C}ern{\'y} and P. Hobza}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {1985}, + Volume = {8}, + Year = {2006}} + +@article{KadVoo-JCP-10, + Author = {{B. Kaduk and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {061102}, + Volume = {133}, + Year = {2010}} + +@article{KalTou-JCP-18, + Author = {C. Kalai and J. Toulouse}, + Doi = {10.1063/1.5025561}, + Journal = {J. Chem. Phys.}, + Pages = {164105}, + Title = {A general range-separated double-hybrid density-functional theory}, + Volume = {148}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5025561}} + +@misc{KalTou-JJJ-XX-note1, + Note = {The geometries are available in the Minnesota Database at http://comp.chem.umn.edu/db/.}} + +@misc{KalTou-JJJ-XX-note2, + Note = {The term ``range-separated double hybrid (RSDH)'' has already been used in Ref.~\onlinecite{SanCivUsvTouShaMas-JCP-15} to designate the RSH+MP2 method and in Refs.~\onlinecite{CorStoJenFro-PRA-13,CorFro-IJQC-14} to generically designate several kinds of range-separated MP2/DFT hybrids. In the present work, we use RSDH to designate the specific scheme corresponding to Eq.~(\ref{EmulRSDH}).}} + +@misc{KalTou-JJJ-XX-note3, + Note = {We use the AE49 set of Fast {\it et al.}~\cite{FasCorSanTru-JPCA-99} to facilitate comparisons with previous related works~\cite{ShaTouSav-JCP-11,SouShaTou-JCP-14,MusReiAngTou-JCP-15} where this set was used. We do not expect any special difficulties with the six molecules that have been dropped from the G2-1 set.}} + +@article{KamSekTsuHir-JCP-05, + Author = {M. Kamiya and H. Sekino and T. Tsuneda and K. Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {234111}, + Volume = {122}, + Year = {2005}} + +@article{KamTsuHir-JCP-02, + Author = {M. Kamiya and T. Tsuneda and K. Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {6010}, + Volume = {{117}}, + Year = {2002}} + +@article{KanBec-JCTC-10, + Author = {F. O. Kannemann and Axel D. Becke}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1081}, + Title = {{van der Waals interactions in density-functional theory: Intermolecular complexes}}, + Volume = {6}, + Year = {2010}} + +@article{Kar-JCP-03, + Author = {V. V. Karasiev}, + Journal = {J. Chem. Phys.}, + Pages = {8576}, + Volume = {118}, + Year = {2003}} + +@article{KarKroKum-JCP-13, + Author = {A. Karolewski and L. Kronik and S. K\"ummel}, + Journal = {J. Chem. Phys.}, + Pages = {204115}, + Volume = {138}, + Year = {2013}} + +@article{KarMar-JCP-11, + Author = {Amit Karton and J. M. L. Martin}, + Journal = {J. Chem. Phys.}, + Pages = {144119}, + Volume = {135}, + Year = {2011}} + +@article{KarTarLamSchMar-JPCA-08, + Author = {Amir Karton and Alex Tarnopolsky and Jean-Francois Lam\`ere and George C. Schatz and Jan M. L. Martin}, + Journal = {J. Phys. Chem. A}, + Pages = {12868}, + Volume = {112}, + Year = {2008}} + +@article{Kat-CPAM-57, + Author = {T. Kato}, + Journal = {Comm. Pure Appl. 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Phys.}, + Pages = {114108}, + Volume = {128}, + Year = {2008}} + +@incollection{KlaGil-AQC-12, + Author = {Shachar Klaiman and Ido Gilary}, + Booktitle = {Advances in Quantum Chemistry Vol. 63}, + Editor = {Cleanthes A. Nicolaides and Erkki Br\"andas and John R. Sabin}, + Pages = {1}, + Publisher = {Academic Press}, + Title = {On Resonance: A First Glance into the Behavior of Unstable States}, + Year = {2012}} + +@article{Kla-PRB-03, + Author = {T. Klamroth}, + Journal = {Phys. Rev. B}, + Pages = {245421}, + Volume = {68}, + Year = {2003}} + +@article{KlePic-JCP-76, + Author = {D. J. Klein and H. M. Pickett}, + Journal = {J. Chem. Phys.}, + Pages = {4811}, + Title = {{Nodal hypersurfaces and Anderson's random-walk simulation of the Schr\"odinger equation}}, + Volume = {64}, + Year = {1976}} + +@article{KliMic-JCP-12, + Author = {J. Klime{\v s} and A. Michaelides}, + Journal = {J. Chem. 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Werner}, + Booktitle = {Modern Methods and Algorithms of Quantum Chemistry}, + Editor = {J. Grotendorst}, + Pages = {61-151}, + Publisher = {NIC}, + Title = {Ab Initio Methods for Electron Correlation in Molecules}, + Volume = {1}, + Year = {2000}} + +@article{KnoWer-CPL-88, + Author = {P. J. Knowles and H-J. Werner}, + Journal = {Chem. Phys. Lett.}, + Pages = {145}, + Volume = {{514}}, + Year = {1988}} + +@book{KocHol-BOOK-01, + Address = {New York}, + Author = {W. Koch and M. C. Holthausen}, + Publisher = {Wiley-VCH}, + Title = {A Chemist's Guide To Density Functional Theory}, + Year = {2001}} + +@article{Kog-JCP-01b, + Author = {T. Koga}, + Journal = {J. Chem. Phys.}, + Pages = {102}, + Volume = {114}, + Year = {2001}} + +@article{Kog-JCP-02, + Author = {T. Koga}, + Journal = {J. Chem. Phys.}, + Pages = {6614}, + Volume = {116}, + Year = {2002}} + +@article{Kog-JCP-90, + Author = {T. Koga}, + Journal = {J. Chem. 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Phys.}, + Pages = {074105}, + Volume = {123}, + Year = {2005}} + +@article{KriLiIaf-PRA-92a, + Author = {J. B. Krieger and Y. Li and G. J. Iafrate}, + Journal = {Phys. Rev. A}, + Pages = {101}, + Volume = {45}, + Year = {1992}} + +@article{KriLiIaf-PRA-92, + Author = {J. B. Krieger and Y. Li and G. J. Iafrate}, + Journal = {Phys. Rev. A}, + Pages = {5453}, + Volume = {46}, + Year = {1992}} + +@article{Kro-AP-84, + Author = {E. Krotscheck}, + Journal = {Ann. Phys.}, + Pages = {1}, + Volume = {{155}}, + Year = {1984}} + +@article{Kro-JLTP-77, + Author = {E. Krotscheck}, + Journal = {J. Low Temp. Phys.}, + Pages = {199}, + Volume = {{27}}, + Year = {1977}} + +@article{KroKohQia-PRB-85, + Author = {E. Krotscheck and W. Kohn and G.-X. Qian}, + Journal = {Phys. Rev. B}, + Pages = {5693}, + Volume = {{32}}, + Year = {1985}} + +@article{Kro-PRA-77, + Author = {E. Krotscheck}, + Journal = {Phys. Rev. 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Phys.}, + Pages = {9905}, + Volume = {113}, + Year = {2000}} + +@article{LanMeh-PRB-83, + Author = {D. C. Langreth and M. J. Mehl}, + Journal = {Phys. Rev. B}, + Pages = {1809}, + Volume = {{28}}, + Year = {1983}} + +@article{LanMeh-PRL-81, + Author = {D. C. Langreth and M. J. Mehl}, + Journal = {Phys. Rev. Lett.}, + Pages = {446}, + Volume = {{47}}, + Year = {1981}} + +@article{LanPer-PRB-77, + Author = {D. C. Langreth and J. P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {2884}, + Volume = {{15}}, + Year = {1977}} + +@article{LanPer-PRB-80, + Author = {D. C. Langreth and J. P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {5469}, + Volume = {{21}}, + Year = {1980}} + +@article{LanPer-SSC-75, + Author = {D. C. Langreth and J. P. Perdew}, + Journal = {Solid State Commun.}, + Pages = {1425}, + Volume = {17}, + Year = {1975}} + +@article{LanRohHer-JPCB-08, + Author = {A. W. Lange and M. A. Rohrdanz and J. M. Hubert}, + Journal = {J. Phys. Chem. 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Quantum Chem.}, + Pages = {24-94}, + Title = {Density functional approach to the many-body problem: key concepts and exact functionals}, + Volume = {43}, + Year = {2003}} + +@article{LeeBae-PRA-94, + Author = {{R. van Leeuwen and E. J. Baerends}}, + Journal = {Phys. Rev. A}, + Pages = {2421}, + Volume = {49}, + Year = {1994}} + +@article{LeeConNemLopDru-PRE-11, + Author = {{R. M. Lee, G. J. Conduit, N. Nemec, P. L\'opez Rios, and N. D. Drummond}}, + Journal = {Phys. Rev. E}, + Pages = {066706}, + Title = {{Strategies for improving the efficiency of quantum Monte Carlo calculations}}, + Volume = {83}, + Year = {2011}} + +@incollection{LeeDah-INC-94, + Address = {Amsterdam}, + Author = {{R. van Leeuwen and N. E. Dahlen}}, + Booktitle = {The Electron Liquid Paradigm in Condensed Matter Physics}, + Editor = {G. F. Giuliani and G. Vignale}, + Publisher = {IOS Press}, + Series = {Proceedings of the International School of Physics ``Enrico Fermi'', Vol. 157}, + Year = {2004}} + +@article{LeeGil-CPL-99, + Author = {A. M. Lee and P. M. W Gill}, + Journal = {Chem. Phys. Lett.}, + Pages = {271}, + Volume = {313}, + Year = {1999}} + +@article{LeeGriBae-ZPD-95, + Author = {{R. van Leeuwen, O. Gritsenko, and E. J. Baerends}}, + Journal = {Z. Phys. D}, + Pages = {229}, + Volume = {33}, + Year = {1995}} + +@article{LeeMelRap-JCP-05, + Author = {Myung Won Lee and Massimo Mella and Andrew M. Rappe}, + Journal = {J. Chem. Phys.}, + Pages = {244103}, + Volume = {112}, + Year = {2005}} + +@article{LeeMurKonLunLan-PRB-10, + Author = {K. Lee and E. D. Murray and L. Kong and B. I. Lundqvist and D. C. Langreth}, + Journal = {Phys. Rev. B}, + Pages = {081101}, + Title = {Higher-accuracy van der Waals density functional}, + Volume = {82}, + Year = {2010}} + +@article{LeeRic-CPL-88, + Author = {T. J. Lee and J. E. 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B}, + Pages = {13431}, + Volume = {{61}}, + Year = {2000}} + +@article{LeiStoWerSav-CPL-97, + Author = {T. Leininger and H. Stoll and H.-J. Werner and A. Savin}, + Journal = {Chem. Phys. Lett.}, + Pages = {151}, + Title = {Combining long-range configuration interaction with short-range density functionals}, + Volume = {{275}}, + Year = {1997}} + +@article{LeiTou-AC-14, + Author = {T. Leininger and J. Toulouse}, + Journal = {L'Actualit\'e Chimique}, + Pages = {13-21}, + Title = {{Relever le d\'efi de la r\'esolution de l'\'equation de Schr\"odinger}}, + Volume = {382-383}, + Year = {2014}} + +@article{LemRogChe-PRA-95, + Author = {A. Lembarki and F. Rogemond and H. Chermette}, + Journal = {Phys. Rev. A}, + Pages = {3704}, + Volume = {52}, + Year = {1995}} + +@article{LenBal-JCP-83, + Author = {J. H. van Lenthe and G. G. Balint-Kurti}, + Journal = {J. Chem. Phys.}, + Pages = {5699}, + Volume = {78}, + Year = {1983}} + +@article{Len-JCP-80, + Author = {{B. H. 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Quantum Chem.}, + Pages = {307}, + Volume = {2}, + Year = {1968}} + +@incollection{Lev-INC-95, + Address = {New York}, + Author = {M. Levy}, + Booktitle = {Density Functional Theory}, + Editor = {E.K.U. Gross and R.M. Dreizler}, + Publisher = {Plenum Press}, + Title = {Coordinate scaling requirements for approximating exchange and correlation}, + Year = {1995}} + +@article{LevMarHan-JCP-96, + Author = {M. Levy and N. H. March and N. C. Handy}, + Journal = {J. Chem. Phys.}, + Pages = {1989}, + Volume = {104}, + Year = {1996}} + +@article{LevNag-PRL-99, + Author = {M. Levy and A. Nagy}, + Journal = {Phys. Rev. Lett.}, + Pages = {4361}, + Volume = {83}, + Year = {1999}} + +@incollection{LevPer-INC-85, + Address = {New York}, + Author = {M. Levy and J. P. Perdew}, + Booktitle = {Density Functional Methods in Physics}, + Editor = {R. M. Dreizler and J. da Providencia}, + Publisher = {Plenum}, + Year = {1985}} + +@article{LevPer-PRA-85, + Author = {M. Levy and J. P. Perdew}, + Journal = {Phys. Rev. A}, + Pages = {2010}, + Volume = {32}, + Year = {1985}} + +@article{LevPer-PRB-93, + Author = {M. Levy and J. P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {11638}, + Volume = {48}, + Year = {1993}} + +@article{LevPerSah-PRA-84, + Author = {M. Levy and J. P. Perdew and V. Sahni}, + Journal = {Phys. Rev. A}, + Pages = {2745}, + Volume = {30}, + Year = {1984}} + +@article{Lev-PNAS-79, + Author = {M. Levy}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {6062}, + Volume = {76}, + Year = {1979}} + +@article{Lev-PRA-82, + Author = {M. Levy}, + Journal = {Phys. Rev. A}, + Pages = {1200}, + Volume = {26}, + Year = {1982}} + +@article{Lev-PRA-91, + Author = {M. Levy}, + Journal = {Phys. Rev. A}, + Pages = {4637}, + Volume = {43}, + Year = {1991}} + +@article{LevSov-PRA-84, + Author = {Z. H. Levine and P. Soven}, + Journal = {Phys. Rev. A}, + Pages = {625}, + Volume = {29}, + Year = {1984}} + +@article{LevYanPar-JCP-85, + Author = {M. Levy and W. Yang and R. G. Parr}, + Journal = {J. Chem. Phys.}, + Pages = {2334}, + Volume = {83}, + Year = {1985}} + +@article{LieCle-JCP-74a, + Author = {George C. Lie and Enrico Clementi}, + Journal = {J. Chem. Phys.}, + Pages = {1275}, + Title = {Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree-Fock density and its application to the hydrides of the second row atoms}, + Volume = {60}, + Year = {1974}} + +@article{LieCle-JCP-74b, + Author = {George C. Lie and Enrico Clementi}, + Journal = {J. Chem. Phys.}, + Pages = {1288}, + Title = {Study of the electronic structure of molecules. XXII. Correlation energy corrections as a functional of the Hartree-Fock type density and its application to the homonuclear diatomic molecules of the second row atoms}, + Volume = {60}, + Year = {1974}} + +@article{Lie-IJQC-83, + Author = {E. H. Lieb}, + Journal = {Int. J. Quantum Chem.}, + Pages = {24}, + Volume = {{24}}, + Year = {1983}} + +@article{LieOxf-IJQC-81, + Author = {E. H. Lieb and S. Oxford}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {427}, + Volume = {{19}}, + Year = {1981}} + +@misc{lifetimes-note1, + Note = {For $\ell=0$, $R_2(r)$ only diverges as $1/r$ at $r=0$ which is normalizable, i.e. $\int_0^\infty \text{d}r r^2 |R_2(r)|^2 < \infty$. However, even in this case, the expectation value of the Hamiltonian operator is infinite. For $\ell \geq 1$, $R_2(r)$ is not even normalizable.}} + +@misc{lifetimes-note2, + Note = {The general solution of the Schr\"odinger equation given in Eqs.~(\ref{solR})-(\ref{solR2}) is valid for $Z\not=0$. For $Z=0$, $R_1(r)$ in Eq.~(\ref{solR1}) becomes identically zero, and should be replaced by a function which has the same expression as $R_2(r)$ with the substitution $\sqrt{-2E} \to -\sqrt{-2E}$. The continuum scattering states are then obtained as a linear combination of these two functions. However, our analysis of complex-energy states remains unchanged. Thus, our procedure for determining the lifetimes is still valid for $Z=0$.}} + +@misc{lifetimes-note3, + Note = {Because we do not impose spherical symmetry in our calculations, we do not have exactly degenerate s, p, and d states.}} + +@article{LikMorSen-PRB-97, + Author = {C. N. Likos and S. Moroni and G. Senatore}, + Journal = {Phys. Rev. B}, + Pages = {8867}, + Volume = {{55}}, + Year = {1997}} + +@article{LilTavRotSeb-PRL-04, + Author = {O. A. von Lilienfeld and I. Tavernelli and U. Rothlisberger}, + Journal = {Phys. Rev. Lett.}, + Pages = {153004}, + Volume = {93}, + Year = {2004}} + +@article{LimCarLuoMaOlsTruGag-JCTC-14, + Author = {{G. Li Manni, R. K. Carlson, S. Luo, D. Ma, J. Olsen, D. G. Truhlar, and L. Gagliardi}}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3669}, + Volume = {10}, + Year = {2014}} + +@article{LinRyuLiu-JCP-91, + Author = {R. Lindh and U. Ryu and B. Liu}, + Journal = {J. Chem. Phys.}, + Pages = {5889}, + Volume = {{95}}, + Year = {1991}} + +@article{LinSal-AQC-03, + Author = {Ingvar Lindgren and Sten Salomonson}, + Journal = {Adv. Quantum Chem.}, + Pages = {95-117}, + Title = {Differentiability in density-functional theory}, + Volume = {43}, + Year = {2003}} + +@article{LinTsaLiCha-JCP-12, + Author = {Y.-S. Lin and C.-W. Tsai and G.-D. Li and J.-D. Chai}, + Journal = {J. Chem. Phys.}, + Pages = {154109}, + Volume = {136}, + Year = {2012}} + +@article{LinZhaRap-JCP-00, + Author = {Xi Lin and Hongkai Zhang and Andrew M. Rappe}, + Journal = {J. Chem. Phys.}, + Pages = {2650}, + Volume = {112}, + Year = {2000}} + +@article{LiuEggRefKroNea-JCP-17, + Author = {Zhen-Fei Liu and David A. Egger and Sivan Refaely-Abramson and Leeor Kronik and Jeffrey B. Neaton}, + Journal = {J. Chem. Phys.}, + Pages = {092326}, + Volume = {146}, + Year = {2017}} + +@article{LiuParNag-PRA-95, + Author = {S. Liu and R. G. Parr and A. Nagy}, + Journal = {Phys. Rev. A}, + Pages = {2645}, + Volume = {52}, + Year = {1995}} + +@article{LivBae-PCCP-07, + Author = {E. Livshits and R. Baer}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {2932}, + Volume = {9}, + Year = {2007}} + +@article{LjuKovFerFoeSan-PRB-15, + Author = {M. P. Ljungberg and P. Koval and F. Ferrari and D. Foerster and D. S\'anchez-Portal}, + Journal = {Phys. Rev. B}, + Pages = {075422}, + Volume = {92}, + Year = {2015}} + +@article{LocHea-JCP-07, + Author = {Rohini C. Lochan and Martin Head-Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {164101}, + Volume = {126}, + Year = {2007}} + +@article{Lon-DFS-65, + Author = {H. C. Longuet-Higgins}, + Journal = {Discuss. Faraday Soc.}, + Pages = {7}, + Volume = {40}, + Year = {1965}} + +@article{Lon-ZP-30, + Author = {F. London}, + Journal = {Z. Physik}, + Pages = {245}, + Volume = {63}, + Year = {1930}} + +@article{LooGil-WIRES-16, + Author = {Pierre-Francois Loos and Peter M. W. Gill}, + Date-Modified = {2019-04-07 14:04:07 +0200}, + Doi = {doi: 10.1002/wcms.1257}, + Journal = {WIREs Comput. Mol. Sci.}, + Pages = {410}, + Title = {The uniform electron gas}, + Volume = {6}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1002/wcms.1257}} + +@article{LopGov-JCTC-11, + Author = {K. Lopata and N. Govind}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1344}, + Title = {Modeling Fast Electron Dynamics with Real-Time Time-Dependent Density Functional Theory: Application to Small Molecules and Chromophores}, + Volume = {7}, + Year = {2011}} + +@article{LopGov-JCTC-13, + Author = {K. Lopata and N. Govind}, + Journal = {J. Chem. Theory Comput.}, + Pages = {4939}, + Volume = {9}, + Year = {2013}} + +@article{LopMaDruTowNee-PRE-06, + Author = {{P. L\'opez Rios, A. Ma, N. D. Drummond, M. D. Towler, and R. J. Needs}}, + Journal = {Phys. Rev. E}, + Pages = {066701}, + Title = {{Inhomogeneous backflow transformations in quantum Monte Carlo calculations}}, + Volume = {74}, + Year = {2006}} + +@article{LopRamGarFer-JCP-87, + Author = {{R. L\'opez, G. Ram\'irez, J. M. Garc\'ia de la Vega and J. Fern\'andez Rico}}, + Journal = {J. chim. phys.}, + Pages = {695}, + Volume = {{84}}, + Year = {1987}} + +@article{LosFdeAguMar-JPC-07, + Author = {{A. M. Losa, I. Fdez.-Galv\'an, M. A. Aguilar, and M. E. Mart\'in}}, + Journal = {J. Phys. Chem. B}, + Pages = {9864}, + Volume = {111}, + Year = {2007}} + +@article{LotBar-JCP-11, + Author = {V. Lotrich and R. J. Bartlett}, + Journal = {J. Chem. Phys.}, + Pages = {184108}, + Volume = {134}, + Year = {2011}} + +@article{Low-AP-56, + Author = {P.-O. L\"owdin}, + Journal = {Adv. Phys.}, + Pages = {1}, + Volume = {5}, + Year = {1956}} + +@article{Low-JCP-50, + Author = {P.-O. L\"owdin}, + Journal = {J. Chem. 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Phys.}, + Pages = {154110}, + Volume = {133}, + Year = {2010}} + +@article{LupHea-JCP-13, + Author = {E. Luppi and M. Head-Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {164121}, + Title = {{The role of Rydberg and continuum levels in computing high harmonic generation spectra of the hydrogen atom using time-dependent configuration interaction}}, + Volume = {139}, + Year = {2013}} + +@article{Lut-ZPC-23, + Author = {A. Luthy}, + Journal = {Z. Phys. Chem., Stoechiom. Verwandtschaftsl.}, + Pages = {284}, + Volume = {107}, + Year = {1923}} + +@article{LynTru-JPCA-03, + Author = {B. J. Lynch and D. G. Truhlar}, + Journal = {J. Phys. Chem. A}, + Pages = {8996}, + Title = {Small Representative Benchmarks for Thermochemical Calculations}, + Volume = {107}, + Year = {2003}} + +@misc{LynZhaTru-JJJ-XX, + Note = {The geometries are available in the Minnesota Databases for Chemistry and Solid-State Physics at http://comp.chem.umn.edu/db/.}} + +@article{MaBru-PR-68, + Author = {S.-K. Ma and K. A. Brueckner}, + Journal = {Phys. Rev.}, + Pages = {165}, + Volume = {{165}}, + Year = {1968}} + +@article{MacVos-JPC-79, + Author = {A. H. MacDonald and S. H. Vosko}, + Journal = {J. Phys. C}, + Pages = {2977}, + Volume = {12}, + Year = {1978}} + +@article{MaDruTowNee-PRE-05, + Author = {A. Ma and N. D. Drummond and M. D. Towler and R. J. Needs}, + Journal = {Phys. Rev. E}, + Pages = {066704}, + Volume = {71}, + Year = {2005}} + +@book{Mah-BOOK-09, + Address = {Princeton}, + Author = {Gerald D. Mahan}, + Publisher = {Princeton University Press}, + Title = {Quantum Mechanics in a Nutshell}, + Year = {2009}} + +@article{MaiZhaCavBur-JCP-04, + Author = {N. T. Maitra and F. Zhang and R. J. Cave and K. Burke}, + Journal = {J. Chem. Phys.}, + Pages = {5932}, + Volume = {120}, + Year = {2004}} + +@article{MalMcd-CPL-98, + Author = {N. O. J. Malcolm and J. J. W. McDouall}, + Journal = {Chem. Phys. Lett.}, + Pages = {121}, + Volume = {282}, + Year = {1998}} + +@article{MalMcd-JPC-96, + Author = {N. O. J. Malcolm and J. J. W. McDouall}, + Journal = {J. Phys. Chem.}, + Pages = {10131}, + Volume = {100}, + Year = {1996}} + +@article{MalPenYanBalHol-TCA-14, + Author = {A. Malek and D. Peng and W. Yang and R. Balawender and A. Holas}, + Journal = {Theor. Chem. Acc.}, + Pages = {1559}, + Volume = {133}, + Year = {2014}} + +@article{ManLuc-JCP-01, + Author = {S. Manten and A. L\"uchow}, + Journal = {J. Chem. Phys.}, + Pages = {5362}, + Volume = {115}, + Year = {2001}} + +@article{MarAzaCasSor-JCP-09, + Author = {M. Marchi and S. Azadi and M. Casula and S. Sorella}, + Journal = {J. Chem. Phys.}, + Pages = {154116}, + Title = {Correlated geminal wave function for molecules: An efficient resonating valence bond approach}, + Volume = {131}, + Year = {2009}} + +@article{MarCasMalMulBot-JCP-07, + Author = {M. A. L. Marques and A. Castro and G. Malloci and G. Mulas and S. Botti}, + Journal = {J. Chem. Phys.}, + Pages = {014107}, + Volume = {127}, + Year = {2007}} + +@article{Mar-CPL-96, + Author = {J. M. L. Martin}, + Journal = {Chem. Phys. Lett.}, + Pages = {669}, + Volume = {259}, + Year = {1996}} + +@article{MarGarRub-PRL-06, + Abstract = {We present a first-principles description of anisotropic materials + characterized by having both weak (dispersionlike) and strong covalent + bonds, based on the adiabatic-connection fluctuation-dissipation + theorem with density functional theory. For hexagonal boron nitride + the in-plane and out-of-plane bonding as well as vibrational dynamics + are well described both at equilibrium and when the layers are pulled + apart. Bonding in covalent and ionic solids is also described. The + formalism allows us to ping down the deficiencies of common exchange-correlation + functionals and provides insight toward the inclusion of dispersion + interactions into the correlation functional.}, + Author = {Marini, A. and Garc\'ia-Gonz\'alez, P. and Rubio, A.}, + Journal = {Phys. Rev. Lett.}, + Pages = {136404}, + Title = {First-Principles Description of Correlation Effects in Layered Materials}, + Volume = {96}, + Year = {2006}} + +@article{MarHeiKle-WIRES-18, + Author = {Christel M. Marian and Adrian Heil and Martin Kleinschmidt}, + Journal = {WIREs Comput. Mol. Sci.}, + Note = {doi: 10.1002/wcms.1394}, + Pages = {e1394}, + Title = {The DFT/MRCI method}, + Year = {2018}} + +@article{MarLosFdeAgu-JCP-04, + Author = {{M. E. Mart\'in, A. M. Losa, I. Fdez.-Galv\'an, and M. A. Aguilar}}, + Journal = {J. Chem. Phys.}, + Pages = {3710}, + Volume = {121}, + Year = {2004}} + +@article{MarMea-JCP-78, + Author = {D. J. Margoliash and W. J. Meath}, + Journal = {J. Chem. Phys.}, + Pages = {1426}, + Volume = {68}, + Year = {1978}} + +@article{MaRohMol-JCTC-10, + Author = {Y. Ma and M. Rohlfing and C. Molteni}, + Journal = {J. Chem. Theory Comput.}, + Pages = {257}, + Volume = {6}, + Year = {2010}} + +@article{MaRohMol-PRB-09, + Author = {Y. Ma and M. Rohlfing and C. Molteni}, + Journal = {Phys. Rev. B}, + Pages = {241405}, + Volume = {80}, + Year = {2009}} + +@article{Mar-PR-58, + Author = {N. H. March}, + Journal = {Phys. Rev.}, + Pages = {604}, + Volume = {{110}}, + Year = {1958}} + +@article{MarWer-JPCA-09, + Author = {O. Marchetti and H.-J. Werner}, + Journal = {J. Phys. Chem. A}, + Pages = {11580}, + Volume = {113}, + Year = {2009}} + +@article{Math10-PROG-15, + Note = {{Wolfram Research, Inc., Mathematica, Version 10.3, Champaign, IL (2015)}}} + +@article{Math9-PROG-12, + Note = {{Wolfram Research, Inc., Mathematica, Version 9.0, Champaign, IL (2012)}}} + +@article{MatKogRomDeh-PRA-98, + Author = {H. Matsuyama and T. Koga and E. Romera and J. S. 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E}, + Numpages = {22}, + Pages = {026702}, + Publisher = {American Physical Society}, + Title = {{Stochastic series expansion algorithm for the $S=1∕2$ $XY$ model with four-site ring exchange}}, + Url = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702}, + Volume = {72}, + Year = {2005}, + Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevE.72.026702}} + +@article{MenAnd-JCP-81, + Author = {F. Mentch and J. B. Anderson}, + Journal = {J. Chem. Phys.}, + Pages = {6307}, + Volume = {74}, + Year = {1981}} + +@incollection{MerValUga-INC-03, + Address = {Dordrecht}, + Author = {J. M. Mercero and E. Valderrama and J. M. Ugalde}, + Booktitle = {NATO-ASI Series in Metal-Ligand Interaction in Molecular-, Nano-, Micro, and Macro-systems in Complex Environments}, + Editor = {N. Russo, D. R. Salahub and M. Witko}, + Publisher = {Kluwer Academic Publishers}, + Year = {2003}} + +@article{MetRosRosTelTel-JCP-53, + Author = {N. 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Rev.}, + Pages = {A442}, + Title = {{Ground state of liquid He$^4$}}, + Volume = {138}, + Year = {1965}} + +@article{MisJezSza-PRL-03, + Author = {A. J. Misquitta and B. Jeziorski and K. Szalewicz}, + Journal = {Phys. Rev. Lett.}, + Pages = {033201}, + Volume = {91}, + Year = {2003}} + +@article{Mit-PRA-81, + Author = {M. H. Mittleman}, + Journal = {Phys. Rev. A}, + Pages = {1167}, + Volume = {24}, + Year = {1981}} + +@article{MiyAryKotSchUsuTer-PRB-02, + Author = {Miyake, T. and Aryasetiawan, F. and Kotani, T. and Schilfgaarde, M. v. and Usuda, M. and Terakura, K.}, + Journal = {Phys. Rev. B.}, + Pages = {245103}, + Title = {Total energy of solids: An exchange and random-phase approximation correlation study}, + Volume = {66}, + Year = {2002}} + +@book{Moi-BOOK-11, + Address = {Cambridge}, + Author = {Nimrod Moiseyev}, + Publisher = {Cambridge University Press}, + Title = {Non-Hermitian Quantum Mechanics}, + Year = {2011}} + +@article{MolPle-PR-34, + Author = {C. M{\o}ller and M. S. Plesset}, + Journal = {Phys. Rev.}, + Pages = {618}, + Volume = {46}, + Year = {1934}} + +@misc{Molpro-PROG-02, + Address = {Birmingham, UK}, + Author = {R. D. Amos and A. Bernhardsson and A. Berning and P. Celani and D. L. Cooper and M. J. O. Deegan and A. J. Dobbyn and F. Eckert and C. Hampel and G. Hetzer and P. J. Knowles and T. Korona and R. Lindh and A. W. Lloyd and S. J. {McNicholas} and F. R. Manby and W. Meyer and M. E. Mura and A. Nicklass and P. Palmieri and R. Pitzer and G. Rauhut and M. {Sch\"{u}tz} and U. Schumann and H. Stoll and A. J. Stone and R. Tarroni and T. Thorsteinsson and H.-J. Werner}, + Title = {MOLPRO, a package of ab initio programs designed by {H.-J.~Werner} and {P.~J. Knowles}, version 2002.2}, + Year = {2002}} + +@misc{Molpro-PROG-10, + Address = {Cardiff, UK}, + Author = {H.-J. Werner and P. J. Knowles and G. Knizia and F. R. Manby and M. {Sch\"{u}tz} and P. Celani and T. Korona and R. Lindh and A. Mitrushenkov and G. Rauhut and K. R. Shamasundar and T. 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Manby and M. {Sch\"{u}tz} and others}, + Note = {see www.molpro.net}, + Title = {MOLPRO, version 2008.2, a package of ab initio programs}, + Year = {2008}} + +@misc{Molproshort-PROG-10, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {Cardiff, UK, 2010, see \url{http://www.molpro.net}}, + Title = {MOLPRO, version 2010.1, a package of ab initio programs}} + +@misc{Molproshort-PROG-12, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {Cardiff, UK, 2012, see \url{http://www.molpro.net}}, + Title = {MOLPRO, version 2012.1, a package of ab initio programs}} + +@misc{Molproshort-PROG-15, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {{Cardiff, UK, 2015, see \url{http://www.molpro.net}}}, + Title = {{MOLPRO, version 2015.1, a package of ab initio programs}}} + +@misc{Molproweb-PROG-XX, + Note = {\url{http://www.molpro.net}}, + Title = {MOLPRO, a package of ab initio programs}} + +@article{MomShi-JCP-87, + Author = {T. Momose and T. Shida}, + Journal = {J. Chem. Phys.}, + Pages = {2832}, + Volume = {87}, + Year = {1987}} + +@article{MorCepSen-PRL-95, + Author = {S. Moroni and D. M. Ceperley and G. Senatore}, + Journal = {Phys. Rev. Lett.}, + Pages = {689}, + Volume = {75}, + Year = {1995}} + +@article{MorCohYan-JCP-06a, + Author = {Paula Mori-S\'anchez and Aron J. Cohen and Weitao Yang}, + Journal = {J. Chem. Phys.}, + Pages = {091102}, + Volume = {124}, + Year = {2006}} + +@article{MorCohYan-JCP-06, + Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {201102}, + Volume = {125}, + Year = {2006}} + +@article{MorCohYan-PRA-12, + Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {Phys. Rev. A}, + Pages = {042507}, + Volume = {85}, + Year = {2012}} + +@article{MorCohYan-PRL-08, + Author = {Paula Mori-S\'anchez and Aron J. Cohen and Weitao Yang}, + Journal = {Phys. Rev. Lett.}, + Pages = {146401}, + Volume = {100}, + Year = {2008}} + +@article{MorCohYan-PRL-09, + Author = {Mori-S\'anchez, Paula and Cohen, Aron and Yang, Weitao}, + Journal = {Phys. Rev. Lett.}, + Pages = {066403}, + Title = {Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems}, + Volume = {102}, + Year = {2009}} + +@article{MorMcmClaKimScu-JCTC-12, + Author = {M. A. Morales and J. McMinis and B. K. Clark and J. Kim and G. E. Scuseria}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2181}, + Volume = {8}, + Year = {2012}} + +@article{Mor-PR-29, + Author = {P. M. Morse}, + Journal = {Phys. 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This study is completed by illustrating the well-known isomorphism between the exchange hole and the square of the dominant localized orbital lying in the space region of the reference point of the exchange hole function. 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G. \'Angy\'an}, + Doi = {http://dx.doi.org/10.1007/s00214-015-1751-2}, + Journal = {Theor. Chem. Acc.}, + Pages = {148}, + Volume = {134}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00214-015-1751-2}} + +@incollection{MusCocAssOttUmrTou-AQC-18, + Author = {B. Mussard and E. Coccia and R. Assaraf and M. Otten and C. J. Umrigar and J. Toulouse}, + Booktitle = {Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems}, + Doi = {10.1016/bs.aiq.2017.05.005}, + Editor = {P. E. Hoggan}, + Pages = {255-270}, + Publisher = {Academic Press}, + Series = {Advances in Quantum Chemistry Vol. 76}, + Title = {Time-dependent linear-response variational Monte Carlo}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1016/bs.aiq.2017.05.005}} + +@article{MusReiAngTou-JCP-15, + Author = {B. Mussard and P. Reinhardt and J. G. \'Angy\'an and J. Toulouse}, + title = {Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights}, + Journal = {J. Chem. Phys.}, + Note = {Erratum: J. Chem. Phys. {\bf 142}, 219901 (2015)}, + Pages = {154123}, + Volume = {142}, + Year = {2015}} + +@misc{MusReiAngTou-JJJ-XX-note, + Note = {See the supplementary material for the detailed results of the calculations on the AE49 and DBH24/08 datasets.}} + +@article{MusRocJanAng-JCTC-16, + Author = {B. Mussard and D. Rocca and G. Jansen and J. G. \'Angy\'an}, + Doi = {10.1021/acs.jctc.5b01129}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2191-2202}, + Title = {Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01129}} + +@article{MusRocJanAng-JJJ-XX, + Author = {B. Mussard and D. Rocca and G. Jansen and J. G. \'Angy\'an}, + Note = {unpublished}} + +@article{MusSzaAng-JCTC-14, + Author = {B. Mussard and P. G. Szalay and J. G. \'Angy\'an}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1968}, + Volume = {10}, + Year = {2014}} + +@misc{MusTou-JJJ-XX, + Author = {B. Mussard and J. Toulouse}, + Note = {Fractional-charge and fractional-spin errors in range-separated density-functional theory, Mol. Phys., to appear (2016); preprint arXiv:1607.03621}} + +@article{MusTou-MP-17, + Author = {Bastien Mussard and Julien Toulouse}, + Journal = {Mol. Phys.}, + Pages = {161-173}, + Title = {Fractional-charge and fractional-spin errors in range-separated density-functional theory}, + Volume = {115}, + Year = {2017}} + +@article{Nag-IJQC-04, + Author = {A. Nagy}, + Journal = {Int. J. Quantum Chem.}, + Pages = {256}, + Volume = {99}, + Year = {2004}} + +@article{Nag-IJQC-98, + Author = {A. Nagy}, + Journal = {Int. J. 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Phys.}, + Note = {[In Eq.~(70) of this paper the minimization over potentials should actually be a maximization.]}, + Pages = {399-407}, + Publisher = {AIP}, + Title = {Legendre transforms and Maxwell relations in density functional theory}, + Volume = {77}, + Year = {1982}} + +@article{NalPar-JCP-fr-82, + Author = {Roman F. Nalewajski and Robert G. Parr}, + Journal = {J. Chem. Phys.}, + Note = {[Dans l'\'equation~(70) de cet article la minimisation sur le potentiel est en r\'ealit\'e une maximisation.]}, + Pages = {399-407}, + Publisher = {AIP}, + Title = {Legendre transforms and Maxwell relations in density functional theory}, + Volume = {77}, + Year = {1982}} + +@article{NeeSchKosSchGri-JCTC-09, + Author = {F. Neese and T. Schwabe and S. Kossmann and B. Schirmer and S. Grimme}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3060}, + Volume = {5}, + Year = {2009}} + +@article{NesPey-JPB-90, + Author = {B. M. Nestmann and S. D. Peyerimhoff}, + Journal = {J. Phys. 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Lett.}, + Pages = {230201}, + Title = {Semistochastic Projector Monte Carlo Method}, + Volume = {109}, + Year = {2012}} + +@article{PetKenDun-JCP-93b, + Author = {{K. A. Peterson, R. A. Kendall and T. H. Dunning Jr.}}, + Journal = {J. Chem. Phys.}, + Pages = {9790}, + Volume = {99}, + Year = {1993}} + +@article{PetTouUmr-JCP-11, + Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {064104}, + Title = {Basis set construction for molecular electronic structure theory: Natural orbital and Gauss--Slater basis for smooth pseudopotentials}, + Volume = {134}, + Year = {2011}} + +@article{PetTouUmr-JCP-12, + Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {124116}, + Title = {{Approaching chemical accuracy with quantum Monte Carlo}}, + Volume = {136}, + Year = {2012}} + +@article{PevHea-JCP-13, + Author = {Roberto Peverati and Martin Head-Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {024110}, + Title = {Orbital optimized double-hybrid density functionals}, + Volume = {139}, + Year = {2013}} + +@article{PevTru-JPCL-11, + Author = {Roberto Peverati and Donald G. Truhlar}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {2810}, + Volume = {2}, + Year = {2011}} + +@article{PevTru-JPCL-12, + Author = {Roberto Peverati and Donald G. Truhlar}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {117}, + Volume = {3}, + Year = {2012}} + +@article{PevTru-PTRSA-14, + Abstract = {Kohn{\textendash}Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange{\textendash}correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading{\textemdash}as a long-range goal{\textemdash}to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed{\textemdash}building on earlier work of our group{\textemdash}a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.}, + Author = {Peverati, Roberto and Truhlar, Donald G.}, + Doi = {10.1098/rsta.2012.0476}, + Isbn = {1471-2962}, + Issn = {1364-503X}, + Journal = {Phil. Trans. R. Soc. A}, + Note = {preprint at http://arxiv.org/abs/1212.0944}, + Number = {2011}, + Pages = {20120476}, + Publisher = {The Royal Society}, + Title = {Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics}, + Volume = {372}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1098/rsta.2012.0476}} + +@article{PhiKanZgi-JCP-15, + Author = {J. J. Phillips and A. A. Kananenka and D. Zgid}, + Journal = {J. Chem. Phys.}, + Pages = {194108}, + Volume = {142}, + Year = {2015}} + +@article{PicGos-MP-73, + Author = {B. T. Pickup and O. Goscinski}, + Journal = {Mol. Phys.}, + Pages = {1013}, + Volume = {26}, + Year = {1973}} + +@book{PinNoz-BOOK-89, + Author = {D. Pines and P. Nozi\`eres}, + Publisher = {Addison-Wesley Publishing Company}, + Title = {The Theory of Quantum Liquids}, + Year = {1989}} + +@article{PisDov-IJQC-80, + Author = {C. Pisani and R. Dovesi}, + Journal = {Int. J. Quantum Chem.}, + Pages = {501}, + Volume = {17}, + Year = {1980}} + +@article{PisMasCasHalSchUsv-JCC-08, + Author = {C. Pisani and L. Maschio and S. Casassa and M. Halo and M. Sch\"utz and D. Usvyat}, + Journal = {J. Comput. Chem.}, + Pages = {2113}, + Volume = {29}, + Year = {2008}} + +@article{BytLaiRuedenJCP05, + Author = {Bytautas,Laimutis and Ruedenberg,Klaus}, + Doi = {10.1063/1.1869493}, + Eprint = {https://doi.org/10.1063/1.1869493}, + Journal = {The Journal of Chemical Physics}, + Number = {15}, + Pages = {154110}, + Title = {Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine}, + Url = {https://doi.org/10.1063/1.1869493}, + Volume = {122}, + Year = {2005}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1869493}} + +@article{pittner:10275, + Author = {Jiri Pittner and Petr Nachtigall and Petr Carsky and Jozef Masik and Ivan Hubac}, + Journal = {The Journal of Chemical Physics}, + Keywords = {organic compounds; silicon compounds; coupled cluster calculations; configuration interactions}, + Number = {21}, + Pages = {10275-10282}, + Publisher = {AIP}, + Title = {Assessment of the single-root multireference Brillouin--Wigner coupled- cluster method: Test calculations on CH[sub 2], SiH[sub 2], and twisted ethylene}, + Url = {http://link.aip.org/link/?JCP/110/10275/1}, + Volume = {110}, + Year = {1999}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/110/10275/1}} + +@article{PolColLeiStoWerSav-IJQC-03, + Author = {R. Pollet and F. Colonna and T. Leininger and H. Stoll and H.-J. Werner and A. Savin}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {84}, + Title = {Exchange-Correlation Energies and Correlation Holes for Some Two- and Four-Electron Atoms along a Nonlinear Adiabatic Connection in Density Functional Theory}, + Volume = {{91}}, + Year = {2003}} + +@article{PolSavLeiSto-JCP-02, + Author = {R. Pollet and A. Savin and T. Leininger and H. Stoll}, + Journal = {J. Chem. Phys.}, + Pages = {1250}, + Title = {Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules}, + Volume = {{116}}, + Year = {2002}} + +@phdthesis{Pol-THESIS-01, + Author = {R. Pollet}, + School = {Universit\'e Paris 6}, + Title = {D\'eveloppement et applications d'une m\'ethode g\'en\'eralisant la th\'eorie de la fonctionnelle de la densit\'e \`a plusieurs d\'eterminants de Slater}, + Type = {Th\`ese de doctorat}, + Year = {2001}} + +@article{Pop-RMP-99, + Author = {J. A. Pople}, + Journal = {Rev. Mod. Phys.}, + Pages = {1267}, + Title = {{Nobel Lecture: Quantum chemical models}}, + Volume = {{71}}, + Year = {1999}} + +@article{PorDer-PRA-02, + Author = {S. G. Porsev and A. Derevianko}, + Journal = {Phys. Rev. A}, + Pages = {020701(R)}, + Volume = {65}, + Year = {2002}} + +@article{PraWooPetDunWil-TCA-11, + Author = {{B. P. Prascher, D. E. Woon, K. A. Peterson, T. H. Dunning, Jr., and A. K. Wilson}}, + Journal = {Theor. Chem. Acc.}, + Pages = {69}, + Volume = {128}, + Year = {2011}} + +@article{PreBevFah-PRB-02, + Author = {David Prendergast and David Bevan and Stephen Fahy}, + Journal = {Phys. Rev. B}, + Pages = {155104}, + Volume = {66}, + Year = {2002}} + +@article{PreNolFilFahGre-JCP-01, + Author = {D. Prendergast and M. Nolan and C. Filippi and S. Fahy and J. C. Greer}, + Journal = {J. Chem. Phys.}, + Pages = {1626}, + Volume = {{115}}, + Year = {2001}} + +@book{PreTeuVetFla-BOOK-92, + Address = {Cambridge}, + Author = {W. Press and S. Teukolsky and W. Vetterling and B. Flannery}, + Publisher = {Cambridge University Press}, + Title = {Numerical Recipes}, + Year = {1992}} + +@article{Pul-MP-69, + Author = {P. Pulay}, + Journal = {Mol. Phys.}, + Pages = {197}, + Volume = {17}, + Year = {1969}} + +@article{PurZhaKra-JCP-09, + Author = {W. Purwanto and S. Zhang and H. Krakauer}, + Journal = {J. Chem. Phys.}, + Pages = {094107}, + Volume = {130}, + Year = {2009}} + +@misc{Qmc-PROG-XX, + Note = {QMCMOL, a quantum Monte Carlo program written by R. Assaraf, F. Colonna, X. Krokidis, P. Reinhardt and coworkers.}, + Url = {http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/}, + Bdsk-Url-1 = {http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/}} + +@misc{Quantumexpressoweb-PROG-XX, + Note = {\url{http://www.quantum-espresso.org}}, + Title = {QUANTUM ESPRESSO, an integrated suite of Open-Source computer codes for electronic-structure calculations and materials modeling at the nanoscale}} + +@article{RabBaeNeu-PRB-15, + Author = {E. Rabani and R. Baer and D. Neuhauser}, + Journal = {Phys. Rev. B}, + Pages = {235302}, + Volume = {91}, + Year = {2015}} + +@article{rabinovitch:1807, + Author = {B. S. Rabinovitch and John E. Douglas and F. S. Looney}, + Journal = {The Journal of Chemical Physics}, + Number = {11}, + Pages = {1807-1808}, + Publisher = {AIP}, + Title = {The Thermal Trans-Cis Isomerization of Dideuteroethylene}, + Url = {http://link.aip.org/link/?JCP/20/1807/2}, + Volume = {20}, + Year = {1952}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/20/1807/2}} + +@book{Rai-BOOK-72, + Address = {Amsterdam-London}, + Author = {S. Raimes}, + Publisher = {North-Holland Publishing Company}, + Title = {Many-electron theory}, + Year = {1972}} + +@article{Raj-ACP-80, + Author = {A. K. Rajagopal}, + Journal = {Adv. Chem. Phys.}, + Pages = {59}, + Volume = {41}, + Year = {1980}} + +@article{RajCal-PRB-73, + Author = {A. K. Rajagopal and J. Callaway}, + Journal = {Phys. Rev. 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Toulouse}, + Note = {unpublished}} + +@article{RebSavTou-MP-13, + Author = {E. Rebolini and A. Savin and J. Toulouse}, + Journal = {Mol. Phys.}, + Pages = {1219}, + Title = {Electronic excitations from a linear-response range-separated hybrid scheme}, + Volume = {111}, + Year = {2013}} + +@article{RebTeaHelSavTou-MP-18, + Author = {E. Rebolini and A. M. Teale and T. Helgaker and A. Savin and J. Toulouse}, + Doi = {doi.org/10.1080/00268976.2017.1422811}, + Journal = {Mol. Phys.}, + Pages = {1443-1451}, + Title = {Excitation energies from G\"orling--Levy perturbation theory along the range-separated adiabatic connection}, + Volume = {116}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2017.1422811}} + +@phdthesis{Reb-THESIS-14, + Author = {E. Rebolini}, + School = {Universit\'e Pierre et Marie Curie}, + Title = {Range-separated density-functional theory for molecular excitation energies}, + Type = {{Th\`ese de doctorat}}, + Url = {https://tel.archives-ouvertes.fr/tel-01027522}, + Year = {2014}, + Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + +@phdthesis{Reb-THESIS-14_eng, + Author = {E. Rebolini}, + School = {Universit\'e Pierre et Marie Curie}, + Title = {Range-separated density-functional theory for molecular excitation energies}, + Type = {{PhD thesis}}, + Url = {https://tel.archives-ouvertes.fr/tel-01027522}, + Year = {2014}, + Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + +@article{RebTou-JCP-16, + Author = {E. Rebolini and J. Toulouse}, + Doi = {http://dx.doi.org/10.1063/1.4943003}, + Journal = {J. Chem. Phys.}, + Pages = {094107}, + Title = {Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel}, + Volume = {144}, + Year = {2016}, + Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4943003}} + +@misc{RebTou-JJJ-XX-note1, + Note = {The last two terms of the kernel in Eq. (31) of Ref.~\onlinecite{ZhaSteYan-JCP-13} contain non-antisymmetrized two-electron integrals. However, these terms can also be written with a factor of $1/2$ and antisymmetrized two-electron integrals, leading to our Eq.~(\ref{eq:eff kernel iajb}).}} + +@incollection{RebTouSav-INC-13, + Author = {E. Rebolini and J. Toulouse and A. Savin}, + Booktitle = {Electronic Structure and Reactivity}, + Editor = {S. K. Ghosh and P. K. Chattaraj}, + Note = {preprint at http://arxiv.org/abs/1304.1314}, + Pages = {367-390}, + Publisher = {CRC Press}, + Series = {Concepts and Methods in Modern Theoretical Chemistry Vol. 1}, + Title = {Electronic excitation energies of molecular systems from the Bethe-Salpeter equation: Example of the H$_2$ molecule}, + Year = {2013}} + +@misc{RebTouSav-JJJ-XX-note, + Note = {With the notations used here, the Hubbard model is obtained for $\Delta\varepsilon = 2 t$ and $J_{11}=J_{22}=J_{12}=J_{12}=K_{12}=U/2$ where $t$ is the hopping parameter and $U$ is the on-site Coulomb interaction.}} + +@article{RebTouTeaHelSav-JCP-14, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1063/1.4890652}, + Journal = {Journal of Chemical Physics}, + Pages = {044123}, + Title = {Excitation energies along a range-separated adiabatic connection}, + Volume = {141}, + Year = {2014}, + Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4890652}} + +@misc{RebTouTeaHelSav-JJJ-XX-sup, + Note = {See supplementary material at http://xxxxxxxx for the fits of the total and excitation energies.}} + +@article{RebTouTeaHelSav-MP-15, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1080/00268976.2015.1011248}, + Journal = {Mol. Phys.}, + Pages = {1740}, + Title = {Excited states from range-separated density-functional perturbation theory}, + Volume = {113}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2015.1011248}} + +@article{RebTouTeaHelSav-PRA-15, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1103/PhysRevA.91.032519}, + Journal = {Phys. Rev. A}, + Pages = {032519}, + Title = {Calculating excitation energies by extrapolation along adiabatic connections}, + Volume = {91}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.91.032519}} + +@article{RefJaiShaNeaKro-PRB-15, + Author = {Sivan Refaely-Abramson and Manish Jain and Sahar Sharifzadeh and Jeffrey B. Neaton and Leeor Kronik}, + Journal = {Phys. Rev. B}, + Pages = {081204(R)}, + Volume = {92}, + Year = {2015}} + +@article{RefShaGovAutNeaBaeKro-PRL-12, + Author = {S. Refaely-Abramson and Sahar Sharifzadeh and Niranjan Govind and Jochen Autschbach and Jeffrey B. Neaton and Roi Baer and Leeor Kronik}, + Journal = {Phys. Rev. Lett.}, + Pages = {226405}, + Volume = {109}, + Year = {2012}} + +@article{RegTha-JPB-84, + Author = {P. E. Regier and A. J. Thakkar}, + Journal = {J. Phys. 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Hoggan}, + Booktitle = {Advances in Quantum Monte Carlo}, + Editor = {{S. Tanaka, S. M. Rothstein, and W. A. Lester, Jr.}}, + Pages = {53-63}, + Publisher = {American Chemical Society}, + Series = {ACS Symposium Series Vol. 1094}, + Title = {Quantum Monte Carlo Facing the Hartree-Fock Symmetry Dilemma: The Case of Hydrogen Rings}, + Year = {2012}} + +@article{ReiTouSav-TCA-18, + Author = {Peter Reinhardt and Julien Toulouse and Andreas Savin}, + Doi = {10.1007/s00214-018-2370-5}, + Journal = {Theor. Chem. Acc.}, + Pages = {168}, + Volume = {137}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1007/s00214-018-2370-5}} + +@article{RenRinBluWieTkaSanReuSch-NJP-12, + Author = {Xinguo Ren and Patrick Rinke and Volker Blum and Jurgen Wieferink and Alexandre Tkatchenko and Andrea Sanfilippo and Karsten Reuter and Matthias Scheffler}, + Journal = {New J. Phys.}, + Pages = {053020}, + Volume = {14}, + Year = {2012}} + +@article{RenRinJoaSch-JMS-12, + Affiliation = {Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany}, + Author = {Ren, Xinguo and Rinke, Patrick and Joas, Christian and Scheffler, Matthias}, + Journal = {J. Mater. Sci.}, + Keyword = {Chemistry and Materials Science}, + Optnote = {10.1007/s10853-012-6570-4}, + Opturl = {http://dx.doi.org/10.1007/s10853-012-6570-4}, + Owner = {gambort}, + Pages = {7447}, + Publisher = {Springer Netherlands}, + Timestamp = {2012.07.06}, + Title = {Random-phase approximation and its applications in computational chemistry and materials science}, + Volume = {47}, + Year = {2012}} + +@article{RenRinSch-PRB-09, + Author = {Ren, Xinguo and Rinke, Patrick and Scheffler, Matthias}, + Doi = {10.1103/PhysRevB.80.045402}, + Journal = {Phys. Rev. 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E. and Toulouse, J. and Peverati, R. and Truhlar, D. G. and Szalewicz, K.}, + Doi = {http://dx.doi.org/10.1063/1.4961095}, + Journal = {J. Chem. Phys.}, + Pages = {124105}, + Title = {Blind test of density-functional-based methods on intermolecular interaction energies}, + Url = {http://scitation.aip.org/content/aip/journal/jcp/145/12/10.1063/1.4961095}, + Volume = {145}, + Year = {2016}, + Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/145/12/10.1063/1.4961095}, + Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.4961095}} + +@book{TDDFT-BOOK-06, + Address = {Berlin}, + Editor = {M. L. Marques and C. A. Ullrich and F. Nogueira and A. Rubio and K. Burke and E. K. U. Gross}, + Publisher = {Springer}, + Series = {Lecture Notes in Physics Vol. 706}, + Title = {Time-Dependent Density Functional Theory}, + Year = {2006}} + +@book{TDDFT-BOOK-12, + Address = {Berlin}, + Editor = {M. A. L. Marques and N. T. Maitra, F. M. S. Nogueira, E. K. U. Gross, A. Rubio}, + Publisher = {Springer}, + Series = {Lecture Notes in Physics Vol. 837}, + Title = {Fundamentals of Time-Dependent Density Functional Theory}, + Year = {2012}} + +@article{TeaCorHel-JCP-09, + Author = {A. M. Teale and S. Coriani and T. Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {104111}, + Title = {{The calculation of adiabatic-connection curves from full configuration-interaction densities: Two-electron systems}}, + Volume = {130}, + Year = {2009}} + +@article{TeaCorHel-JCP-10b, + Author = {Andrew M. Teale and S. Coriani and Trygve Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {164112}, + Volume = {133}, + Year = {2010}} + +@article{TeaCorHel-JCP-10, + Author = {Andrew M. Teale and S. Coriani and Trygve Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {164115}, + Volume = {132}, + Year = {2010}} + +@article{TeaDepToz-JCP-08, + Author = {{A. M. Teale, F. De Proft, and D. J. Tozer}}, + Journal = {J. Chem. Phys.}, + Pages = {044110}, + Volume = {129}, + Year = {2008}} + +@article{TecGomEksVis-PCCP-11, + Author = {P. Tecmer and A. S. P. Gomes and U. Ekstr\"om and L. Visscher}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {6249}, + Volume = {13}, + Year = {2011}} + +@article{TelKvaSagEksTeaHel-PRA-12, + Author = {E. I. Tellgren and S. Kvaal and E. Sagvolden and U. Ekstr\"om and A. M. Teale and T. Helgaker}, + Journal = {Phys. Rev. A}, + Pages = {062506}, + Volume = {86}, + Year = {2012}} + +@article{TelSosRozChu-PRA-13, + Author = {D. A. Telnov and K. E. Sosnova and E. Rozenbaum and S.-I. Chu}, + Journal = {Phys. Rev. A}, + Pages = {053406}, + Volume = {87}, + Year = {2013}} + +@article{Tha-CPL-03, + Author = {A. J. Thakkar}, + Journal = {Chem. Phys. Lett.}, + Pages = {80}, + Volume = {381}, + Year = {2003}} + +@incollection{Tha-INC-87, + Address = {Dordrecht}, + Author = {A. J. Thakkar}, + Booktitle = {Density Matrices and Density Functionals}, + Editor = {R. M. Erdahl and V. H. Smith}, + Pages = {553-581}, + Publisher = {Reidel}, + Year = {1987}} + +@article{ThaSmi-CPL-76, + Author = {A. J. Thakkar and V. H. Smith}, + Journal = {Chem. Phys. Lett.}, + Pages = {476}, + Volume = {42}, + Year = {1976}} + +@article{ThaSmi-JCP-77, + Author = {A. J. Thakkar and V. H. Smith}, + Journal = {J. Chem. Phys.}, + Pages = {1191}, + Volume = {67}, + Year = {1977}} + +@article{ThaTriSmi-IJQC-84, + Author = {A. J. Thakkar and A. N. Tripathi and V. H. Smith}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {157}, + Volume = {26}, + Year = {1984}} + +@article{ThaTriSmi-PRA-84, + Author = {A. J. Thakkar and A. N. Tripathi and V. H. Smith}, + Journal = {Phys. Rev. A}, + Pages = {1108}, + Volume = {29}, + Year = {1984}} + +@book{Tho-BOOK-61, + Address = {New York}, + Author = {D. J. Thouless}, + Publisher = {Academic Press}, + Title = {The Quantum Mechanics of Many Body Systems}, + Year = {1961}} + +@article{Tho-NAT-25, + Author = {W. Thomas}, + Journal = {Naturwissenschaften}, + Pages = {627}, + Volume = {13}, + Year = {1925}} + +@article{Tho-NP-61, + Author = {D. J. Thouless}, + Journal = {Nucl. Phys.}, + Pages = {78}, + Volume = {22}, + Year = {1961}} + +@article{ThyFleJen-JCP-08, + Author = {J. Thyssen and T. Fleig and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {034109}, + Volume = {129}, + Year = {2008}} + +@article{TiaChe-PRB-06, + Author = {M. L. Tiago and J. R. Chelikowsky}, + Journal = {Phys. Rev. B}, + Pages = {205334}, + Volume = {73}, + Year = {2006}} + +@article{TiaChe-SSC-05, + Author = {M. L. Tiago and J. R. Chelikowsky}, + Journal = {Solid State Commun.}, + Pages = {333}, + Volume = {136}, + Year = {2005}} + +@article{TiaKenHooReb-JCP-08, + Author = {M. L. Tiago and P. R. C. Kent and R. Q. Hood and F. A. Reboredo}, + Journal = {J. Chem. Phys.}, + Pages = {084311}, + Volume = {129}, + Year = {2008}} + +@article{TkaSch-PRL-09, + Author = {A. Tkatchenko and M. Scheffler}, + Journal = {Phys. Rev. Lett.}, + Pages = {073005}, + Title = {{Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data}}, + Volume = {102}, + Year = {2009}} + +@article{TofSteDec-PRA-06, + Author = {D. Toffoli and M. Stener and P. Decleva}, + Journal = {Phys. Rev. A}, + Pages = {042704}, + Volume = {73}, + Year = {2006}} + +@article{ToiWoo-PRB-70, + Author = {F. Toigo and T. O. Woodruff}, + Journal = {Phys. Rev. B}, + Pages = {3958}, + Volume = {{2}}, + Year = {1970}} + +@article{ToiWoo-PRB-71, + Author = {F. Toigo and T. O. Woodruff}, + Journal = {Phys. Rev. B}, + Pages = {371}, + Volume = {{4}}, + Year = {1971}} + +@incollection{Tos-INC-99, + Address = {University of Oxford}, + Author = {M. P. Tosi}, + Booktitle = {Electron Correlation in the Solid State}, + Editor = {N. H. March}, + Publisher = {World Scientific Publishing Company}, + Title = {Many-Body Effects in Jellium}, + Year = {1999}} + +@incollection{TouAssUmr-INC-16, + Author = {J. Toulouse and R. Assaraf and C. J. Umrigar}, + Booktitle = {Electron Correlation in Molecules - ab initio Beyond Gaussian Quantum Chemistry}, + Doi = {10.1016/bs.aiq.2015.07.003}, + Editor = {P. E. Hoggan and T. Ozdogan}, + Pages = {285-314}, + Publisher = {Academic Press}, + Series = {Advances in Quantum Chemistry Vol. 73}, + Title = {Introduction to the Variational and Diffusion Monte Carlo Methods}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1016/bs.aiq.2015.07.003}} + +@article{TouAssUmr-JCP-07, + Author = {J. Toulouse and R. Assaraf and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {244112}, + Title = {{Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density}}, + Volume = {126}, + Year = {2007}} + +@incollection{TouCafReiHogUmr-INC-12, + Address = {Dordrecht Heidelberg London New York}, + Author = {J. Toulouse and M. Caffarel and P. Reinhardt and P. E. Hoggan and C. J. Umrigar}, + Booktitle = {Advances in the Theory of Quantum Systems in Chemistry and Physics}, + Editor = {P. E. Hoggan and J. Maruani and P. Piecuch and G. Delgado-Barrio and E. J. Br\"andas}, + Pages = {345-353}, + Publisher = {Springer}, + Series = {Progress in Theoretical Chemistry and Physics Vol. 22}, + Title = {Quantum Monte Carlo calculations of electronic excitation energies: The case of the singlet $n\to\pi^*$ (CO) transition in acrolein}, + Year = {2012}} + +@article{TouColSav-JCP-05, + Author = {J. Toulouse and F. Colonna and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {014110}, + Title = {Short-range exchange and correlation energy density functionals: Beyond the local-density approximation}, + Volume = {122}, + Year = {2005}} + +@article{TouColSav-MP-05, + Author = {Julien Toulouse and Francois Colonna and Andreas Savin}, + Journal = {Mol. Phys.}, + Pages = {2725}, + Title = {Exchange-correlation potentials and local energies per particle along non-linear adiabatic connections}, + Volume = {103}, + Year = {2005}} + +@article{TouColSav-PRA-04, + Author = {J. Toulouse and F. Colonna and A. Savin}, + Journal = {Phys. Rev. A}, + Keywords = {density functional theory; wave functions; exchange interactions (electron); electron correlations}, + Number = {6}, + Pages = {062505}, + Publisher = {APS}, + Title = {Long-range--short-range separation of the electron-electron interaction in density-functional theory}, + Volume = {70}, + Year = {2004}} + +@misc{TouGerJanSavAng-JJJ-XX-note, + Note = {For Ne$_{2}$ at equilibrium distance with aug-cc-pVQZ basis, the counterpoise correction on the interaction energy is 16 $\mu$H for RSH+RPAx and 62 $\mu$H for standard MP2.}} + +@article{TouGerJanSavAng-PRL-09, + Author = {J. Toulouse and I. C. Gerber and G. Jansen and A. Savin and J. G. \'Angy\'an}, + Journal = {Phys. Rev. Lett.}, + Pages = {096404}, + Title = {Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation}, + Volume = {102}, + Year = {2009}} + +@article{TouGorSav-IJQC-06, + Author = {J. Toulouse and P. Gori-Giorgi and A. Savin}, + Journal = {Int. J. Quantum Chem.}, + Pages = {2026}, + Title = {Scaling relations, virial theorem and energy densities for long-range and short-range density functionals}, + Volume = {106}, + Year = {2006}} + +@article{TouGorSav-TCA-05, + Author = {J. Toulouse and P. Gori-Giorgi and A. Savin}, + Date-Modified = {2019-04-07 14:55:33 +0200}, + Journal = {Theor. Chem. Acc.}, + Pages = {305}, + Title = {A short-range correlation energy density functional with multi-determinantal reference}, + Volume = {114}, + Year = {2005}} + +@misc{Tou-JJJ-XX, + Author = {S. Dubillard and E. Eliav and L. Visscher and R. Bast and T. Saue}, + Note = {unpublished}} + +@article{Tou-PRB-05, + Author = {Julien Toulouse}, + Journal = {Phys. Rev. B}, + Pages = {035117}, + Title = {Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction}, + Volume = {72}, + Year = {2005}} + +@article{TouRebGouDobSeaAng-JCP-13, + Author = {Julien Toulouse and Elisa Rebolini and Tim Gould and John F. Dobson and Prasenjit Seal and J\'anos G. \'Angy\'an}, + Journal = {J. Chem. Phys.}, + Pages = {194106}, + Title = {Assessment of range-separated time-dependent density-functional theory for calculating $C_6$ dispersion coefficients}, + Volume = {138}, + Year = {2013}} + +@article{TouSavFla-IJQC-04, + Author = {J. Toulouse and A. Savin and H.-J. Flad}, + Journal = {Int. J. Quantum Chem.}, + Pages = {1047}, + Title = {Short-range exchange-correlation energy of a uniform electron gas with modified electron-electron interaction}, + Volume = {100}, + Year = {2004}} + +@misc{TouSav-JJJ-XX, + Author = {J. Toulouse and A. Savin}, + Title = {in preparation}} + +@article{TouSav-JMS-06, + Author = {Julien Toulouse and Andreas Savin}, + Journal = {J. Mol. Struct. (Theochem)}, + Pages = {147}, + Title = {Local density approximation for long-range or for short-range energy functionals?}, + Volume = {762}, + Year = {2006}} + +@article{TouShaBreAda-JCP-11, + Author = {J. Toulouse and K. Sharkas and E. Br\'emond and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {101102}, + Title = {Rationale for a new class of double-hybrid approximations in density-functional theory}, + Volume = {135}, + Year = {2011}} + +@phdthesis{Tou-THESIS-05, + Author = {J. Toulouse}, + Note = {tel.archives-ouvertes.fr/tel-00550772}, + School = {Universit\'e Pierre et Marie Curie (Paris 6)}, + Year = {2005}} + +@article{TouUmr-JCP-07, + Author = {J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {084102}, + Title = {{Optimization of quantum Monte Carlo wave functions by energy minimization}}, + Volume = {126}, + Year = {2007}} + +@article{TouUmr-JCP-08, + Author = {J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {174101}, + Title = {{Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules}}, + Volume = {128}, + Year = {2008}} + +@misc{TouUmr-JJJ-XX, + Author = {J. Toulouse and C. J. Umrigar}, + Note = {unpublished}} + +@misc{TouZhuAngSav-JJJ-XX-note2, + Note = {In the context of density-functional theory RPA is usually derived from the Kohn-Sham reference, while in the context of many-body perturbation theory (see appendices) RPA is usually derived from the HF reference. Therefore, both PBE+RPA and HF+RPA are theoretically justified.}} + +@misc{TouZhuAngSav-JJJ-XX-note3, + Note = {The inverse of a 4-point function $\chi (1,2;1',2')$ is defined according to $\int d1'd2' \chi (1,2;1',2') \chi^{-1} (2',1';4,3) = \delta(1,3) \delta (2,4)$.}} + +@misc{TouZhuAngSav-JJJ-XX-note, + Note = {The short-range self-energy correction $\Delta \Sigma^\sr_\l$ is wrongly missing in Eq.~(11) of Ref.~\onlinecite{TouGerJanSavAng-PRL-09}. However, in practice, this term vanishes in the RPA or RPAx approximation so that the results of Ref.~\onlinecite{TouGerJanSavAng-PRL-09} are correct.}} + +@article{TouZhuAngSav-PRA-10, + Author = {Julien Toulouse and Wuming Zhu and J\'anos G. \'Angy\'an and Andreas Savin}, + Journal = {Phys. Rev. A}, + Pages = {032502}, + Title = {Range-separated density-functional theory with the random-phase approximation: Detailed formalism and illustrative applications}, + Volume = {82}, + Year = {2010}} + +@article{TouZhuSavJanAng-JCP-11, + Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angy\'an}, + Journal = {J. Chem. Phys.}, + Pages = {084119}, + Title = {Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions}, + Volume = {135}, + Year = {2011}} + +@misc{TouZhuSavJanAng-JJJ-XX, + Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angyan}, + Note = {unpublished}} + +@misc{TouZhuSavJanAng-JJJ-XX-note, + Note = {In Ref.~\onlinecite{Hes-JCP-11}, AC-RPA, NRPA1, NRPA3, and NRPA4 refer to what we call here RPAx-I, RPAx-II, RPA-SO2, and RPA-SO1, respectively. In addition, NRPA2 corresponds to the variant of Fukuda {\it et al.}, i.e. $2E_{c,\RPAxII}-E_{c,\text{MP2}}$.}} + +@article{TowZupCau-CPC-96, + Author = {M. D. Towler and A. Zupan and M. Caus\'a}, + Journal = {Comp. Phys. Comm.}, + Pages = {181}, + Volume = {98}, + Year = {1996}} + +@article{TozHan-JCP-98, + Author = {D. J. Tozer and N. C. Handy}, + Journal = {J. Chem. Phys.}, + Pages = {10180}, + Volume = {109}, + Year = {1998}} + +@article{Tri-JPB-80, + Author = {H. P. Trivedi}, + Journal = {J. Phys. B}, + Pages = {839}, + Volume = {13}, + Year = {1980}} + +@article{Tru-CPL-98, + Author = {D. G. Truhlar}, + Journal = {Chem. Phys. Lett.}, + Pages = {45}, + Volume = {294}, + Year = {1998}} + +@article{TsuScu-JCP-11, + Author = {T. Tsuchimochi and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {064101}, + Volume = {134}, + Year = {2011}} + +@article{TsuScuSav-JCP-10, + Author = {T. Tsuchimochi and G. E. Scuseria and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {024111}, + Volume = {132}, + Year = {2010}} + +@article{TsuSonSuzHir-JCP-10, + Author = {Takao Tsuneda and Jong-Won Song and Satoshi Suzuki and Kimihiko Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {174101}, + Volume = {133}, + Year = {2010}} + +@article{TsuSuzHir-JCP-99, + Author = {Takao Tsuneda and Toshihisa Suzumura and Kimihiko Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {5656}, + Volume = {111}, + Year = {1999}} + +@article{UgaBoy-IJQC-85, + Author = {J. M. Ugalde and R. J. Boyd}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {439}, + Volume = {27}, + Year = {1985}} + +@book{Ull-BOOK-11, + Author = {Carsten A. Ullrich}, + Publisher = {OUP Oxford}, + Title = {Time-Dependent Density-Functional Theory: Concepts and Applications}, + Year = {2011}} + +@article{UllKoh-PRL-01, + Author = {C. A. Ullrich and W. Kohn}, + Journal = {Phys. Rev. Lett.}, + Pages = {093001}, + Volume = {87}, + Year = {2001}} + +@article{UmrFil-PRL-05, + Author = {C. J. Umrigar and C. Filippi}, + Journal = {Phys. Rev. Lett.}, + Pages = {150201}, + Title = {{Energy and variance optimization of many-body wave functions}}, + Volume = {94}, + Year = {2005}} + +@misc{UmrFil-PRL-05-note, + Note = {The convergence in 2 iterations, mentioned near the end of Ref.~\onlinecite{UmrFil-PRL-05} was obtained using the correlated sampling adjustment of $a_\diag$ and the TU Hessian.}} + +@incollection{UmrGon-INC-93, + Address = {Singapore}, + Author = {C. J. Umrigar and X. Gonze}, + Booktitle = {High Performance Computing and its Application to the Physical Sciences, Proceedings of the Mardi Gras '93 Conference}, + Editor = {D. A. Browne {\it et al.}}, + Publisher = {World Scientific}, + Year = {1993}} + +@article{UmrGon-PRA-94, + Author = {C. J. Umrigar and X. Gonze}, + Journal = {Phys. Rev. A}, + Pages = {3827}, + Volume = {50}, + Year = {1994}} + +@article{Umr-IJQC-89, + Author = {C. J. Umrigar}, + Journal = {Int. J. Quantum Chem.}, + Pages = {217}, + Volume = {{23}}, + Year = {1989}} + +@incollection{Umr-INC-99, + Address = {Dordrecht}, + Author = {C. J. Umrigar}, + Booktitle = {Quantum Monte Carlo Methods in Physics and Chemistry}, + Editor = {M. P. Nightingale and C. J. Umrigar}, + Pages = {129}, + Publisher = {Kluwer}, + Series = {NATO ASI Ser. C 525}, + Year = {1999}} + +@article{UmrNigRun-JCP-93, + Author = {C. J. Umrigar and M. P. Nightingale and K. J. Runge}, + Journal = {J. Chem. Phys.}, + Pages = {2865}, + Title = {{A diffusion Monte Carlo algorithm with very small time-step errors}}, + Volume = {99}, + Year = {1993}} + +@article{Umr-PRL-93, + Author = {C. J. Umrigar}, + Journal = {Phys. Rev. Lett.}, + Pages = {408}, + Title = {{Accelerated Metropolis method}}, + Volume = {71}, + Year = {1993}} + +@incollection{UmrSavGon-INC-98, + Author = {Umrigar, C.J. and Savin, A. and Gonze, Xavier}, + Booktitle = {Electronic Density Functional Theory}, + Doi = {10.1007/978-1-4899-0316-7_12}, + Editor = {Dobson, John F. and Vignale, Giovanni and Das, Mukunda P.}, + Pages = {167-176}, + Publisher = {Springer US}, + Title = {Are Unoccupied Kohn-Sham Eigenvalues Related to Excitation Energies?}, + Year = {1998}, + Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4899-0316-7_12}} + +@article{UmrTouFilSorHen-PRL-07, + Author = {C. J. Umrigar and J. Toulouse and C. Filippi and S. Sorella and R. G. Hennig}, + Journal = {Phys. Rev. Lett.}, + Pages = {110201}, + Title = {Alleviation of the Fermion-sign problem by optimization of many-body wave functions}, + Volume = {98}, + Year = {2007}} + +@misc{Umr-UNP-XXb, + Author = {C. J. Umrigar}, + Note = {unpublished}} + +@misc{Umr-UNP-XX, + Author = {C. J. Umrigar}, + Note = {unpublished}} + +@misc{Umr-UNP-XX_fr, + Author = {C. J. Umrigar}, + Note = {non publi{\'e}}} + +@incollection{UmrWilWil-INC-88, + Address = {Berlin}, + Author = {C. J. Umrigar and K. G. Wilson and J. W. Wilkins}, + Booktitle = {Computer Simulation Studies in Condensed Matter Physics: Recent Developments}, + Editor = {D. P. Landau and K. K. Mon and H. B. Sch\"uttler}, + Publisher = {Springer}, + Year = {1988}} + +@article{UmrWilWil-PRL-88, + Author = {C. J. Umrigar and K. G. Wilson and J. W. Wilkins}, + Journal = {Phys. Rev. Lett.}, + Pages = {1719}, + Title = {{Optimized trial wave functions for quantum Monte Carlo calculations}}, + Volume = {60}, + Year = {1988}} + +@article{UtsIch-PRB-80a, + Author = {K. Utsumi and S. Ichimaru}, + Journal = {Phys. Rev. B}, + Pages = {1522}, + Volume = {{22}}, + Year = {1980}} + +@article{UtsIch-PRB-80, + Author = {K. Utsumi and S. Ichimaru}, + Journal = {Phys. Rev. B}, + Pages = {5203}, + Volume = {{22}}, + Year = {1980}} + +@article{Val-JCP-80a, + Author = {S. M. Valone}, + Journal = {J. Chem. Phys.}, + Pages = {4653}, + Volume = {73}, + Year = {1980}} + +@article{VasSin-PRB-72, + Author = {P. Vashista and K.S. Singwi}, + Journal = {Phys. Rev. B}, + Pages = {875}, + Volume = {{6}}, + Year = {1972}} + +@article{VeiCle-JCP-69, + Author = {A. Veillard and E. Clementi}, + Journal = {J. Chem. Phys.}, + Pages = {2415}, + Volume = {{49}}, + Year = {1969}} + +@article{VitDelGor-JCP-05, + Author = {{V. Vitale, F. Della Sala, and A. G\"orling}}, + Journal = {J. Chem. Phys.}, + Pages = {244102}, + Volume = {122}, + Year = {2005}} + +@phdthesis{Vog-THESIS-03, + Author = {M. Vogt}, + School = {University of Cambridge}, + Title = {Spectral Moments in the Homogeneous Electron Gas}, + Year = {2003}} + +@article{VogZimNee-PRB-04, + Author = {M. Vogt and R. Zimmermann and R. J. Needs}, + Journal = {Phys. Rev. B}, + Pages = {045113}, + Volume = {{69}}, + Year = {2004}} + +@article{VosWilNus-CJP-80, + Author = {S. J. Vosko and L. Wilk and M. Nusair}, + Journal = {Can. J. Phys.}, + Pages = {1200}, + Volume = {{58}}, + Year = {1980}} + +@article{VrbDepRot-JCP-88, + Author = {J. Vrbik and M. F. DePasquale and S. M. Rothstein}, + Journal = {J. Chem. Phys.}, + Pages = {3784}, + Volume = {88}, + Year = {1988}} + +@article{VutCamGurHutparPatPetSpaDoyGabDem-JPB-10, + Author = {A. C. Vutha and W. C. Campbell and Y. V. Gurevich and N. R. Hutzler and M. Parsons and D. Patterson and E. Petrik and B. Spaun and J. M. Doyle and G. Gabrielse and D. DeMille}, + Journal = {J. Phys. B}, + Pages = {074007}, + Volume = {43}, + Year = {2010}} + +@article{VydScu-JCP-06, + Author = {O. A. Vydrov and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {234109}, + Volume = {125}, + Year = {2006}} + +@article{VydScuPer-JCP-07, + Author = {Vydrov, O. A. and Scuseria, G. E. and Perdew, J. P.}, + Journal = {J. Chem. Phys.}, + Pages = {154109}, + Title = {Tests of functionals for systems with fractional electron number}, + Volume = {126}, + Year = {2007}} + +@article{VydVoo-JCP-09, + Author = {O. A. Vydrov and T. van Voorhis}, + Journal = {J. Chem. Phys.}, + Pages = {104105}, + Volume = {130}, + Year = {2009}} + +@article{VydVoo-JCP-10b, + Author = {O. A. Vydrov and T. V. Voorhis}, + Journal = {J. Chem. Phys.}, + Pages = {244103}, + Title = {{Nonlocal van der Waals density functional: The simpler the better}}, + Volume = {133}, + Year = {2010}} + +@article{VydVoo-PRL-09, + Author = {O. A. Vydrov and T. van Voorhis}, + Journal = {Phys. Rev. Lett.}, + Pages = {063004}, + Volume = {103}, + Year = {2009}} + +@article{Wal-TFS-45, + Author = {A. D. Walsh}, + Journal = {Trans. Faraday Soc.}, + Pages = {498}, + Volume = {41}, + Year = {1945}} + +@article{WanGauWul-JCP-08, + Author = {{F. Wang, J. Gauss, and C. van W\"ullen}}, + Journal = {J. Chem. Phys.}, + Pages = {064113}, + Volume = {129}, + Year = {2008}} + +@article{WanPer-PRB-91, + Author = {Y. Wang and J.P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {13298}, + Volume = {{44}}, + Year = {1991}} + +@article{WanSch-JCP-96, + Author = {S. G. Wang and W. H. E. Schwarz}, + Journal = {J. Chem. Phys.}, + Pages = {4641}, + Volume = {{105}}, + Year = {1996}} + +@article{WanSchSmi-PRA-00, + Author = {J. Wang and H. L. Schmider and V. H. Smith}, + Journal = {Phys. Rev. A}, + Pages = {016501}, + Volume = {62}, + Year = {2000}} + +@article{WanSmi-IJQC-94, + Author = {J. Wang and V. H. Smith}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {147}, + Volume = {49}, + Year = {1994}} + +@article{WanTriSmi-JCP-92, + Author = {J. Wang and A. N. Tripathi and V. H. Smith}, + Journal = {J. Chem. Phys.}, + Pages = {9188}, + Volume = {97}, + Year = {1992}} + +@article{WanTriSmi-JCP-94, + Author = {J. Wang and A. N. Tripathi and V. H. Smith}, + Journal = {J. Chem. Phys.}, + Pages = {4842}, + Volume = {101}, + Year = {1994}} + +@article{WanZie-JCP-04, + Author = {F. Wang and T. Ziegler}, + Journal = {J. Chem. Phys.}, + Pages = {12191}, + Volume = {121}, + Year = {2004}} + +@article{WasBur-PRL-05, + Author = {A. Wasserman and K. Burke}, + Journal = {Phys. Rev. Lett.}, + Pages = {163006}, + Volume = {95}, + Year = {2005}} + +@article{WasMaiBur-PRL-03, + Author = {A. Wasserman and N. T. Maitra and K. Burke}, + Journal = {Phys. Rev. Lett.}, + Pages = {263001}, + Volume = {91}, + Year = {2003}} + +@article{WatKamYamUdaMul-MP-04, + Author = {Noboru Watanabe and Yohei Kamata and Kota Yamauchi and Yasuo Udagawa and Thomas M\"uller}, + Journal = {Mol. Phys.}, + Pages = {649}, + Volume = {102}, + Year = {2004}} + +@article{WeiDelGor-JCP-08, + Author = {M. Weimer and F. Della Sala and A. G\"orling}, + Journal = {J. Chem. Phys.}, + Pages = {144109}, + Title = {Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation}, + Volume = {128}, + Year = {2008}} + +@article{WenBer-JCTC-11, + Author = {Shuhao Wen and Gregory J. O. Beran}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3733}, + Volume = {7}, + Year = {2011}} + +@article{WerKno-JCP-88, + Author = {H.-J. Werner and P. J. Knowles}, + Journal = {J. Chem. 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Phys.}, + Number = {13}, + Pages = {134108}, + Title = {Relations between coordinate and potential scaling in the high-density limit}, + Volume = {122}, + Year = {2005}} + +@article{WilMouDun-JMS-96, + Author = {A. K. Wilson and T. v. Mourik and T. H. Dunning}, + Journal = {J. Mol. Struct.}, + Pages = {339}, + Volume = {388}, + Year = {1996}} + +@article{WilWooPetDun-JCP-99, + Author = {A.K. Wilson and D.E. Woon and K.A. Peterson and T.H.Dunning}, + Journal = {J. Chem. Phys.}, + Pages = {7667}, + Volume = {110}, + Year = {1999}} + +@article{WodJanRagCor-JPCA-08, + Author = {{M. D. Wodrich, D. F. Jana, P. v. R. Schleyer, and C. Corminboeuf}}, + Journal = {J. Phys. Chem. A}, + Pages = {11495}, + Volume = {112}, + Year = {2008}} + +@article{Wol-PRL-89, + Author = {Wolff, U.}, + Doi = {10.1103/PhysRevLett.62.361}, + Issue = {4}, + Journal = {Phys. Rev. Lett.}, + Numpages = {0}, + Pages = {361--364}, + Publisher = {American Physical Society}, + Title = {{Collective Monte Carlo updating for spin systems}}, + Url = {http://link.aps.org/doi/10.1103/PhysRevLett.62.361}, + Volume = {62}, + Year = {1989}, + Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.62.361}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.62.361}} + +@article{wolinski:3647, + Author = {Krzysztof Wolinski and Peter Pulay}, + Journal = {The Journal of Chemical Physics}, + Keywords = {PERTURBATION THEORY; WAVE FUNCTIONS; ELECTRONIC STRUCTURE; DIPOLE MOMENTS; AFFINITY; IONIZATION POTENTIAL; POTENTIAL ENERGY SURFACES; HYDROFLUORIC ACID; FLUORINE; ETHYLENE; OZONE; FORMALDEHYDE; ELECTRON CORRELATION}, + Number = {7}, + Pages = {3647-3659}, + Publisher = {AIP}, + Title = {Generalized M[o-slash]ller--Plesset perturbation theory: Second order results for two-configuration, open-shell excited singlet, and doublet wave functions}, + Url = {http://link.aip.org/link/?JCP/90/3647/1}, + Volume = {90}, + Year = {1989}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/90/3647/1}} + +@article{WooDun-JCP-93, + Author = {D.E. Woon and T.H. Dunning}, + Journal = {J. Chem. Phys.}, + Pages = {1358}, + Volume = {98}, + Year = {1993}} + +@article{WooDun-JCP-94, + Author = {D.E. Woon and T.H. Dunning}, + Journal = {J. Chem. Phys.}, + Pages = {2975}, + Volume = {100}, + Year = {1994}} + +@article{WooDun-JCP-95, + Author = {D.E. Woon and T.H. Dunning}, + Journal = {J. Chem. Phys.}, + Pages = {4572}, + Volume = {103}, + Year = {1995}} + +@article{WouNec-EPJD-14, + Author = {{S. Wouters and D. Van Neck}}, + Journal = {Eur. Phys. J. D}, + Pages = {272}, + Title = {The density matrix renormalization group for ab initio quantum chemistry}, + Volume = {68}, + Year = {2014}} + +@article{WuAyeYan-JCP-03, + Author = {Qin Wu and Paul W. Ayers and Weitao Yang}, + Journal = {J. Chem. Phys.}, + Keywords = {density functional theory; variational techniques; electron affinity; negative ions}, + Number = {6}, + Pages = {2978-2990}, + Publisher = {AIP}, + Title = {Density-functional theory calculations with correct long-range potentials}, + Url = {http://link.aip.org/link/?JCP/119/2978/1}, + Volume = {119}, + Year = {2003}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/119/2978/1}} + +@article{WuCheVoo-JCP-07, + Author = {{Q. Wu, C.-L. Cheng, and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {164119}, + Title = {Configuration interaction based on constrained density functional theory: A multireference method}, + Volume = {127}, + Year = {2007}} + +@article{WuKadVoo-JCP-09, + Author = {{Q. Wu, B. Kaduk, and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {034109}, + Volume = {130}, + Year = {2009}} + +@incollection{Wul-INC-10, + Address = {Netherlands}, + Author = {{C. van W\"ullen}}, + Booktitle = {Relativistic Methods for Chemists, Challenges and Advances in Computational Chemistry and Physics 10}, + Editor = {M. Barysz and Y. Ishikawa}, + Pages = {191-214}, + Publisher = {Springer}, + Title = {RELATIVISTIC DENSITY FUNCTIONAL THEORY}, + Year = {2010}} + +@article{WuSha-CPL-99, + Author = {W. Wu and S. Shaik}, + Journal = {Chem. Phys. Lett.}, + Pages = {37}, + Volume = {301}, + Year = {1999}} + +@article{WuShaHib-xx, + Author = {P. Su and J. Wu. and J. Gu and W. Wu and S. Shaik and P. C. Hiberty}, + Journal = {J. Chem. Theory Comput.}, + Pages = {121}, + Volume = {7}, + Year = {2011}} + +@article{WuSonCaoZhaSha-JPCA-02, + Author = {W. Wu and L. Song and Z. Cao and Q. Zhang and S. Shaik}, + Journal = {J. Phys. Chem. A}, + Pages = {2721}, + Volume = {106}, + Year = {2002}} + +@article{WuVarNayLotSco-JCP-01, + Author = {X. Wu and M. C. Vargas and S. Nayak and V. Lotrich and G. Scoles}, + Journal = {J. Chem. Phys.}, + Pages = {8748}, + Volume = {115}, + Year = {2001}} + +@article{WuWuMo-IJQC-98, + Author = {W. Wu and A. Wu and Y. Mo and M. Lin and Q. Zhang}, + Journal = {Int. J. Quantum Chem.}, + Pages = {287}, + Volume = {67}, + Year = {1998}} + +@article{WuYan-JCP-02, + Author = {Q. Wu and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {515}, + Volume = {116}, + Year = {2002}} + +@article{WuYan-JCP-03, + Author = {Qin Wu and Weitao Yang}, + Journal = {J. Chem. Phys.}, + Number = {6}, + Pages = {2498-2509}, + Title = {A direct optimization method for calculating density functionals and exchange--correlation potentials from electron densities}, + Volume = {118}, + Year = {2003}} + +@article{xantheas:8054, + Author = {Sotiris S. Xantheas and Gregory J. Atchity and Stephen T. Elbert and Klaus Ruedenberg}, + Journal = {The Journal of Chemical Physics}, + Keywords = {OZONE; ELECTRONIC STRUCTURE; POTENTIAL ENERGY; SELF–CONSISTENT FIELD; CONFIGURATION INTERACTION; POTENTIAL ENERGY SURFACES; QUANTUM CHEMISTRY}, + Number = {12}, + Pages = {8054-8069}, + Publisher = {AIP}, + Title = {Potential energy surfaces of ozone. I}, + Url = {http://link.aip.org/link/?JCP/94/8054/1}, + Volume = {94}, + Year = {1991}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/94/8054/1}} + +@article{YamKocTen-JCP-07, + Author = {D. Yamaki and H. Koch and S. Ten-no}, + Journal = {J. Chem. Phys.}, + Pages = {144104}, + Volume = {127}, + Year = {2007}} + +@article{YamNakUkaTakYam-IJQC-06, + Author = {S. Yamanaka and K. Nakata and T. Ukai and T. Takada and K. Yamaguchi}, + Journal = {Int. J. Quantum Chem.}, + Pages = {3312}, + Title = {Multireference Density Functional Theory With Orbital-Dependent Correlation Corrections}, + Volume = {106}, + Year = {2006}} + +@article{YanAyeWu-PRL-04, + Author = {Weitao Yang and Paul W. Ayers and Qin Wu}, + Journal = {Phys. Rev. Lett.}, + Pages = {146404}, + Volume = {92}, + Year = {2003}} + +@article{YanCohMor-JCP-12, + Author = {Weitao Yang and Aron J. Cohen and Paula Mori-S\'anchez}, + Journal = {J. Chem. Phys.}, + Pages = {204111}, + Volume = {136}, + Year = {2012}} + +@article{YanHarHan-MP-05, + Author = {T. Yanai and R. J. Harrison and N. C. Handy}, + Journal = {Mol. Phys.}, + Pages = {413}, + Volume = {103}, + Year = {2005}} + +@article{Yan-JCP-98, + Author = {W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {10107}, + Title = {Generalized adiabatic connection in density functional theory}, + Volume = {{109}}, + Year = {1998}} + +@article{YanMorCoh-JCP-13, + Author = {W. Yang and P. Mori-S{\'a}nchez and A. J. Cohen}, + Journal = {J. Chem. Phys.}, + Pages = {104114}, + Volume = {139}, + Year = {2013}} + +@article{YanPerKur-PRB-00, + Author = {Yan, Z. and Perdew, J. P. and Kurth, S.}, + Journal = {Phys. Rev. B.}, + Pages = {16430-16439}, + Title = {Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes}, + Volume = {61}, + Year = {2000}} + +@article{YanTewHan-CPL-04, + Author = {Takeshi Yanai and David P. Tew and Nicholas C. Handy}, + Journal = {Chem. Phys. Lett.}, + Pages = {51}, + Volume = {393}, + Year = {2004}} + +@article{YanWu-PRL-02, + Author = {Weitao Yang and Qin Wu}, + Journal = {Phys. Rev. Lett.}, + Pages = {143002}, + Title = {Direct Method for Optimized Effective Potentials in Density-Functional Theory}, + Volume = {89}, + Year = {2002}} + +@article{YanZhaAye-PRL-00, + Author = {Weitao Yang and Yingkai Zhang and Paul W. Ayers}, + Journal = {Phys. Rev. Lett.}, + Pages = {5172}, + Volume = {84}, + Year = {2000}} + +@article{Yar-CPL-81, + Author = {D. R. Yarkony}, + Journal = {Chem. Phys. Lett.}, + Pages = {634}, + Volume = {77}, + Year = {1981}} + +@article{Yas-PRL-02, + Author = {Koji Yasuda}, + Eid = {053001}, + Journal = {Physical Review Letters}, + Keywords = {density functional theory; electron density; electron correlations; Schrodinger equation; scaling phenomena; electron gas}, + Number = {5}, + Numpages = {4}, + Pages = {053001}, + Publisher = {APS}, + Title = {Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory}, + Url = {http://link.aps.org/abstract/PRL/v88/e053001}, + Volume = {88}, + Year = {2002}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRL/v88/e053001}} + +@article{YeaJor-JCP-79, + Author = {D. L. Yeager and P. J{\o}rgensen}, + Journal = {J. Chem. Phys.}, + Pages = {755}, + Volume = {{71}}, + Year = {1979}} + +@article{YinSuCheShaWu-JCTC-12, + Author = {F. Ying and P. Su and Z. Chen and S. Shaik and W. Wu}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1608}, + Volume = {8}, + Year = {2012}} + +@article{Yu-IJQC-13, + Author = {F. Yu}, + Journal = {Int. J. Quantum Chem.}, + Pages = {2355}, + Volume = {113}, + Year = {2013}} + +@article{ZahLeaGor-JCP-13, + Author = {F. Zahariev and S. S. Leang and M. S. Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {244108}, + Volume = {138}, + Year = {2013}} + +@book{ZalPapMezLes-BOOK-11, + Address = {Netherlands}, + Editor = {R. Zalesny and M. G. Papadopoulos and P. G. Mezey and J. Leszczynski}, + Publisher = {Springer}, + Series = {Challenges and Advances in Computational Chemistry and Physics Vol. 13}, + Title = {Linear-Scaling Techniques in Computational Chemistry and Physics}, + Year = {2011}} + +@article{ZanSov-PRA-80, + Author = {A. Zangwill and P. Soven}, + Journal = {Phys. Rev. A}, + Pages = {1561}, + Volume = {21}, + Year = {1980}} + +@article{ZarKoh-PRB-76, + Author = {E. Zaremba and W. Kohn}, + Journal = {Phys. Rev. B}, + Pages = {2270}, + Volume = {13}, + Year = {1976}} + +@article{ZecGorMorBac-PRB-04, + Author = {Lorenzo Zecca and Paola Gori-Giorgi and Saverio Moroni and Giovanni B. Bachelet}, + Journal = {Phys. Rev. B}, + Keywords = {density functional theory; Monte Carlo methods; ground states; electron gas; electron density; electron correlations}, + Number = {20}, + Pages = {205127}, + Publisher = {APS}, + Title = {Local density functional for the short-range part of the electron-electron interaction}, + Volume = {70}, + Year = {2004}} + +@article{ZeiMea-MP-77, + Author = {G. D. Zeiss and W. J. Meath}, + Journal = {Mol. Phys.}, + Pages = {1155}, + Volume = {33}, + Year = {1977}} + +@article{ZhaBur-PRA-04, + Author = {F. Zhang and K. Burke}, + Journal = {Phys. Rev. A}, + Pages = {052510}, + Volume = {69}, + Year = {2004}} + +@article{ZhaLuoXu-JCP-10b, + Author = {I. Y. Zhang and Y. Luo and X. Xu}, + Journal = {J. Chem. Phys.}, + Pages = {104105}, + Volume = {133}, + Year = {2010}} + +@article{ZhaLuoXu-JCP-10, + Author = {I. Y. Zhang and Y. Luo and X. Xu}, + Journal = {J. Chem. Phys.}, + Pages = {194105}, + Volume = {132}, + Year = {2010}} + +@article{ZhaLynTru-JPCA-04, + Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar}, + Journal = {J. Phys. Chem. A}, + Pages = {4786}, + Volume = {108}, + Year = {2004}} + +@article{ZhaLynTru-PCCP-05, + Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {43}, + Volume = {7}, + Year = {2005}} + +@article{ZhaPar-PRA-92, + Author = {Q. Zhao and R. G. Parr}, + Journal = {Phys. Rev. A.}, + Pages = {2337}, + Volume = {{46}}, + Year = {1992}} + +@article{ZhaSchTru-JCTC-06, + Author = {Y. Zhao and N. E. Schultz and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {364}, + Volume = {2}, + Year = {2006}} + +@article{ZhaSteYan-JCP-13, + Abstract = {We present a dynamical second-order kernel for the Bethe-Salpeter equation to calculate electronic excitation energies. The derivation takes explicitly the functional derivative of the exact second-order self energy with respect to the one-particle Green's function. It includes naturally a frequency dependence, going beyond the adiabatic approximation. Perturbative calculations under the Tamm-Dancoff approximation, using the configuration interaction singles (CIS) eigenvectors, reveal an appreciable improvement over CIS, time-dependent Hartree-Fock, and adiabatic time-dependent density functional theory results. The perturbative results also compare well with equation-of-motion coupled-cluster and experimental results.}, + Author = {Zhang, Du and Steinmann, Stephan N and Yang, Weitao}, + Journal = {J. Chem. Phys.}, + Month = oct, + Number = {15}, + Pages = {154109}, + Pmid = {24160502}, + Publisher = {American Institute of Physics}, + Title = {{Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation.}}, + Volume = {139}, + Year = {2013}} + +@article{ZhaSuBreAdaXu-JCP-12, + Author = {I. Y. Zhang and N. Q. Su and E. A. G. Br\'emond and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {174103}, + Volume = {136}, + Year = {2012}} + +@article{ZhaTru-JCTC-07, + Author = {Y. Zhao and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {289}, + Title = {Density Functionals for Noncovalent Interaction Energies of Biological Importance}, + Volume = {3}, + Year = {2007}} + +@article{ZhaTru-TCA-08, + Author = {Y. Zhao and D. G. Truhlar}, + Journal = {Theor. Chem. Acc.}, + Pages = {215}, + Volume = {120}, + Year = {2008}} + +@article{ZhaWuXu-CC-10, + Author = {I. Y. Zhang and J. Wu and X. Xu}, + Journal = {Chem. Commun.}, + Pages = {3057}, + Volume = {46}, + Year = {2010}} + +@article{ZhaXuGod-PNAS-09, + Author = {{Y. Zhang, X. Xu and W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {4963}, + Volume = {106}, + Year = {2009}} + +@article{ZhaXuGod-PNAS-09_fr, + Author = {{Y. Zhang, X. Xu et W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {4963}, + Volume = {106}, + Year = {2009}} + +@article{ZhaXu-IRPC-11, + Author = {I. Y. Zhang and X. Xu}, + Journal = {Int. Rev. Phys. Chem.}, + Pages = {115}, + Volume = {30}, + Year = {2011}} + +@article{ZhaXu-JPCL-13, + Author = {I. Y. Zhang and X. Xu}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {1669}, + Volume = {4}, + Year = {2013}} + +@article{ZhaXuJunGod-PNAS-11, + Author = {{I. Y. Zhang, X. Xu, Y. Jung, and W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {19896}, + Volume = {108}, + Year = {2011}} + +@article{ZhaYan-JCP-98, + Author = {Y. Zhang and W. 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Savin and J. G. \'Angy\'an}, + Note = {unpublished}} + +@article{ZieCio-PA-05, + Author = {P. Ziesche and J. Cioslowski}, + Journal = {Physica A}, + Year = {to appear}} + +@article{Zie-JPC-80, + Author = {P. Ziesche}, + Journal = {J. Phys. C}, + Pages = {3625}, + Volume = {13}, + Year = {1980}} + +@article{ZieSetKryAutWan-JCP-09, + Author = {T. Ziegler and M. Seth and M. Krykunov and J. Autschbach and F. Wang}, + Journal = {J. Chem. Phys.}, + Pages = {154102}, + Volume = {130}, + Year = {2009}} + +@article{ZimParKou-JCP-04, + Author = {U. Zimmerli and M. Parrinello and P. Koumoutsakos}, + Journal = {J. Chem. Phys.}, + Pages = {2693}, + Volume = {120}, + Year = {2004}} + +@article{ZimTouZhaMusUmr-JCP-09, + Author = {P. M. Zimmerman and J. Toulouse and Z. Zhang and C. B. Musgrave and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {124103}, + Title = {Excited states of methylene from quantum Monte Carlo}, + Volume = {131}, + Year = {2009}} + +@article{ZucPodMosJezSza-JCP-08, + Author = {P. S. Zuchowski and R. Podeszwa and R. Moszynski and B. Jeziorski and K. Szalewicz}, + Journal = {J. Chem. Phys.}, + Pages = {084101}, + Title = {{Symmetry-adapted perturbation theory utilizing density functional description of monomers for high-spin open-shell complexes}}, + Volume = {129}, + Year = {2008}} + +@article{FerGinTou-JCP-18, + Author = {Fert{\'e},Anthony and Giner,Emmanuel and Toulouse,Julien}, + Date-Modified = {2019-04-07 14:03:44 +0200}, + Doi = {10.1063/1.5082638}, + Journal = {J. Chem. Phys.}, + Number = {8}, + Pages = {084103}, + Title = {Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density}, + Volume = {150}, + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}} + +@article{GoriSav-PRA-06, + Author = {Gori-Giorgi, Paola and Savin, Andreas}, + Doi = {10.1103/PhysRevA.73.032506}, + Issue = {3}, + Journal = {Phys. Rev. A}, + Month = {Mar}, + Numpages = {9}, + Pages = {032506}, + Publisher = {American Physical Society}, + Title = {Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.73.032506}} + +@article{PazMorGorBac-PRB-06, + Author = {Paziani, Simone and Moroni, Saverio and Gori-Giorgi, Paola and Bachelet, Giovanni B.}, + Date-Modified = {2019-04-07 14:56:44 +0200}, + Doi = {10.1103/PhysRevB.73.155111}, + Issue = {15}, + Journal = {Phys. Rev. B}, + Month = {Apr}, + Numpages = {9}, + Pages = {155111}, + Publisher = {American Physical Society}, + Title = {Local-spin-density functional for multideterminant density functional theory}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.73.155111}} + +@article{GinTewGarAla-JCTC-18, + Author = {Giner, Emmanuel and Tew, David P. and Garniron, Yann and Alavi, Ali}, + Doi = {10.1021/acs.jctc.8b00591}, + Eprint = {https://doi.org/10.1021/acs.jctc.8b00591}, + Journal = {Journal of Chemical Theory and Computation}, + Note = {PMID: 30347156}, + Number = {12}, + Pages = {6240-6252}, + Title = {Interplay between Electronic Correlation and Metal--Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes}, + Url = {https://doi.org/10.1021/acs.jctc.8b00591}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}} + +@article{LooBogSceCafJAc-JCTC-19, + Author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis}, + Date-Modified = {2019-04-07 14:02:34 +0200}, + Doi = {10.1021/acs.jctc.8b01205}, + Journal = {J. Chem. Theory Comput.}, + Number = {3}, + Pages = {1939-1956}, + Title = {Reference Energies for Double Excitations}, + Volume = {15}, + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01205}} + +@article{LooSceBloGarCafJac-JCTC-18, + Author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Blondel, Aymeric and Garniron, Yann and Caffarel, Michel and Jacquemin, Denis}, + Date-Modified = {2019-04-07 14:03:07 +0200}, + Doi = {10.1021/acs.jctc.8b00406}, + Journal = {J. Chem. Theory Comput.}, + Number = {8}, + Pages = {4360-4379}, + Title = {A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} + +@article{HolUmrSha-JCP-17, + Author = {Holmes,Adam A. and Umrigar,C. J. and Sharma,Sandeep}, + Doi = {10.1063/1.4998614}, + Eprint = {https://doi.org/10.1063/1.4998614}, + Journal = {J. Chem. Phys.}, + Number = {16}, + Pages = {164111}, + Title = {Excited states using semistochastic heat-bath configuration interaction}, + Url = {https://doi.org/10.1063/1.4998614}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4998614}} + +@article{stochastic_pt_yan, + Author = {Yann Garniron and Anthony Scemama and Pierre-Fran{\c c}ois Loos and Michel Caffarel}, + Doi = {10.1063/1.4992127}, + Journal = {J. Chem. Phys.}, + Number = {3}, + Pages = {034101}, + Title = {Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory}, + Url = {https://doi.org/10.1063/1.4992127}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4992127}} + +@article{GorSav-PRA-06, + Author = {Gori-Giorgi, Paola and Savin, Andreas}, + Doi = {10.1103/PhysRevA.73.032506}, + Issue = {3}, + Journal = {Phys. Rev. A}, + Month = {Mar}, + Numpages = {9}, + Pages = {032506}, + Publisher = {American Physical Society}, + Title = {Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.73.032506}} + +@article{HalHelJorKloKocOlsWil-CPL-98, + Abstract = {Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.}, + Author = {Asger Halkier and Trygve Helgaker and Poul J{\o}rgensen and Wim Klopper and Henrik Koch and Jeppe Olsen and Angela K. Wilson}, + Date-Modified = {2019-04-07 14:59:22 +0200}, + Doi = {https://doi.org/10.1016/S0009-2614(98)00111-0}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Number = {3}, + Pages = {243 - 252}, + Title = {Basis-set convergence in correlated calculations on Ne, N2, and H2O}, + Url = {http://www.sciencedirect.com/science/article/pii/S0009261498001110}, + Volume = {286}, + Year = {1998}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261498001110}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0009-2614(98)00111-0}} + +@article{DasHer-JCC-17, + Author = {Dasgupta, Saswata and Herbert, John M.}, + Doi = {10.1002/jcc.24761}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.24761}, + Journal = {J. Comput. Chem.}, + Number = {12}, + Pages = {869-882}, + Title = {Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3}, + Volume = {38}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1002/jcc.24761}} + +@article{Tenno-CPL-04, +title = "Initiation of explicitly correlated Slater-type geminal theory", +journal = "Chem. Phys. Lett.", +volume = "398", +number = "1", +pages = "56 - 61", +year = "2004", +issn = "0009-2614", +doi = "https://doi.org/10.1016/j.cplett.2004.09.041", +url = "http://www.sciencedirect.com/science/article/pii/S000926140401379X", +author = "Seiichiro Ten-no", +abstract = "We employ the Slater-type function as a geminal basis function to incorporate the inter-electron distance in explicitly correlated theory. It is shown that the use of the Slater-type geminals confers numerical and computational advantages over the previous explicitly correlated methods. The performance of the resulting method is examined in some benchmark calculations at the second order Møller–Plesset perturbation theory. The results reveal that the Slater-type function is promising compared to the ordinary Gaussian-type geminals and linear r12 function." +} diff --git a/JPCL/G2-srDFT.tex b/JPCL/G2-srDFT.tex new file mode 100644 index 0000000..5ec6b9f --- /dev/null +++ b/JPCL/G2-srDFT.tex @@ -0,0 +1,525 @@ +\documentclass[aip,jcp,preprint,noshowkeys]{revtex4-1} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,xspace,wrapfig} +\usepackage{mathpazo,libertine} + +\usepackage{natbib} +\bibliographystyle{achemso} +\AtBeginDocument{\nocite{achemso-control}} + +\newcommand{\alert}[1]{\textcolor{red}{#1}} +\definecolor{darkgreen}{HTML}{009900} +\usepackage[normalem]{ulem} +\newcommand{\titou}[1]{\textcolor{red}{#1}} +\newcommand{\juju}[1]{\textcolor{purple}{#1}} +\newcommand{\manu}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\toto}[1]{\textcolor{brown}{#1}} +\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} +\newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}} +\newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}} +\newcommand{\trashAS}[1]{\textcolor{brown}{\sout{#1}}} +\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}} +\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}} +\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} +\newcommand{\AS}[1]{\toto{(\underline{\bf TOTO}: #1)}} + +\usepackage{hyperref} +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, + citecolor=blue +} +\newcommand{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\SI}{\textcolor{blue}{supporting information}} +\newcommand{\QP}{\textsc{quantum package}} + +% second quantized operators +\newcommand{\ai}[1]{\hat{a}_{#1}} +\newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\InAA}[1]{#1 \AA} +\newcommand{\kcal}{kcal/mol} + +% methods +\newcommand{\D}{\text{D}} +\newcommand{\T}{\text{T}} +\newcommand{\Q}{\text{Q}} +\newcommand{\X}{\text{X}} +\newcommand{\UEG}{\text{UEG}} +\newcommand{\HF}{\text{HF}} +\newcommand{\ROHF}{\text{ROHF}} +\newcommand{\LDA}{\text{LDA}} +\newcommand{\PBE}{\text{PBE}} +\newcommand{\FCI}{\text{FCI}} +\newcommand{\CBS}{\text{CBS}} +\newcommand{\exFCI}{\text{exFCI}} +\newcommand{\CCSDT}{\text{CCSD(T)}} +\newcommand{\lr}{\text{lr}} +\newcommand{\sr}{\text{sr}} + +\newcommand{\Ne}{N} +\newcommand{\NeUp}{\Ne^{\uparrow}} +\newcommand{\NeDw}{\Ne^{\downarrow}} +\newcommand{\Nb}{N_{\Bas}} +\newcommand{\Ng}{N_\text{grid}} +\newcommand{\nocca}{n_{\text{occ}^{\alpha}}} +\newcommand{\noccb}{n_{\text{occ}^{\beta}}} + +\newcommand{\n}[2]{n_{#1}^{#2}} +\newcommand{\Ec}{E_\text{c}} +\newcommand{\E}[2]{E_{#1}^{#2}} +\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}} +\newcommand{\bEc}[1]{\Bar{E}_\text{c,md}^{#1}} +\newcommand{\e}[2]{\varepsilon_{#1}^{#2}} +\newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}} +\newcommand{\bec}[1]{\Bar{e}^{#1}} +\newcommand{\wf}[2]{\Psi_{#1}^{#2}} +\newcommand{\W}[2]{W_{#1}^{#2}} +\newcommand{\w}[2]{w_{#1}^{#2}} +\newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}} +\newcommand{\rsmu}[2]{\mu_{#1}^{#2}} +\newcommand{\V}[2]{V_{#1}^{#2}} +\newcommand{\SO}[2]{\phi_{#1}(\br{#2})} + +\newcommand{\modY}{Y} +\newcommand{\modZ}{Z} + +% basis sets +\newcommand{\Bas}{\mathcal{B}} +\newcommand{\BasFC}{\mathcal{A}} +\newcommand{\FC}{\text{FC}} +\newcommand{\occ}{\text{occ}} +\newcommand{\virt}{\text{virt}} +\newcommand{\val}{\text{val}} +\newcommand{\Cor}{\mathcal{C}} + +% operators +\newcommand{\hT}{\Hat{T}} +\newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}} +\newcommand{\updw}{\uparrow\downarrow} +\newcommand{\f}[2]{f_{#1}^{#2}} +\newcommand{\Gam}[2]{\Gamma_{#1}^{#2}} + +% coordinates +\newcommand{\br}[1]{\mathbf{r}_{#1}} +\newcommand{\dbr}[1]{d\br{#1}} + +\newcommand{\ra}{\rightarrow} + +% frozen core +\newcommand{\WFC}[2]{\widetilde{W}_{#1}^{#2}} +\newcommand{\fFC}[2]{\widetilde{f}_{#1}^{#2}} +\newcommand{\rsmuFC}[2]{\widetilde{\mu}_{#1}^{#2}} +\newcommand{\nFC}[2]{\widetilde{n}_{#1}^{#2}} + + +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Sorbonne Universit\'e, CNRS, Paris, France} +\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France} + + +\begin{document} + +\title{A Density-Based Basis-Set Correction For Wave Function Theory} + +\author{Pierre-Fran\c{c}ois Loos} +\email{loos@irsamc.ups-tlse.fr} +\affiliation{\LCPQ} +\author{Bath\'elemy Pradines} +\affiliation{\LCT} +\affiliation{\ISCD} +\author{Anthony Scemama} +\affiliation{\LCPQ} +\author{Julien Toulouse} +\email{toulouse@lct.jussieu.fr} +\affiliation{\LCT} +\author{Emmanuel Giner} +\email{emmanuel.giner@lct.jussieu.fr} +\affiliation{\LCT} + +\begin{abstract} +\begin{wrapfigure}[7]{o}[-1.2cm]{0.4\linewidth} + \centering + \includegraphics[width=\linewidth]{TOC} +\end{wrapfigure} +We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. +The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. +Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ that automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error. +As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets. +\end{abstract} + +\maketitle + +%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Introduction} +%%%%%%%%%%%%%%%%%%%%%%%% +Contemporary quantum chemistry has developed in two directions --- wave function theory (WFT) \cite{Pop-RMP-99} and density-functional theory (DFT). \cite{Koh-RMP-99} +Although both spring from the same Schr\"odinger equation, each of these philosophies has its own \textit{pros} and \textit{cons}. + +WFT is attractive as it exists a well-defined path for systematic improvement as well as powerful tools, such as perturbation theory, to guide the development of new WFT \textit{ans\"atze}. +The coupled cluster (CC) family of methods is a typical example of the WFT philosophy and is well regarded as the gold standard of quantum chemistry for weakly correlated systems. +By increasing the excitation degree of the CC expansion, one can systematically converge, for a given basis set, to the exact, full configuration interaction (FCI) limit, although the computational cost associated with such improvement is usually high. +One of the most fundamental drawbacks of conventional WFT methods is the slow convergence of energies and properties with respect to the size of the one-electron basis set. +This undesirable feature was put into light by Kutzelnigg more than thirty years ago. \cite{Kut-TCA-85} +To palliate this, following Hylleraas' footsteps, \cite{Hyl-ZP-29} Kutzelnigg proposed to introduce explicitly the interelectronic distance $r_{12} = \abs{\br{1} - \br{2}}$ to properly describe the electronic wave function around the coalescence of two electrons. \cite{Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94} +The resulting F12 methods yield a prominent improvement of the energy convergence, and achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12} +For example, at the CCSD(T) level, one can obtain quintuple-$\zeta$ quality correlation energies with a triple-$\zeta$ basis, \cite{TewKloNeiHat-PCCP-07} although computational overheads are introduced by the large auxiliary basis used to resolve three- and four-electron integrals. \cite{BarLoo-JCP-17} +To reduce further the computational cost and/or ease the transferability of the F12 correction, approximated and/or universal schemes have recently emerged. \cite{TorVal-JCP-09, KonVal-JCP-10, KonVal-JCP-11, BooCleAlaTew-JCP-2012, IrmHumGru-arXiv-2019, IrmGru-arXiv-2019} + +Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. \cite{KohSha-PR-65} +The attractiveness of DFT originates from its very favorable accuracy/cost ratio as it often provides reasonably accurate energies and properties at a relatively low computational cost. +Thanks to this, KS-DFT \cite{HohKoh-PR-64, KohSha-PR-65} has become the workhorse of electronic structure calculations for atoms, molecules and solids. \cite{ParYan-BOOK-89} +Although there is no clear way on how to systematically improve density-functional approximations, \cite{Bec-JCP-14} climbing Perdew's ladder of DFT is potentially the most satisfactory way forward. \cite{PerSch-AIPCP-01, PerRuzTaoStaScuCso-JCP-05} +In the context of the present work, one of the interesting feature of density-based methods is their much faster convergence with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15} + +Progress toward unifying WFT and DFT are on-going. +In particular, range-separated DFT (RS-DFT) (see Ref.~\onlinecite{TouColSav-PRA-04} and references therein) rigorously combines these two approaches via a decomposition of the electron-electron (e-e) interaction into a non-divergent long-range part and a (complementary) short-range part treated with WFT and DFT, respectively. +As the WFT method is relieved from describing the short-range part of the correlation hole around the e-e coalescence points, the convergence with respect to the one-electron basis set is greatly improved. \cite{FraMusLupTou-JCP-15} +Therefore, a number of approximate RS-DFT schemes have been developed within single-reference \cite{AngGerSavTou-PRA-05, GolWerSto-PCCP-05, TouGerJanSavAng-PRL-09,JanHenScu-JCP-09, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15} or multi-reference \cite{LeiStoWerSav-CPL-97, FroTouJen-JCP-07, FroCimJen-PRA-10, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-18} WFT approaches. +Very recently, a major step forward has been taken by some of the present authors thanks to the development of a density-based basis-set correction for WFT methods. \cite{GinPraFerAssSavTou-JCP-18} +The present work proposes an extension of this new methodological development alongside the first numerical tests on molecular systems. + +%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Theory} +%%%%%%%%%%%%%%%%%%%%%%%% +The present basis-set correction relies on the RS-DFT formalism to capture the missing part of the short-range correlation effects, a consequence of the incompleteness of the one-electron basis set. +Here, we only provide the main working equations. +We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} for a more formal derivation. + +Let us assume we have both the energy $\E{\modY}{\Bas}$ and density $\n{\modZ}{\Bas}$ of a $\Ne$-electron system described by two methods $\modY$ and $\modZ$ (potentially identical) in an incomplete basis set $\Bas$. +According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that $\E{\modY}{\Bas}$ and $\n{\modZ}{\Bas}$ are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as +\begin{equation} + \label{eq:e0basis} + \E{}{} + \approx \E{\modY}{\Bas} + + \bE{}{\Bas}[\n{\modZ}{\Bas}], +\end{equation} +where +\begin{equation} + \label{eq:E_funcbasis} + \bE{}{\Bas}[\n{}{}] + = \min_{\wf{}{} \to \n{}{}} \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}} + - \min_{\wf{}{\Bas} \to \n{}{}} \mel*{\wf{}{\Bas}}{\hT + \hWee{}}{\wf{}{\Bas}} +\end{equation} +is the basis-dependent complementary density functional, $\hT$ is the kinetic operator and $\hWee{} = \sum_{il000;ztnFOQoq8N{hw+H+1jPXzsO6<^2k&Qs3PCb?LGTH{ywI*2>w~W zeoXzKJ^c8)y%qY#)cwbj{=@XouaDM0ra* zWSlOv`xv)&lKYo_MrbQ+E%l=_<|$24qUzBFdrmhk#iyeB!y8SA@V7CIW3J;zq2C2G z^MNPP+zAuLoOsNgE0N4S5rz~NJ3>GI!W5fYh^w-TTvO=p3X%3QRhlQR=WdzUG4${>FtaQ1xp8R1VzHENa{3zuGKS3OjTeJ!y2d^7kMneyVW zOMNmh0%I6(^S73=uC1BIJw67ETkQ13m#sYKN6-_c2BeNYb8HmZ^C?O&m8vglj1EWd8ws z#+{7(WQ6)8chZhpOGaBlLdhE&T})&-M|)BWb$r^lZuKdIWR$A+I@^3}k|J6$iW}F1 zTtyJ14Yp7xLfa?F=r2QN8DV;3HaiNmO@X|6@EUBmlP*lUN$~_iH>{6#@Qy!$)VgFh93rUHD0}Im+o=8 z@@r;H7wy7#kjMB#8uR~}hWR*^<-Ay<#B(i?yAQr6JMDF*#5c%jwnnzL1H+lmK7ukU zn$Mv70igByJN$j9)qrf8MnCh3d%=kzMp2gHhuw%F&z=AFu(*_`VzpuMU(>o3`dCZ1 zZo&$7HwpUecne8~G8-+uBk)&2cY8hjTFrO>PihS&XcYZ3^tcp1>#GxQwQI<*D=GBT 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z$lt#SIF4@apStBZ+5GKp|E~4_;{?WW-t}Ky`@g#Oe|7Eu>e~O+wg0PY|5w-kude<7 z8eKc&+rSJM%^cUYL%wMgj-ekYdSd(U=b?W_KmY&g+K=4y9RPjTwL_23?Ee@7|1ALe ze^l2FAhMq$N}o{%ADtcwq(v_fDPRrQkJf_x}fU`0osC2gH8)Y@BexnIL0pyqzBq^)Lx*j zN9{tN2juZB|L<)_=M9vFZvRofz$fa?DB#|($TfFjJ9zuJ)e2!7zQM*lI}{bfTS`H;YM`?E~|iT>vP z$p-A813-SVAq0@T0EhFFO#lM>Ek6Mm90ojGe@chsg8<<~zu5R;0>CZsQ#u3^AQXPF z3Gg9!f2}iML-QLyohtwVI^}m8{MRxBAW%S&_UpL_81Vi4bAB*hAP(v`8~nF2U{LsP z^@BkLe)XRK4Eb9-kiaGMn_qaLzxfo&i{SmW&VUX5O!=wKNM0oJ*ZLv(pvd3KfT9(T zznlw2pw+BD=f@A+m%rO!zxp1@4+SE{emxg>HOB8Y{@==gLHUoJ>x?o6;=oWxuaD5M z@-#zV<7mc7-QM1r`RES%`lvyNY%w2whaS;cPR_0$ for $\ell=0$ and $f\lr_\ell <0$ for $\ell \geq 1$.}} + +@article{FreHuxMor-PRA-84, + Author = {{D. E. Freund, B. D. Huxtable, and J. D. Morgan III}}, + Journal = {Phys. Rev. A}, + Pages = {980}, + Volume = {29}, + Year = {1984}} + +@article{FreLev-JCP-82, + Author = {Karl F. Freed and Mel Levy}, + Journal = {The Journal of Chemical Physics}, + Keywords = {ALGORITHMS; ELECTRON DENSITY; FUNCTIONALS; SERIES EXPANSION; WAVE FUNCTIONS; GROUND STATES}, + Number = {1}, + Pages = {396-398}, + Publisher = {AIP}, + Title = {Direct first principles algorithm for the universal electron density functional}, + Url = {http://link.aip.org/link/?JCP/77/396/1}, + Volume = {77}, + Year = {1982}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/77/396/1}} + +@article{Fre-PRB-77, + Author = {D. L. Freeman}, + Journal = {Phys. Rev. B}, + Pages = {5512}, + Volume = {{15}}, + Year = {1977}} + +@article{FroCimJen-PRA-10, + Author = {Fromager, Emmanuel and Cimiraglia, Renzo and Jensen, Hans J\o{}rgen Aa.}, + Doi = {10.1103/PhysRevA.81.024502}, + Issue = {2}, + Journal = {Phys. Rev. A}, + Month = {Feb}, + Numpages = {4}, + Pages = {024502}, + Publisher = {American Physical Society}, + Title = {Merging multireference perturbation and density-functional theories by means of range separation: Potential curves for ${\mathrm{Be}}_{2}$, ${\mathrm{Mg}}_{2}$, and ${\mathrm{Ca}}_{2}$}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.81.024502}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.81.024502}} + +@article{Fro-JCP-11, + Author = {E. Fromager}, + Journal = {J. Chem. Phys.}, + Pages = {244106}, + Volume = {135}, + Year = {2011}} + +@article{FroJen-JCP-11, + Author = {E. Fromager and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {034116}, + Volume = {135}, + Year = {2011}} + +@article{FroJen-PRA-08, + Author = {E. Fromager and H. J. Aa. Jensen}, + Journal = {Phys. Rev. A}, + Pages = {022504}, + Volume = {78}, + Year = {2008}} + +@misc{FroKneJen-ARX-12, + Author = {Emmanuel Fromager and Stefan Knecht and H. J. Aa. Jensen}, + Note = {\url{http://fr.arxiv.org/abs/1211.4829v1}}} + +@article{FroKneJen-JCP-13, + Author = {E. Fromager and S. Knecht and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {084101}, + Title = {{Multi-configuration time-dependent density-functional theory based on range separation}}, + Volume = {138}, + Year = {2013}} + +@article{FroReaWahWahJen-JCP-09, + Author = {E. Fromager and F. R\'eal and P. W{\aa}hlin and U. Wahlgren and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {054107}, + Volume = {131}, + Year = {2009}} + +@article{FroTouJen-JCP-07, + Author = {E. Fromager and J. Toulouse and H. J. Aa. Jensen}, + Journal = {J. Chem. Phys.}, + Pages = {074111}, + Title = {On the universality of the long-/short-range separation in multiconfigurational density-functional theory}, + Volume = {126}, + Year = {2007}} + +@article{FucGon-PRB-02, + Author = {M. Fuchs and X. Gonze}, + Journal = {Phys. Rev. B}, + Pages = {235109}, + Volume = {65}, + Year = {2002}} + +@article{FucNiqGonBur-JCP-05, + Abstract = {We show that density functional theory within the RPA (random phase + approximation for the exchange-correlation energy) provides a correct + description of bond dissociation in H2 in a spin-restricted Kohn-<96>Sham + formalism, i.e., without artificial symmetry breaking. We present + accurate adiabatic connection curves both at equilibrium and beyond + the Coulson-Fisher point. The strong curvature at large bond length + implies important static (left-<96>right) correlation, justifying modern + hybrid functional constructions but also demonstrating their limitations. + Although exact at infinite separation and accurate near the equilibrium + bond length, the RPA dissociation curve displays unphysical repulsion + at larger but finite bond lengths. Going beyond the RPA by including + the exact exchange kernel (RPA + X), we find a similar repulsion. + We argue that this deficiency is due to the absence of double excitations + in adiabatic linear response theory. Further analyzing the H2 dissociation + limit we show that the RPA + X is not size consistent, in contrast + to the RPA.}, + Author = {Fuchs, M. and Niquet, Y. M. and Gonze, X. and Burke, K.}, + Doi = {10.1063/1.1858371}, + Journal = {J. Chem. Phys.}, + Pages = {094116}, + Title = {Describing static correlation in bond dissociation by Kohn-Sham density functional theory}, + Volume = {122}, + Year = {2005}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1858371}} + +@article{FukIwaSaw-PR-64, + Author = {N. Fukuda and F. Iwamoto and K. Sawada}, + Journal = {Phys. Rev.}, + Pages = {A932}, + Volume = {135}, + Year = {1964}} + +@book{Ful-BOOK-93, + Address = {Berlin}, + Author = {P. Fulde}, + Publisher = {Springer}, + Title = {Electron Correlations in Molecules and Solids}, + Year = {1993}} + +@article{Fur-JCP-01, + Author = {F. Furche}, + Journal = {J. Chem. Phys.}, + Pages = {5982}, + Volume = {114}, + Year = {2001}} + +@article{Fur-JCP-08, + Author = {F. Furche}, + Journal = {J. Chem. Phys.}, + Pages = {114105}, + Volume = {129}, + Year = {2008}} + +@article{FurPer-JCP-06, + Author = {F. Furche and J. P. Perdew}, + Journal = {J. Chem. Phys.}, + Pages = {044103}, + Volume = {124}, + Year = {2006}} + +@article{Fur-PRA-04, + Author = {Filipp Furche}, + Eid = {022514}, + Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, + Keywords = {density functional theory; HF calculations; boson systems; electron pairs; ground states; Schrodinger equation}, + Number = {2}, + Numpages = {10}, + Pages = {022514}, + Publisher = {APS}, + Title = {Towards a practical pair density-functional theory for many-electron systems}, + Url = {http://link.aps.org/abstract/PRA/v70/e022514}, + Volume = {70}, + Year = {2004}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v70/e022514}} + +@article{Fur-PRB-01, + Author = {F. Furche}, + Journal = {Phys. Rev. B}, + Pages = {195120}, + Volume = {64}, + Year = {2001}} + +@incollection{FurRap-INC-05, + Address = {Amsterdam}, + Author = {F. Furche and D. Rappoport}, + Booktitle = {Computational Photochemistry}, + Editor = {M. 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Davidson}, + Journal = {J. Chem. Phys.}, + Pages = {084113}, + Volume = {127}, + Year = {2007}} + +@article{JacDucBla-JCTC-15, + Author = {D. Jacquemin and I. Duchemin and X. Blase}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3290}, + Volume = {11}, + Year = {2015}} + +@article{JacPerCioAda-JCC-08, + Author = {D. Jacquemin and E. A. Perp\`ete and I. Ciofini and C. Adamo}, + Journal = {J. Comput. Chem.}, + Pages = {921}, + Volume = {29}, + Year = {2008}} + +@article{JacPerScaFriKobAda-JCP-07, + Author = {D. Jacquemin and E. A. Perp\`ete and G. Scalmani and M. J. Frisch and R. Kobayashi and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {144105}, + Volume = {126}, + Year = {2007}} + +@article{JacWatPerAda-JCTC-09, + Author = {D. Jacquemin and V. Wathelet and E. A. Perp\'ete and C. Adamo}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2420}, + Volume = {5}, + Year = {2009}} + +@article{JamCasSal-JCP-96, + Author = {C. Jamorski and M. E. Casida and D. R. Salahub}, + Journal = {J. Chem. Phys.}, + Pages = {5134}, + Volume = {104}, + Year = {1996}} + +@article{JanHenScu-JCP-09b, + Author = {B. G. Janesko and T. M. Henderson and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {034110}, + Volume = {131}, + Year = {2009}} + +@article{JanHenScu-JCP-09, + Author = {B. G. Janesko and T. M. Henderson and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {081105}, + Title = {Long-range-corrected hybrids including random phase approximation correlation}, + Volume = {130}, + Year = {2009}} + +@article{JanLiuAng-JCP-10, + Author = {G. Jansen and R.-F. Liu and J. G. \'Angyan}, + Journal = {J. Chem. Phys.}, + Pages = {154106}, + Volume = {133}, + Year = {2010}} + +@article{Jan-NC-62, + Author = {B. Jancovici}, + Journal = {Nuovo Cimento}, + Pages = {428}, + Volume = {XXV}, + Year = {1962}} + +@article{Jan-PRB-78, + Author = {J. F. Janak}, + Journal = {Phys. Rev. B}, + Pages = {7165}, + Volume = {18}, + Year = {1978}} + +@article{JanScu-JCP-09, + Author = {B. G. Janesko and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {154106}, + Volume = {131}, + Year = {2009}} + +@article{JanScu-PCCP-09, + Author = {B. G. Janesko and G. E. Scuseria}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {9677}, + Volume = {11}, + Year = {2009}} + +@article{JarDav-PRA-98, + Author = {A. A. Jarzecki and E. R. Davidson}, + Journal = {Phys. Rev. A}, + Pages = {1902}, + Title = {Ground-state energies of isoelectronic atomic series from density-functional theory: Exploring the accuracy of density functionals}, + Volume = {{58}}, + Year = {1998}} + +@article{JenAgr-CP-86, + Author = {H. J. Aa. Jensen and H. Agren}, + Journal = {Chem. Phys.}, + Pages = {229}, + Volume = {104}, + Year = {1986}} + +@article{JenAgr-CPL-84, + Author = {H. J. Aa. Jensen and H. Agren}, + Journal = {Chem. Phys. Lett.}, + Pages = {140}, + Volume = {110}, + Year = {1984}} + +@article{JenBun-JCP-88, + Author = {P. Jensen and P. R. Bunker}, + Journal = {J. Chem. Phys.}, + Pages = {1327}, + Volume = {89}, + Year = {1988}} + +@article{JenDyaSauFae-JCP-96, + Author = {H. J. Aa. Jensen and K. G. Dyall and T. Saue and K. F{\ae}gri}, + Journal = {J. Chem. Phys.}, + Pages = {4083}, + Volume = {104}, + Year = {1996}} + +@incollection{Jen-INC-94, + Address = {New York}, + Author = {H. J. Aa. Jensen}, + Booktitle = {Relativistic and Electron Correlation Effects in Molecules and Solids}, + Editor = {G. L. Malli}, + Pages = {179}, + Publisher = {Plenum}, + Year = {1994}} + +@article{JenJorAgr-JCP-87, + Author = {H. J. Aa. Jensen and P. Jorgensen and H. Agren}, + Journal = {J. Chem. Phys.}, + Pages = {451}, + Volume = {{87}}, + Year = {1987}} + +@article{JenJorAgrOls-JCP-88, + Author = {H. J. Aa. Jensen and P. J{\o}rgensen and H. Agren and J. Olsen}, + Journal = {J. Chem. Phys.}, + Pages = {3834}, + Volume = {{88}}, + Year = {1988}} + +@article{JenJor-JCP-84, + Author = {H. J. Aa. Jensen and P. J{\o}rgensen}, + Journal = {J. Chem. Phys.}, + Pages = {1204}, + Volume = {{80}}, + Year = {1984}} + +@article{JiaEng-JCP-07, + Author = {Hong Jiang and Eberhard Engel}, + Doi = {10.1063/1.2795707}, + Journal = {J. Chem. Phys.}, + Keywords = {density functional theory; eigenvalues and eigenfunctions; ground states; ionisation potential; orbital calculations; perturbation theory; potential energy functions}, + Pages = {184108}, + Title = {Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms}, + Volume = {127}, + Year = {2007}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.2795707}} + +@article{JieNorSer-JCP-05, + Author = {A. Jiemchooroj and P. Norman and Bo E. Sernelius}, + Journal = {J. Chem. Phys.}, + Pages = {124312}, + Volume = {123}, + Year = {2005}} + +@article{JieNorSer-JCP-06, + Author = {A. Jiemchooroj and P. Norman and Bo E. Sernelius}, + Journal = {J. Chem. Phys.}, + Pages = {124306}, + Volume = {125}, + Year = {2006}} + +@article{JohBec-JCP-05b, + Author = {E. R. Johnson and A. D. Becke}, + Journal = {J. Chem. Phys.}, + Pages = {024101}, + Volume = {123}, + Year = {2005}} + +@article{JohMorCohYan-JCP-08, + Author = {E. R. Johnson and P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {204112}, + Volume = {129}, + Year = {2008}} + +@article{JonGun-RMP-89, + Author = {R. O. Jones and O. Gunnarsson}, + Journal = {Rev. Mod. Phys.}, + Pages = {689}, + Volume = {{61}}, + Year = {1989}} + +@article{jones:325, + Author = {R. O. Jones}, + Journal = {The Journal of Chemical Physics}, + Keywords = {OZONE; SULFUR DIOXIDE; GROUND STATES; EXCITED STATES; ELECTRONIC STRUCTURE; CONFIGURATION INTERACTION; DISSOCIATION ENERGY; ATMOSPHERIC CHEMISTRY}, + Number = {1}, + Pages = {325-332}, + Publisher = {AIP}, + Title = {Energy surfaces of low-lying states of O[sub 3] and SO[sub 2]}, + Url = {http://link.aip.org/link/?JCP/82/325/1}, + Volume = {82}, + Year = {1985}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/82/325/1}} + +@article{JorSim-JCP-83, + Author = {P. J{\o}rgensen and J. Simons}, + Journal = {J. Chem. Phys.}, + Pages = {334}, + Volume = {79}, + Year = {1983}} + +@article{JouSri-JCP-98, + Author = {Daniel P. Joubert and G. P. Strivastava}, + Journal = {J. Chem. Phys.}, + Pages = {5212}, + Volume = {109}, + Year = {1998}} + +@article{JurSpoCerHob-PCCP-06, + Author = {P. Jure{\v c}ka and J. {\v S}poner and J. {\v C}ern{\'y} and P. Hobza}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {1985}, + Volume = {8}, + Year = {2006}} + +@article{KadVoo-JCP-10, + Author = {{B. Kaduk and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {061102}, + Volume = {133}, + Year = {2010}} + +@article{KalTou-JCP-18, + Author = {C. Kalai and J. Toulouse}, + Doi = {10.1063/1.5025561}, + Journal = {J. Chem. Phys.}, + Pages = {164105}, + Title = {A general range-separated double-hybrid density-functional theory}, + Volume = {148}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5025561}} + +@misc{KalTou-JJJ-XX-note1, + Note = {The geometries are available in the Minnesota Database at http://comp.chem.umn.edu/db/.}} + +@misc{KalTou-JJJ-XX-note2, + Note = {The term ``range-separated double hybrid (RSDH)'' has already been used in Ref.~\onlinecite{SanCivUsvTouShaMas-JCP-15} to designate the RSH+MP2 method and in Refs.~\onlinecite{CorStoJenFro-PRA-13,CorFro-IJQC-14} to generically designate several kinds of range-separated MP2/DFT hybrids. In the present work, we use RSDH to designate the specific scheme corresponding to Eq.~(\ref{EmulRSDH}).}} + +@misc{KalTou-JJJ-XX-note3, + Note = {We use the AE49 set of Fast {\it et al.}~\cite{FasCorSanTru-JPCA-99} to facilitate comparisons with previous related works~\cite{ShaTouSav-JCP-11,SouShaTou-JCP-14,MusReiAngTou-JCP-15} where this set was used. We do not expect any special difficulties with the six molecules that have been dropped from the G2-1 set.}} + +@article{KamSekTsuHir-JCP-05, + Author = {M. Kamiya and H. Sekino and T. Tsuneda and K. Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {234111}, + Volume = {122}, + Year = {2005}} + +@article{KamTsuHir-JCP-02, + Author = {M. Kamiya and T. Tsuneda and K. Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {6010}, + Volume = {{117}}, + Year = {2002}} + +@article{KanBec-JCTC-10, + Author = {F. O. Kannemann and Axel D. Becke}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1081}, + Title = {{van der Waals interactions in density-functional theory: Intermolecular complexes}}, + Volume = {6}, + Year = {2010}} + +@article{Kar-JCP-03, + Author = {V. V. Karasiev}, + Journal = {J. Chem. Phys.}, + Pages = {8576}, + Volume = {118}, + Year = {2003}} + +@article{KarKroKum-JCP-13, + Author = {A. Karolewski and L. Kronik and S. K\"ummel}, + Journal = {J. Chem. Phys.}, + Pages = {204115}, + Volume = {138}, + Year = {2013}} + +@article{KarMar-JCP-11, + Author = {Amit Karton and J. M. L. Martin}, + Journal = {J. Chem. Phys.}, + Pages = {144119}, + Volume = {135}, + Year = {2011}} + +@article{KarTarLamSchMar-JPCA-08, + Author = {Amir Karton and Alex Tarnopolsky and Jean-Francois Lam\`ere and George C. Schatz and Jan M. L. Martin}, + Journal = {J. Phys. Chem. A}, + Pages = {12868}, + Volume = {112}, + Year = {2008}} + +@article{Kat-CPAM-57, + Author = {T. Kato}, + Journal = {Comm. Pure Appl. 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Phys.}, + Pages = {114108}, + Volume = {128}, + Year = {2008}} + +@incollection{KlaGil-AQC-12, + Author = {Shachar Klaiman and Ido Gilary}, + Booktitle = {Advances in Quantum Chemistry Vol. 63}, + Editor = {Cleanthes A. Nicolaides and Erkki Br\"andas and John R. Sabin}, + Pages = {1}, + Publisher = {Academic Press}, + Title = {On Resonance: A First Glance into the Behavior of Unstable States}, + Year = {2012}} + +@article{Kla-PRB-03, + Author = {T. Klamroth}, + Journal = {Phys. Rev. B}, + Pages = {245421}, + Volume = {68}, + Year = {2003}} + +@article{KlePic-JCP-76, + Author = {D. J. Klein and H. M. Pickett}, + Journal = {J. Chem. Phys.}, + Pages = {4811}, + Title = {{Nodal hypersurfaces and Anderson's random-walk simulation of the Schr\"odinger equation}}, + Volume = {64}, + Year = {1976}} + +@article{KliMic-JCP-12, + Author = {J. Klime{\v s} and A. Michaelides}, + Journal = {J. Chem. Phys.}, + Pages = {120901}, + Title = {Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory}, + Volume = {137}, + Year = {2012}} + +@article{KloBakJorOlsHel-JPB-99, + Author = {W. Klopper and K. L. Bak and P. J{\o}rgensen and J. Olsen and T. Helgaker}, + Journal = {J. Phys. B}, + Pages = {R103}, + Volume = {32}, + Year = {1999}} + +@article{Klo-MP-01, + Author = {W. Klopper}, + Journal = {Mol. Phys.}, + Pages = {481}, + Volume = {99}, + Year = {2001}} + +@article{KloSam-JCP-02, + Author = {W. Klopper and C. M. Samson}, + Journal = {J. Chem. Phys.}, + Pages = {6397}, + Volume = {116}, + Year = {2002}} + +@article{KloTeaCorPedHel-CPL-11, + Author = {W. Klopper and A. M. Teale and S. Coriani and T. B. Pedersen and T. Helgaker}, + Journal = {Chem. Phys. Lett.}, + Pages = {147}, + Volume = {510}, + Year = {2011}} + +@incollection{KnoSchWer-INC-00, + Address = {J\"{u}lich}, + Author = {P. J. Knowles and M. Sch\"{u}tz and H.-J. Werner}, + Booktitle = {Modern Methods and Algorithms of Quantum Chemistry}, + Editor = {J. Grotendorst}, + Pages = {61-151}, + Publisher = {NIC}, + Title = {Ab Initio Methods for Electron Correlation in Molecules}, + Volume = {1}, + Year = {2000}} + +@article{KnoWer-CPL-88, + Author = {P. J. Knowles and H-J. Werner}, + Journal = {Chem. Phys. Lett.}, + Pages = {145}, + Volume = {{514}}, + Year = {1988}} + +@book{KocHol-BOOK-01, + Address = {New York}, + Author = {W. Koch and M. C. Holthausen}, + Publisher = {Wiley-VCH}, + Title = {A Chemist's Guide To Density Functional Theory}, + Year = {2001}} + +@article{Kog-JCP-01b, + Author = {T. Koga}, + Journal = {J. Chem. Phys.}, + Pages = {102}, + Volume = {114}, + Year = {2001}} + +@article{Kog-JCP-02, + Author = {T. Koga}, + Journal = {J. Chem. Phys.}, + Pages = {6614}, + Volume = {116}, + Year = {2002}} + +@article{Kog-JCP-90, + Author = {T. Koga}, + Journal = {J. Chem. 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Lett.}, + Pages = {167}, + Volume = {208}, + Year = {1993}} + +@misc{KohHan-JJJ-XXa, + Author = {W. Kohn and W. Hanke}, + Note = {unpublished}} + +@misc{KohHan-JJJ-XX, + Author = {W. Kohn and W. Hanke}, + Note = {unpublished}} + +@article{Koh-JCP-72, + Author = {A. D. Kohl}, + Journal = {J. Chem. Phys.}, + Pages = {4236}, + Volume = {56}, + Year = {1972}} + +@article{KohMeiMak-PRL-98, + Author = {W. Kohn and Y. Meir and D. E. Makarov}, + Journal = {Phys. Rev. Lett.}, + Pages = {4153}, + Volume = {80}, + Year = {1998}} + +@article{Koh-RMP-99, + Author = {W. Kohn}, + Journal = {Rev. Mod. Phys.}, + Pages = {1253}, + Title = {{Nobel Lecture: Electronic structure of matter - wave functions and density functionals}}, + Volume = {{71}}, + Year = {1999}} + +@article{KohSha-PR-65, + Author = {W. Kohn and L. J. Sham}, + Date-Modified = {2019-04-07 14:53:22 +0200}, + Journal = {Phys. Rev.}, + Pages = {A1133}, + Title = {Self-Consistent Equations Including Exchange and Correlation Effects}, + Volume = {140}, + Year = {1965}} + +@article{KolMit-RPP-11, + Author = {J. Koloren\v{c} and L. Mitas}, + Journal = {Rep. Prog. Phys.}, + Pages = {026502}, + Title = {{Applications of quantum Monte Carlo methods in condensed systems}}, + Volume = {74}, + Year = {2011}} + +@misc{KolReiAss-JJJ-XX, + Author = {A. Kollias and P. Reinhardt and R. Assaraf}, + Note = {unpublished.}} + +@article{KolTho-NL-12, + Author = {Kolb, Brian and Thonhauser, T.}, + Doi = {10.1142/S1793984412300063}, + Journal = {Nano Life}, + Number = {02}, + Pages = {1230006}, + Title = {Molecular biology at the quantum level: can modern density functional theory forge the path?}, + Volume = {02}, + Year = {2012}, + Bdsk-Url-1 = {https://doi.org/10.1142/S1793984412300063}} + +@article{KopPet-JPCA-02, + Author = {Jacek Koput and Kirk A. Peterson}, + Journal = {J. Phys. Chem. A}, + Pages = {9595}, + Volume = {106}, + Year = {2002}} + +@article{KorBouDucBlaMarBot-JCTC-14, + Author = {S. K\"orbel and P. Boulanger and I. Duchemin and X. Blase and M. A. L. Maarques and S. Botti}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3934}, + Volume = {10}, + Year = {2014}} + +@article{KorLucGri-JPCA-08, + Author = {M. Korth and A. L\"uchow and S. Grimme}, + Journal = {J. Phys. Chem. A}, + Pages = {2104}, + Volume = {112}, + Year = {2008}} + +@article{KosKos-JCP-86, + Author = {R. Kosloff and D. Kosloff}, + Journal = {J. Comput. Phys.}, + Pages = {363}, + Volume = {63}, + Year = {1986}} + +@article{KowYosVoo-JCP-11, + Author = {{T. Kowalczyk, S. R. Yorst, and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {054128}, + Volume = {134}, + Year = {2011}} + +@article{KozGruMar-JPCC-10, + Author = {Sebastian Kozuch and David Gruzman and Jan M. L. Martin}, + Journal = {J. Phys. Chem. 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Phys.}, + Pages = {074105}, + Volume = {123}, + Year = {2005}} + +@article{KriLiIaf-PRA-92a, + Author = {J. B. Krieger and Y. Li and G. J. Iafrate}, + Journal = {Phys. Rev. A}, + Pages = {101}, + Volume = {45}, + Year = {1992}} + +@article{KriLiIaf-PRA-92, + Author = {J. B. Krieger and Y. Li and G. J. Iafrate}, + Journal = {Phys. Rev. A}, + Pages = {5453}, + Volume = {46}, + Year = {1992}} + +@article{Kro-AP-84, + Author = {E. Krotscheck}, + Journal = {Ann. Phys.}, + Pages = {1}, + Volume = {{155}}, + Year = {1984}} + +@article{Kro-JLTP-77, + Author = {E. Krotscheck}, + Journal = {J. Low Temp. Phys.}, + Pages = {199}, + Volume = {{27}}, + Year = {1977}} + +@article{KroKohQia-PRB-85, + Author = {E. Krotscheck and W. Kohn and G.-X. Qian}, + Journal = {Phys. Rev. B}, + Pages = {5693}, + Volume = {{32}}, + Year = {1985}} + +@article{Kro-PRA-77, + Author = {E. Krotscheck}, + Journal = {Phys. Rev. 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However, our analysis of complex-energy states remains unchanged. Thus, our procedure for determining the lifetimes is still valid for $Z=0$.}} + +@misc{lifetimes-note3, + Note = {Because we do not impose spherical symmetry in our calculations, we do not have exactly degenerate s, p, and d states.}} + +@article{LikMorSen-PRB-97, + Author = {C. N. Likos and S. Moroni and G. Senatore}, + Journal = {Phys. Rev. B}, + Pages = {8867}, + Volume = {{55}}, + Year = {1997}} + +@article{LilTavRotSeb-PRL-04, + Author = {O. A. von Lilienfeld and I. Tavernelli and U. Rothlisberger}, + Journal = {Phys. Rev. Lett.}, + Pages = {153004}, + Volume = {93}, + Year = {2004}} + +@article{LimCarLuoMaOlsTruGag-JCTC-14, + Author = {{G. Li Manni, R. K. Carlson, S. Luo, D. Ma, J. Olsen, D. G. Truhlar, and L. Gagliardi}}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3669}, + Volume = {10}, + Year = {2014}} + +@article{LinRyuLiu-JCP-91, + Author = {R. Lindh and U. Ryu and B. Liu}, + Journal = {J. Chem. 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Phys.}, + Pages = {154110}, + Volume = {133}, + Year = {2010}} + +@article{LupHea-JCP-13, + Author = {E. Luppi and M. Head-Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {164121}, + Title = {{The role of Rydberg and continuum levels in computing high harmonic generation spectra of the hydrogen atom using time-dependent configuration interaction}}, + Volume = {139}, + Year = {2013}} + +@article{Lut-ZPC-23, + Author = {A. Luthy}, + Journal = {Z. Phys. Chem., Stoechiom. Verwandtschaftsl.}, + Pages = {284}, + Volume = {107}, + Year = {1923}} + +@article{LynTru-JPCA-03, + Author = {B. J. Lynch and D. G. Truhlar}, + Journal = {J. Phys. Chem. A}, + Pages = {8996}, + Title = {Small Representative Benchmarks for Thermochemical Calculations}, + Volume = {107}, + Year = {2003}} + +@misc{LynZhaTru-JJJ-XX, + Note = {The geometries are available in the Minnesota Databases for Chemistry and Solid-State Physics at http://comp.chem.umn.edu/db/.}} + +@article{MaBru-PR-68, + Author = {S.-K. Ma and K. A. Brueckner}, + Journal = {Phys. Rev.}, + Pages = {165}, + Volume = {{165}}, + Year = {1968}} + +@article{MacVos-JPC-79, + Author = {A. H. MacDonald and S. H. Vosko}, + Journal = {J. Phys. C}, + Pages = {2977}, + Volume = {12}, + Year = {1978}} + +@article{MaDruTowNee-PRE-05, + Author = {A. Ma and N. D. Drummond and M. D. Towler and R. J. Needs}, + Journal = {Phys. Rev. E}, + Pages = {066704}, + Volume = {71}, + Year = {2005}} + +@book{Mah-BOOK-09, + Address = {Princeton}, + Author = {Gerald D. Mahan}, + Publisher = {Princeton University Press}, + Title = {Quantum Mechanics in a Nutshell}, + Year = {2009}} + +@article{MaiZhaCavBur-JCP-04, + Author = {N. T. Maitra and F. Zhang and R. J. Cave and K. Burke}, + Journal = {J. Chem. Phys.}, + Pages = {5932}, + Volume = {120}, + Year = {2004}} + +@article{MalMcd-CPL-98, + Author = {N. O. J. Malcolm and J. J. W. McDouall}, + Journal = {Chem. Phys. Lett.}, + Pages = {121}, + Volume = {282}, + Year = {1998}} + +@article{MalMcd-JPC-96, + Author = {N. O. J. Malcolm and J. J. W. McDouall}, + Journal = {J. Phys. Chem.}, + Pages = {10131}, + Volume = {100}, + Year = {1996}} + +@article{MalPenYanBalHol-TCA-14, + Author = {A. Malek and D. Peng and W. Yang and R. Balawender and A. Holas}, + Journal = {Theor. Chem. Acc.}, + Pages = {1559}, + Volume = {133}, + Year = {2014}} + +@article{ManLuc-JCP-01, + Author = {S. Manten and A. L\"uchow}, + Journal = {J. Chem. Phys.}, + Pages = {5362}, + Volume = {115}, + Year = {2001}} + +@article{MarAzaCasSor-JCP-09, + Author = {M. Marchi and S. Azadi and M. Casula and S. Sorella}, + Journal = {J. Chem. Phys.}, + Pages = {154116}, + Title = {Correlated geminal wave function for molecules: An efficient resonating valence bond approach}, + Volume = {131}, + Year = {2009}} + +@article{MarCasMalMulBot-JCP-07, + Author = {M. A. L. Marques and A. Castro and G. Malloci and G. Mulas and S. Botti}, + Journal = {J. Chem. Phys.}, + Pages = {014107}, + Volume = {127}, + Year = {2007}} + +@article{Mar-CPL-96, + Author = {J. M. L. Martin}, + Journal = {Chem. Phys. Lett.}, + Pages = {669}, + Volume = {259}, + Year = {1996}} + +@article{MarGarRub-PRL-06, + Abstract = {We present a first-principles description of anisotropic materials + characterized by having both weak (dispersionlike) and strong covalent + bonds, based on the adiabatic-connection fluctuation-dissipation + theorem with density functional theory. For hexagonal boron nitride + the in-plane and out-of-plane bonding as well as vibrational dynamics + are well described both at equilibrium and when the layers are pulled + apart. Bonding in covalent and ionic solids is also described. The + formalism allows us to ping down the deficiencies of common exchange-correlation + functionals and provides insight toward the inclusion of dispersion + interactions into the correlation functional.}, + Author = {Marini, A. and Garc\'ia-Gonz\'alez, P. and Rubio, A.}, + Journal = {Phys. Rev. Lett.}, + Pages = {136404}, + Title = {First-Principles Description of Correlation Effects in Layered Materials}, + Volume = {96}, + Year = {2006}} + +@article{MarHeiKle-WIRES-18, + Author = {Christel M. Marian and Adrian Heil and Martin Kleinschmidt}, + Journal = {WIREs Comput. Mol. Sci.}, + Note = {doi: 10.1002/wcms.1394}, + Pages = {e1394}, + Title = {The DFT/MRCI method}, + Year = {2018}} + +@article{MarLosFdeAgu-JCP-04, + Author = {{M. E. Mart\'in, A. M. Losa, I. Fdez.-Galv\'an, and M. A. Aguilar}}, + Journal = {J. Chem. Phys.}, + Pages = {3710}, + Volume = {121}, + Year = {2004}} + +@article{MarMea-JCP-78, + Author = {D. J. Margoliash and W. J. Meath}, + Journal = {J. Chem. Phys.}, + Pages = {1426}, + Volume = {68}, + Year = {1978}} + +@article{MaRohMol-JCTC-10, + Author = {Y. Ma and M. Rohlfing and C. Molteni}, + Journal = {J. Chem. Theory Comput.}, + Pages = {257}, + Volume = {6}, + Year = {2010}} + +@article{MaRohMol-PRB-09, + Author = {Y. Ma and M. Rohlfing and C. Molteni}, + Journal = {Phys. Rev. B}, + Pages = {241405}, + Volume = {80}, + Year = {2009}} + +@article{Mar-PR-58, + Author = {N. H. March}, + Journal = {Phys. Rev.}, + Pages = {604}, + Volume = {{110}}, + Year = {1958}} + +@article{MarWer-JPCA-09, + Author = {O. Marchetti and H.-J. Werner}, + Journal = {J. Phys. Chem. A}, + Pages = {11580}, + Volume = {113}, + Year = {2009}} + +@article{Math10-PROG-15, + Note = {{Wolfram Research, Inc., Mathematica, Version 10.3, Champaign, IL (2015)}}} + +@article{Math9-PROG-12, + Note = {{Wolfram Research, Inc., Mathematica, Version 9.0, Champaign, IL (2012)}}} + +@article{MatKogRomDeh-PRA-98, + Author = {H. Matsuyama and T. Koga and E. Romera and J. S. 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Phys.}, + Pages = {361}, + Title = {Combining two-body density functionals with multiconfigurational wavefunctions: diatomic molecules}, + Volume = {101}, + Year = {2003}} + +@article{MclBal-RMP-64, + Author = {McLachlan, A. D. and Ball, M. A.}, + Doi = {10.1103/RevModPhys.36.844}, + Journal = {Rev. Mod. Phys.}, + Pages = {844-855}, + Title = {Time-dependent Hartree-Fock Theory for Molecules}, + Volume = {36}, + Year = {1964}, + Bdsk-Url-1 = {https://doi.org/10.1103/RevModPhys.36.844}} + +@book{McW-BOOK-92, + Address = {London}, + Author = {R. McWeeny}, + Publisher = {Academic Press}, + Title = {Methods of Molecular Quantum Mechanics. Second Edition}, + Year = {1992}} + +@article{Mcw-CCA-84, + Author = {R. McWeeny}, + Journal = {Croat. Chem. Acta}, + Pages = {865}, + Volume = {57}, + Year = {1984}} + +@article{MelSan-PRE-05, + Author = {Melko, R. G. and Sandvik, A. W.}, + Doi = {10.1103/PhysRevE.72.026702}, + Issue = {2}, + Journal = {Phys. Rev. E}, + Numpages = {22}, + Pages = {026702}, + Publisher = {American Physical Society}, + Title = {{Stochastic series expansion algorithm for the $S=1∕2$ $XY$ model with four-site ring exchange}}, + Url = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702}, + Volume = {72}, + Year = {2005}, + Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevE.72.026702}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevE.72.026702}} + +@article{MenAnd-JCP-81, + Author = {F. Mentch and J. B. Anderson}, + Journal = {J. Chem. Phys.}, + Pages = {6307}, + Volume = {74}, + Year = {1981}} + +@incollection{MerValUga-INC-03, + Address = {Dordrecht}, + Author = {J. M. Mercero and E. Valderrama and J. M. Ugalde}, + Booktitle = {NATO-ASI Series in Metal-Ligand Interaction in Molecular-, Nano-, Micro, and Macro-systems in Complex Environments}, + Editor = {N. Russo, D. R. Salahub and M. Witko}, + Publisher = {Kluwer Academic Publishers}, + Year = {2003}} + +@article{MetRosRosTelTel-JCP-53, + Author = {N. Metropolis and A. W. Rosenbluth and M. N. Rosenbluth and A. H. Teller and E. Teller}, + Journal = {J. Chem. Phys.}, + Pages = {1087}, + Title = {{Equations of state calculations by fast computing machines}}, + Volume = {21}, + Year = {1953}} + +@article{MeyMulSch-JMS-96, + Author = {H. Meyer and T. M\"uller and A. Schweig}, + Journal = {J. Mol. Struct. (Theochem)}, + Pages = {55}, + Volume = {306}, + Year = {1996}} + +@article{MieSavStoPre-CPL-89, + Author = {B. Miehlich and A. Savin and H. Stoll and H. Preuss}, + Journal = {Chem. Phys. Lett.}, + Pages = {200}, + Volume = {157}, + Year = {1989}} + +@article{MieStoSav-MP-97, + Author = {B. Miehlich and H. Stoll and A. Savin}, + Journal = {Mol. Phys.}, + Pages = {527}, + Title = {A correlation-energy density functional for multideterminantal wavefunctions}, + Volume = {{91}}, + Year = {1997}} + +@article{Mil-PR-65, + Author = {{W. L. McMillan}}, + Journal = {Phys. Rev.}, + Pages = {A442}, + Title = {{Ground state of liquid He$^4$}}, + Volume = {138}, + Year = {1965}} + +@article{MisJezSza-PRL-03, + Author = {A. J. Misquitta and B. Jeziorski and K. Szalewicz}, + Journal = {Phys. Rev. Lett.}, + Pages = {033201}, + Volume = {91}, + Year = {2003}} + +@article{Mit-PRA-81, + Author = {M. H. Mittleman}, + Journal = {Phys. Rev. A}, + Pages = {1167}, + Volume = {24}, + Year = {1981}} + +@article{MiyAryKotSchUsuTer-PRB-02, + Author = {Miyake, T. and Aryasetiawan, F. and Kotani, T. and Schilfgaarde, M. v. and Usuda, M. and Terakura, K.}, + Journal = {Phys. Rev. B.}, + Pages = {245103}, + Title = {Total energy of solids: An exchange and random-phase approximation correlation study}, + Volume = {66}, + Year = {2002}} + +@book{Moi-BOOK-11, + Address = {Cambridge}, + Author = {Nimrod Moiseyev}, + Publisher = {Cambridge University Press}, + Title = {Non-Hermitian Quantum Mechanics}, + Year = {2011}} + +@article{MolPle-PR-34, + Author = {C. M{\o}ller and M. S. Plesset}, + Journal = {Phys. Rev.}, + Pages = {618}, + Volume = {46}, + Year = {1934}} + +@misc{Molpro-PROG-02, + Address = {Birmingham, UK}, + Author = {R. D. Amos and A. Bernhardsson and A. Berning and P. Celani and D. L. Cooper and M. J. O. Deegan and A. J. Dobbyn and F. Eckert and C. Hampel and G. Hetzer and P. J. Knowles and T. Korona and R. Lindh and A. W. Lloyd and S. J. {McNicholas} and F. R. Manby and W. Meyer and M. E. Mura and A. Nicklass and P. Palmieri and R. Pitzer and G. Rauhut and M. {Sch\"{u}tz} and U. Schumann and H. Stoll and A. J. Stone and R. Tarroni and T. Thorsteinsson and H.-J. Werner}, + Title = {MOLPRO, a package of ab initio programs designed by {H.-J.~Werner} and {P.~J. Knowles}, version 2002.2}, + Year = {2002}} + +@misc{Molpro-PROG-10, + Address = {Cardiff, UK}, + Author = {H.-J. Werner and P. J. Knowles and G. Knizia and F. R. Manby and M. {Sch\"{u}tz} and P. Celani and T. Korona and R. Lindh and A. Mitrushenkov and G. Rauhut and K. R. Shamasundar and T. 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Manby and M. {Sch\"{u}tz} and others}, + Note = {see www.molpro.net}, + Title = {MOLPRO, version 2008.2, a package of ab initio programs}, + Year = {2008}} + +@misc{Molproshort-PROG-10, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {Cardiff, UK, 2010, see \url{http://www.molpro.net}}, + Title = {MOLPRO, version 2010.1, a package of ab initio programs}} + +@misc{Molproshort-PROG-12, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {Cardiff, UK, 2012, see \url{http://www.molpro.net}}, + Title = {MOLPRO, version 2012.1, a package of ab initio programs}} + +@misc{Molproshort-PROG-15, + Author = {{H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. {Sch\"{u}tz}, and others}}, + Note = {{Cardiff, UK, 2015, see \url{http://www.molpro.net}}}, + Title = {{MOLPRO, version 2015.1, a package of ab initio programs}}} + +@misc{Molproweb-PROG-XX, + Note = {\url{http://www.molpro.net}}, + Title = {MOLPRO, a package of ab initio programs}} + +@article{MomShi-JCP-87, + Author = {T. Momose and T. Shida}, + Journal = {J. Chem. Phys.}, + Pages = {2832}, + Volume = {87}, + Year = {1987}} + +@article{MorCepSen-PRL-95, + Author = {S. Moroni and D. M. Ceperley and G. Senatore}, + Journal = {Phys. Rev. Lett.}, + Pages = {689}, + Volume = {75}, + Year = {1995}} + +@article{MorCohYan-JCP-06a, + Author = {Paula Mori-S\'anchez and Aron J. Cohen and Weitao Yang}, + Journal = {J. Chem. Phys.}, + Pages = {091102}, + Volume = {124}, + Year = {2006}} + +@article{MorCohYan-JCP-06, + Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {201102}, + Volume = {125}, + Year = {2006}} + +@article{MorCohYan-PRA-12, + Author = {P. Mori-S{\'a}nchez and A. J. Cohen and W. Yang}, + Journal = {Phys. Rev. A}, + Pages = {042507}, + Volume = {85}, + Year = {2012}} + +@article{MorCohYan-PRL-08, + Author = {Paula Mori-S\'anchez and Aron J. Cohen and Weitao Yang}, + Journal = {Phys. Rev. Lett.}, + Pages = {146401}, + Volume = {100}, + Year = {2008}} + +@article{MorCohYan-PRL-09, + Author = {Mori-S\'anchez, Paula and Cohen, Aron and Yang, Weitao}, + Journal = {Phys. Rev. Lett.}, + Pages = {066403}, + Title = {Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems}, + Volume = {102}, + Year = {2009}} + +@article{MorMcmClaKimScu-JCTC-12, + Author = {M. A. Morales and J. McMinis and B. K. Clark and J. Kim and G. E. Scuseria}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2181}, + Volume = {8}, + Year = {2012}} + +@article{Mor-PR-29, + Author = {P. M. Morse}, + Journal = {Phys. Rev.}, + Pages = {57}, + Volume = {34}, + Year = {1929}} + +@article{MorSen-PRB-91, + Author = {S. Moroni and G. Senatore}, + Journal = {Phys. Rev. B}, + Pages = {9864}, + Volume = {{44}}, + Year = {1991}} + +@article{MorWuYan-JCP-05, + Author = {P. Mori-S{\'a}nchez and Q. Wu and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {062204}, + Volume = {123}, + Year = {2005}} + +@article{MosJezSza-IJQC-93, + Author = {R. Moszynski and B. Jeziorski and K. Szalewicz}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {409}, + Volume = {45}, + Year = {1993}} + +@article{MosSan-IJQC-91, + Author = {F. Moscardo and E. San-Fabian}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {23}, + Volume = {{40}}, + Year = {1991}} + +@article{MosSan-PRA-91, + Author = {F. Moscard\'o and E. San-Fabi\'an}, + Journal = {Phys. Rev. A}, + Pages = {1549}, + Volume = {44}, + Year = {1991}} + +@article{MosSchLeeKal-JCP-82, + Author = {J. W. Moskowitz and K. E. Schmidt and M. A. Lee and M. H. Kalos}, + Journal = {J. Chem. Phys.}, + Pages = {349}, + Title = {{A new look at correlation energy in atomic and molecular systems. II. The application of the Green's function Monte Carlo method to LiH}}, + Volume = {77}, + Year = {1982}} + +@article{MosYabBon-TEC-66, + Author = {A. F. Moskvin and O. P. Yablonskii and L. F. Bondar}, + Journal = {Theor. Exp. Chem.}, + Pages = {636}, + Volume = {2}, + Year = {1966}} + +@article{MugPalNavEgu-PR-04, + Author = {J. G. Muga and J. P. Palao and B. Navarro and I. L. Egusquiza}, + Journal = {Phys. Rep.}, + Pages = {357}, + Volume = {395}, + Year = {2004}} + +@article{Mul-PLA-84, + Author = {A. M. K. M{\"u}ller}, + Journal = {Phys. Lett. A}, + Pages = {446}, + Volume = {105}, + Year = {1984}} + +@article{murray:7145, + Author = {Christopher W. Murray and Nicholas C. Handy and Roger D. Amos}, + Journal = {The Journal of Chemical Physics}, + Keywords = {OZONE; SULFUR; BERYLLIUM; HYDROCARBONS; PERTURBATION THEORY; DENSITY FUNCTIONAL METHOD; ACCURACY; DIMERS; GROUND STATES; PHYSICAL PROPERTIES}, + Number = {9}, + Pages = {7145-7151}, + Publisher = {AIP}, + Title = {A study of O[sub 3], S[sub 3], CH[sub 2], and Be[sub 2] using Kohn--Sham theory with accurate quadrature and large basis sets}, + Url = {http://link.aip.org/link/?JCP/98/7145/1}, + Volume = {98}, + Year = {1993}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/98/7145/1}} + +@article{MusAng-CTC-15, + Abstract = {Abstract The charge density response function and the exchange hole are closely related to each other via the fundamental fluctuation--dissipation theorem of physics. A simple approximate model of the static response function is visually compared on several examples in order to demonstrate this relationship. This study is completed by illustrating the well-known isomorphism between the exchange hole and the square of the dominant localized orbital lying in the space region of the reference point of the exchange hole function. The implications of these relationships for the interpretation of common chemical concepts, such as delocalization, are discussed. }, + Author = {Bastien Mussard and J\'anos G. \'Angy\'an}, + Doi = {http://dx.doi.org/10.1016/j.comptc.2014.10.039}, + Issn = {2210-271X}, + Journal = {Computational and Theoretical Chemistry}, + Keywords = {Topological analysis}, + Note = {Special Issue: Understanding structure and reactivity from topology and beyond}, + Number = {0}, + Pages = {44 - 52}, + Title = {Relationships between charge density response functions, exchange holes and localized orbitals}, + Url = {http://www.sciencedirect.com/science/article/pii/S2210271X14004952}, + Volume = {1053}, + Year = {2015}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S2210271X14004952}, + Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.comptc.2014.10.039}} + +@article{MusAng-TCA-15, + Author = {B. Mussard and J. G. \'Angy\'an}, + Doi = {http://dx.doi.org/10.1007/s00214-015-1751-2}, + Journal = {Theor. Chem. Acc.}, + Pages = {148}, + Volume = {134}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00214-015-1751-2}} + +@incollection{MusCocAssOttUmrTou-AQC-18, + Author = {B. Mussard and E. Coccia and R. Assaraf and M. Otten and C. J. Umrigar and J. Toulouse}, + Booktitle = {Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems}, + Doi = {10.1016/bs.aiq.2017.05.005}, + Editor = {P. E. Hoggan}, + Pages = {255-270}, + Publisher = {Academic Press}, + Series = {Advances in Quantum Chemistry Vol. 76}, + Title = {Time-dependent linear-response variational Monte Carlo}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1016/bs.aiq.2017.05.005}} + +@article{MusReiAngTou-JCP-15, + Author = {B. Mussard and P. Reinhardt and J. G. \'Angy\'an and J. Toulouse}, + Journal = {J. Chem. Phys.}, + Note = {Erratum: J. Chem. Phys. {\bf 142}, 219901 (2015)}, + Pages = {154123}, + Title = {Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights}, + Volume = {142}, + Year = {2015}} + +@misc{MusReiAngTou-JJJ-XX-note, + Note = {See the supplementary material for the detailed results of the calculations on the AE49 and DBH24/08 datasets.}} + +@article{MusRocJanAng-JCTC-16, + Author = {B. Mussard and D. Rocca and G. Jansen and J. G. \'Angy\'an}, + Doi = {10.1021/acs.jctc.5b01129}, + Journal = {J. Chem. Theory Comput.}, + Pages = {2191-2202}, + Title = {Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01129}} + +@article{MusRocJanAng-JJJ-XX, + Author = {B. Mussard and D. Rocca and G. Jansen and J. G. \'Angy\'an}, + Note = {unpublished}} + +@article{MusSzaAng-JCTC-14, + Author = {B. 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Jensen}, + Note = {non publi{\'e}}} + +@phdthesis{Ped-THESIS-04, + Address = {Odense}, + Author = {J. K. Pedersen}, + School = {University of Southern Denmark}, + Title = {Description of correlation and relativistic effects in calculations of molecular properties}, + Type = {{PhD thesis}}, + Year = {2004}} + +@article{PeiNecWar-PRA-03, + Author = {K. Peirs and D. Van Neck and M. Waroquier}, + Eid = {012505}, + Issue = {1}, + Journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, + Keywords = {density functional theory; atomic structure; Green's function methods; ab initio calculations}, + Numpages = {12}, + Page = {012505}, + Publisher = {APS}, + Title = {Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms}, + Url = {http://link.aps.org/abstract/PRA/v67/e012505}, + Volume = {67}, + Year = {2003}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v67/e012505}} + +@article{PerBurErn-PRL-96, + Author = {J. P. Perdew and K. Burke and M. Ernzerhof}, + Journal = {Phys. Rev. Lett.}, + Pages = {3865}, + Title = {Generalized Gradient Approximation Made Simple}, + Volume = {77}, + Year = {1996}} + +@article{PerCheVosJacPedSinFio-PRB-92, + Author = {J. P. Perdew and J. A. Chevary and S. H. Vosko and K. A. Jackson and M. R. Pederson and D. J. Singh and C. Fiolhais}, + Journal = {Phys. Rev. B}, + Pages = {6671}, + Volume = {{46}}, + Year = {1992}} + +@book{PerEngDreGroGodNogCasMar-BOOK-03, + Address = {Berlin}, + Editor = {C. Fiolhais and F. Nogueira and M. A. L. Marques}, + Publisher = {Springer}, + Series = {Vol. 620 of Lecture Notes in Physics}, + Title = {A Primer in Density Functional Theory}, + Year = {2003}} + +@article{PerErnBur-JCP-96, + Author = {J. P. Perdew and M. Ernzerhof and K. Burke}, + Journal = {J. Chem. Phys}, + Pages = {9982}, + Volume = {105}, + Year = {1996}} + +@article{PerErnBurSav-IJQC-97, + Author = {J. P. Perdew and M. Ernzerhof and K. Burke and A. Savin}, + Journal = {Int. J. Quantum Chem.}, + Pages = {197}, + Volume = {{61}}, + Year = {1997}} + +@article{PerGieGriBae-JCP-07, + Author = {K. Pernal and K. Giesbertz and O. Gritsenko and E. J. Baerends}, + Journal = {J. Chem. Phys.}, + Pages = {214101}, + Volume = {127}, + Year = {2007}} + +@article{PerGriBae-PRA-07, + Author = {K. Pernal and O. Gritsenko and E. J. Baerends}, + Journal = {Phys. Rev. A}, + Pages = {012506}, + Volume = {75}, + Year = {2007}} + +@article{Per-IJQC-93, + Author = {J. P. Perdew}, + Journal = {Int. J. Quantum. Chem.: Quantum Chem. Symp.}, + Pages = {93}, + Volume = {27}, + Year = {1993}} + +@incollection{Per-INC-91, + Address = {berlin}, + Author = {J. P. Perdew}, + Booktitle = {Electronic Structure of Solids '91}, + Editor = {P. Ziesche and H. Eschrig}, + Publisher = {Akademie Verlag}, + Year = {1991}} + +@article{Per-JCP-12, + Author = {K. Pernal}, + Journal = {J. Chem. Phys.}, + Pages = {184105}, + Title = {{Excitation energies from range-separated time-dependent density and density matrix functional theory}}, + Volume = {136}, + Year = {2012}} + +@article{PerLanSah-PRL-77, + Author = {J. P. Perdew and D. C. Langreth and V. Sahni}, + Journal = {Phys. Rev. Lett.}, + Pages = {1030}, + Volume = {{38}}, + Year = {1977}} + +@article{PerLev-PRL-83, + Author = {J. P. Perdew and M. Levy}, + Journal = {Phys. Rev. Lett.}, + Pages = {1884}, + Volume = {51}, + Year = {1983}} + +@article{PerMcMZun-PRA-81, + Author = {J. P. Perdew and E. R. McMullen and A. Zunger}, + Journal = {Phys. Rev. A}, + Pages = {2785}, + Volume = {{23}}, + Year = {1981}} + +@article{PerParLevBal-PRL-82, + Author = {J. P. Perdew and R. G. Parr and M. Levy and J. L. Balduz}, + Journal = {Phys. Rev. Lett.}, + Pages = {1691}, + Title = {Density-functional theory for fractional particle number: Derivative discontinuity of the energy}, + Volume = {49}, + Year = {1982}} + +@article{PerPerMorIll-JCC-07, + Author = {A. J. P\'erez-Jim\'enez and J. M. P\'erez-Jord\'a and I. De P. R. Moreira and F. Illas}, + Journal = {J. Comput. Chem.}, + Pages = {2559}, + Volume = {28}, + Year = {2007}} + +@article{PerPerSan-JCP-07, + Author = {A. J. P\'erez-Jim\'enez and J. M. P\'erez-Jord\'a and J. C. Sancho-Garc\'ia}, + Journal = {J. Chem. Phys.}, + Pages = {104102}, + Title = {Combining two-body density correlation functionals with multiconfigurational wave functions using natural orbitals and occupation numbers}, + Volume = {127}, + Year = {2007}} + +@article{Per-PRA-10, + Author = {Katarzyna Pernal}, + Journal = {Phys. Rev. A}, + Pages = {052511}, + Volume = {81}, + Year = {2010}} + +@article{Per-PRB-86, + Author = {J. P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {8822}, + Volume = {{33}}, + Year = {1986}} + +@article{Per-PRL-85, + Author = {J. P. Perdew}, + Journal = {Phys. Rev. Lett.}, + Pages = {1665}, + Volume = {{55}}, + Year = {1985}} + +@article{PerSavBur-PRA-95, + Author = {J. P. Perdew and A. Savin and K. Burke}, + Journal = {Phys. Rev. A}, + Pages = {4531}, + Title = {{Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory}}, + Volume = {51}, + Year = {1995}} + +@article{PerWan2-PRB-92, + Author = {J. P. Perdew and Y. Wang}, + Journal = {Phys. Rev. B}, + Pages = {12947}, + Volume = {{46}}, + Year = {1992}} + +@article{PerWan-PRB-86, + Author = {J. P. Perdew and Y. Wang}, + Journal = {Phys. Rev. B}, + Pages = {8800}, + Volume = {{33}}, + Year = {1986}} + +@article{PerWan-PRB-92, + Author = {J. P. Perdew and Y. Wang}, + Journal = {Phys. Rev. B}, + Pages = {13244}, + Volume = {45}, + Year = {1992}} + +@article{PerZun-PRB-81, + Author = {J. P. Perdew and A. Zunger}, + Journal = {Phys. Rev. B}, + Pages = {5048}, + Volume = {23}, + Year = {1981}} + +@article{PetDun-JCP-02, + Author = {{K. A. Peterson and T. H. Dunning, Jr}}, + Journal = {J. Chem. Phys.}, + Pages = {10548}, + Volume = {117}, + Year = {2002}} + +@article{PetDun-JPC-95, + Author = {{K. A. Peterson and T. H. Dunning Jr.}}, + Journal = {J. Phys. Chem.}, + Pages = {3898}, + Volume = {99}, + Year = {1995}} + +@article{PetGosGro-PRL-96, + Author = {M. Petersilka and U. J. Gossmann and E. K. U. Gross}, + Journal = {Phys. Rev. Lett.}, + Pages = {1212}, + Volume = {76}, + Year = {1996}} + +@article{PetGro-IJQC-96, + Author = {M. Petersilka and E. K. U. Gross}, + Journal = {Int. J. Quantum Chem. Symp.}, + Pages = {1393}, + Volume = {30}, + Year = {1996}} + +@article{PetHolChaNigUmr-PRL-12, + Author = {F. R. Petruzielo and A. A. Holmes and H. J. Changlani and M. P. Nightingale and C. J. Umrigar}, + Journal = {Phys. Rev. Lett.}, + Pages = {230201}, + Title = {Semistochastic Projector Monte Carlo Method}, + Volume = {109}, + Year = {2012}} + +@article{PetKenDun-JCP-93b, + Author = {{K. A. Peterson, R. A. Kendall and T. H. Dunning Jr.}}, + Journal = {J. Chem. Phys.}, + Pages = {9790}, + Volume = {99}, + Year = {1993}} + +@article{PetTouUmr-JCP-11, + Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {064104}, + Title = {Basis set construction for molecular electronic structure theory: Natural orbital and Gauss--Slater basis for smooth pseudopotentials}, + Volume = {134}, + Year = {2011}} + +@article{PetTouUmr-JCP-12, + Author = {F. R. Petruzielo and J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {124116}, + Title = {{Approaching chemical accuracy with quantum Monte Carlo}}, + Volume = {136}, + Year = {2012}} + +@article{PevHea-JCP-13, + Author = {Roberto Peverati and Martin Head-Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {024110}, + Title = {Orbital optimized double-hybrid density functionals}, + Volume = {139}, + Year = {2013}} + +@article{PevTru-JPCL-11, + Author = {Roberto Peverati and Donald G. Truhlar}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {2810}, + Volume = {2}, + Year = {2011}} + +@article{PevTru-JPCL-12, + Author = {Roberto Peverati and Donald G. Truhlar}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {117}, + Volume = {3}, + Year = {2012}} + +@article{PevTru-PTRSA-14, + Abstract = {Kohn{\textendash}Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange{\textendash}correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading{\textemdash}as a long-range goal{\textemdash}to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed{\textemdash}building on earlier work of our group{\textemdash}a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.}, + Author = {Peverati, Roberto and Truhlar, Donald G.}, + Doi = {10.1098/rsta.2012.0476}, + Isbn = {1471-2962}, + Issn = {1364-503X}, + Journal = {Phil. Trans. R. Soc. A}, + Note = {preprint at http://arxiv.org/abs/1212.0944}, + Number = {2011}, + Pages = {20120476}, + Publisher = {The Royal Society}, + Title = {Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics}, + Volume = {372}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1098/rsta.2012.0476}} + +@article{PhiKanZgi-JCP-15, + Author = {J. J. Phillips and A. A. Kananenka and D. Zgid}, + Journal = {J. Chem. Phys.}, + Pages = {194108}, + Volume = {142}, + Year = {2015}} + +@article{PicGos-MP-73, + Author = {B. T. Pickup and O. Goscinski}, + Journal = {Mol. Phys.}, + Pages = {1013}, + Volume = {26}, + Year = {1973}} + +@book{PinNoz-BOOK-89, + Author = {D. Pines and P. Nozi\`eres}, + Publisher = {Addison-Wesley Publishing Company}, + Title = {The Theory of Quantum Liquids}, + Year = {1989}} + +@article{PisDov-IJQC-80, + Author = {C. Pisani and R. Dovesi}, + Journal = {Int. J. Quantum Chem.}, + Pages = {501}, + Volume = {17}, + Year = {1980}} + +@article{PisMasCasHalSchUsv-JCC-08, + Author = {C. Pisani and L. Maschio and S. Casassa and M. Halo and M. Sch\"utz and D. Usvyat}, + Journal = {J. Comput. Chem.}, + Pages = {2113}, + Volume = {29}, + Year = {2008}} + +@article{BytLaiRuedenJCP05, + Author = {Bytautas,Laimutis and Ruedenberg,Klaus}, + Doi = {10.1063/1.1869493}, + Eprint = {https://doi.org/10.1063/1.1869493}, + Journal = {The Journal of Chemical Physics}, + Number = {15}, + Pages = {154110}, + Title = {Correlation energy extrapolation by intrinsic scaling. IV. Accurate binding energies of the homonuclear diatomic molecules carbon, nitrogen, oxygen, and fluorine}, + Url = {https://doi.org/10.1063/1.1869493}, + Volume = {122}, + Year = {2005}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1869493}} + +@article{pittner:10275, + Author = {Jiri Pittner and Petr Nachtigall and Petr Carsky and Jozef Masik and Ivan Hubac}, + Journal = {The Journal of Chemical Physics}, + Keywords = {organic compounds; silicon compounds; coupled cluster calculations; configuration interactions}, + Number = {21}, + Pages = {10275-10282}, + Publisher = {AIP}, + Title = {Assessment of the single-root multireference Brillouin--Wigner coupled- cluster method: Test calculations on CH[sub 2], SiH[sub 2], and twisted ethylene}, + Url = {http://link.aip.org/link/?JCP/110/10275/1}, + Volume = {110}, + Year = {1999}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/110/10275/1}} + +@article{PolColLeiStoWerSav-IJQC-03, + Author = {R. Pollet and F. Colonna and T. Leininger and H. Stoll and H.-J. Werner and A. Savin}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {84}, + Title = {Exchange-Correlation Energies and Correlation Holes for Some Two- and Four-Electron Atoms along a Nonlinear Adiabatic Connection in Density Functional Theory}, + Volume = {{91}}, + Year = {2003}} + +@article{PolSavLeiSto-JCP-02, + Author = {R. Pollet and A. Savin and T. Leininger and H. Stoll}, + Journal = {J. Chem. Phys.}, + Pages = {1250}, + Title = {Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules}, + Volume = {{116}}, + Year = {2002}} + +@phdthesis{Pol-THESIS-01, + Author = {R. Pollet}, + School = {Universit\'e Paris 6}, + Title = {D\'eveloppement et applications d'une m\'ethode g\'en\'eralisant la th\'eorie de la fonctionnelle de la densit\'e \`a plusieurs d\'eterminants de Slater}, + Type = {Th\`ese de doctorat}, + Year = {2001}} + +@article{Pop-RMP-99, + Author = {J. A. Pople}, + Journal = {Rev. Mod. Phys.}, + Pages = {1267}, + Title = {{Nobel Lecture: Quantum chemical models}}, + Volume = {{71}}, + Year = {1999}} + +@article{PorDer-PRA-02, + Author = {S. G. Porsev and A. Derevianko}, + Journal = {Phys. Rev. A}, + Pages = {020701(R)}, + Volume = {65}, + Year = {2002}} + +@article{PraWooPetDunWil-TCA-11, + Author = {{B. P. Prascher, D. E. Woon, K. A. Peterson, T. H. Dunning, Jr., and A. K. Wilson}}, + Journal = {Theor. Chem. Acc.}, + Pages = {69}, + Volume = {128}, + Year = {2011}} + +@article{PreBevFah-PRB-02, + Author = {David Prendergast and David Bevan and Stephen Fahy}, + Journal = {Phys. Rev. B}, + Pages = {155104}, + Volume = {66}, + Year = {2002}} + +@article{PreNolFilFahGre-JCP-01, + Author = {D. Prendergast and M. Nolan and C. Filippi and S. Fahy and J. C. Greer}, + Journal = {J. Chem. Phys.}, + Pages = {1626}, + Volume = {{115}}, + Year = {2001}} + +@book{PreTeuVetFla-BOOK-92, + Address = {Cambridge}, + Author = {W. Press and S. Teukolsky and W. Vetterling and B. Flannery}, + Publisher = {Cambridge University Press}, + Title = {Numerical Recipes}, + Year = {1992}} + +@article{Pul-MP-69, + Author = {P. Pulay}, + Journal = {Mol. Phys.}, + Pages = {197}, + Volume = {17}, + Year = {1969}} + +@article{PurZhaKra-JCP-09, + Author = {W. Purwanto and S. Zhang and H. Krakauer}, + Journal = {J. Chem. Phys.}, + Pages = {094107}, + Volume = {130}, + Year = {2009}} + +@misc{Qmc-PROG-XX, + Note = {QMCMOL, a quantum Monte Carlo program written by R. Assaraf, F. Colonna, X. Krokidis, P. Reinhardt and coworkers.}, + Url = {http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/}, + Bdsk-Url-1 = {http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/}} + +@misc{Quantumexpressoweb-PROG-XX, + Note = {\url{http://www.quantum-espresso.org}}, + Title = {QUANTUM ESPRESSO, an integrated suite of Open-Source computer codes for electronic-structure calculations and materials modeling at the nanoscale}} + +@article{RabBaeNeu-PRB-15, + Author = {E. Rabani and R. Baer and D. Neuhauser}, + Journal = {Phys. Rev. B}, + Pages = {235302}, + Volume = {91}, + Year = {2015}} + +@article{rabinovitch:1807, + Author = {B. S. Rabinovitch and John E. Douglas and F. S. Looney}, + Journal = {The Journal of Chemical Physics}, + Number = {11}, + Pages = {1807-1808}, + Publisher = {AIP}, + Title = {The Thermal Trans-Cis Isomerization of Dideuteroethylene}, + Url = {http://link.aip.org/link/?JCP/20/1807/2}, + Volume = {20}, + Year = {1952}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/20/1807/2}} + +@book{Rai-BOOK-72, + Address = {Amsterdam-London}, + Author = {S. Raimes}, + Publisher = {North-Holland Publishing Company}, + Title = {Many-electron theory}, + Year = {1972}} + +@article{Raj-ACP-80, + Author = {A. K. Rajagopal}, + Journal = {Adv. Chem. Phys.}, + Pages = {59}, + Volume = {41}, + Year = {1980}} + +@article{RajCal-PRB-73, + Author = {A. K. Rajagopal and J. Callaway}, + Journal = {Phys. Rev. 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Toulouse}, + Note = {unpublished}} + +@article{RebSavTou-MP-13, + Author = {E. Rebolini and A. Savin and J. Toulouse}, + Journal = {Mol. Phys.}, + Pages = {1219}, + Title = {Electronic excitations from a linear-response range-separated hybrid scheme}, + Volume = {111}, + Year = {2013}} + +@article{RebTeaHelSavTou-MP-18, + Author = {E. Rebolini and A. M. Teale and T. Helgaker and A. Savin and J. Toulouse}, + Doi = {doi.org/10.1080/00268976.2017.1422811}, + Journal = {Mol. Phys.}, + Pages = {1443-1451}, + Title = {Excitation energies from G\"orling--Levy perturbation theory along the range-separated adiabatic connection}, + Volume = {116}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2017.1422811}} + +@phdthesis{Reb-THESIS-14, + Author = {E. Rebolini}, + School = {Universit\'e Pierre et Marie Curie}, + Title = {Range-separated density-functional theory for molecular excitation energies}, + Type = {{Th\`ese de doctorat}}, + Url = {https://tel.archives-ouvertes.fr/tel-01027522}, + Year = {2014}, + Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + +@phdthesis{Reb-THESIS-14_eng, + Author = {E. Rebolini}, + School = {Universit\'e Pierre et Marie Curie}, + Title = {Range-separated density-functional theory for molecular excitation energies}, + Type = {{PhD thesis}}, + Url = {https://tel.archives-ouvertes.fr/tel-01027522}, + Year = {2014}, + Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + +@article{RebTou-JCP-16, + Author = {E. Rebolini and J. Toulouse}, + Doi = {http://dx.doi.org/10.1063/1.4943003}, + Journal = {J. Chem. Phys.}, + Pages = {094107}, + Title = {Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel}, + Volume = {144}, + Year = {2016}, + Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4943003}} + +@misc{RebTou-JJJ-XX-note1, + Note = {The last two terms of the kernel in Eq. (31) of Ref.~\onlinecite{ZhaSteYan-JCP-13} contain non-antisymmetrized two-electron integrals. However, these terms can also be written with a factor of $1/2$ and antisymmetrized two-electron integrals, leading to our Eq.~(\ref{eq:eff kernel iajb}).}} + +@incollection{RebTouSav-INC-13, + Author = {E. Rebolini and J. Toulouse and A. Savin}, + Booktitle = {Electronic Structure and Reactivity}, + Editor = {S. K. Ghosh and P. K. Chattaraj}, + Note = {preprint at http://arxiv.org/abs/1304.1314}, + Pages = {367-390}, + Publisher = {CRC Press}, + Series = {Concepts and Methods in Modern Theoretical Chemistry Vol. 1}, + Title = {Electronic excitation energies of molecular systems from the Bethe-Salpeter equation: Example of the H$_2$ molecule}, + Year = {2013}} + +@misc{RebTouSav-JJJ-XX-note, + Note = {With the notations used here, the Hubbard model is obtained for $\Delta\varepsilon = 2 t$ and $J_{11}=J_{22}=J_{12}=J_{12}=K_{12}=U/2$ where $t$ is the hopping parameter and $U$ is the on-site Coulomb interaction.}} + +@article{RebTouTeaHelSav-JCP-14, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1063/1.4890652}, + Journal = {Journal of Chemical Physics}, + Pages = {044123}, + Title = {Excitation energies along a range-separated adiabatic connection}, + Volume = {141}, + Year = {2014}, + Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4890652}} + +@misc{RebTouTeaHelSav-JJJ-XX-sup, + Note = {See supplementary material at http://xxxxxxxx for the fits of the total and excitation energies.}} + +@article{RebTouTeaHelSav-MP-15, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1080/00268976.2015.1011248}, + Journal = {Mol. Phys.}, + Pages = {1740}, + Title = {Excited states from range-separated density-functional perturbation theory}, + Volume = {113}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2015.1011248}} + +@article{RebTouTeaHelSav-PRA-15, + Author = {E. Rebolini and J. Toulouse and A. M. Teale and T. Helgaker and A. Savin}, + Doi = {http://dx.doi.org/10.1103/PhysRevA.91.032519}, + Journal = {Phys. Rev. A}, + Pages = {032519}, + Title = {Calculating excitation energies by extrapolation along adiabatic connections}, + Volume = {91}, + Year = {2015}, + Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.91.032519}} + +@article{RefJaiShaNeaKro-PRB-15, + Author = {Sivan Refaely-Abramson and Manish Jain and Sahar Sharifzadeh and Jeffrey B. Neaton and Leeor Kronik}, + Journal = {Phys. Rev. B}, + Pages = {081204(R)}, + Volume = {92}, + Year = {2015}} + +@article{RefShaGovAutNeaBaeKro-PRL-12, + Author = {S. Refaely-Abramson and Sahar Sharifzadeh and Niranjan Govind and Jochen Autschbach and Jeffrey B. Neaton and Roi Baer and Leeor Kronik}, + Journal = {Phys. Rev. Lett.}, + Pages = {226405}, + Volume = {109}, + Year = {2012}} + +@article{RegTha-JPB-84, + Author = {P. E. Regier and A. J. Thakkar}, + Journal = {J. Phys. 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Hoggan}, + Booktitle = {Advances in Quantum Monte Carlo}, + Editor = {{S. Tanaka, S. M. Rothstein, and W. A. Lester, Jr.}}, + Pages = {53-63}, + Publisher = {American Chemical Society}, + Series = {ACS Symposium Series Vol. 1094}, + Title = {Quantum Monte Carlo Facing the Hartree-Fock Symmetry Dilemma: The Case of Hydrogen Rings}, + Year = {2012}} + +@article{ReiTouSav-TCA-18, + Author = {Peter Reinhardt and Julien Toulouse and Andreas Savin}, + Doi = {10.1007/s00214-018-2370-5}, + Journal = {Theor. Chem. Acc.}, + Pages = {168}, + Volume = {137}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1007/s00214-018-2370-5}} + +@article{RenRinBluWieTkaSanReuSch-NJP-12, + Author = {Xinguo Ren and Patrick Rinke and Volker Blum and Jurgen Wieferink and Alexandre Tkatchenko and Andrea Sanfilippo and Karsten Reuter and Matthias Scheffler}, + Journal = {New J. 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Seminario}, + Pages = {327-357}, + Publisher = {Elsevier}, + Title = {On Degeneracy, Near Degeneracy and Density Functional Theory}, + Year = {1996}} + +@article{Sav-JCP-11, + Author = {A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {214108}, + Volume = {134}, + Year = {2011}} + +@article{Sav-JCP-14, + Author = {A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {18A509}, + Volume = {140}, + Year = {2014}} + +@article{Sav-JCP-89, + Author = {A. Savin}, + Journal = {J. chim. phys.}, + Pages = {757}, + Volume = {{86}}, + Year = {1989}} + +@article{Sav-JCTC-09, + Author = {A. Savin}, + Journal = {J. Chem. Theory Comput.}, + Pages = {822}, + Volume = {5}, + Year = {2009}} + +@incollection{SavStoPre-INC-84, + Address = {New York}, + Author = {A. Savin}, + Booktitle = {Local Density Approximations in Quantum Chemistry and Solid State Physics}, + Editor = {J. P. Dahl and J. Avery}, + Pages = {263}, + Publisher = {Plenum}, + Year = {1984}} + +@article{SavStoPre-TCA-86, + Author = {A. 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E. and Toulouse, J. and Peverati, R. and Truhlar, D. G. and Szalewicz, K.}, + Doi = {http://dx.doi.org/10.1063/1.4961095}, + Journal = {J. Chem. Phys.}, + Pages = {124105}, + Title = {Blind test of density-functional-based methods on intermolecular interaction energies}, + Url = {http://scitation.aip.org/content/aip/journal/jcp/145/12/10.1063/1.4961095}, + Volume = {145}, + Year = {2016}, + Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/145/12/10.1063/1.4961095}, + Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.4961095}} + +@book{TDDFT-BOOK-06, + Address = {Berlin}, + Editor = {M. L. Marques and C. A. Ullrich and F. Nogueira and A. Rubio and K. Burke and E. K. U. Gross}, + Publisher = {Springer}, + Series = {Lecture Notes in Physics Vol. 706}, + Title = {Time-Dependent Density Functional Theory}, + Year = {2006}} + +@book{TDDFT-BOOK-12, + Address = {Berlin}, + Editor = {M. A. L. Marques and N. T. Maitra, F. M. S. Nogueira, E. K. U. Gross, A. Rubio}, + Publisher = {Springer}, + Series = {Lecture Notes in Physics Vol. 837}, + Title = {Fundamentals of Time-Dependent Density Functional Theory}, + Year = {2012}} + +@article{TeaCorHel-JCP-09, + Author = {A. M. Teale and S. Coriani and T. Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {104111}, + Title = {{The calculation of adiabatic-connection curves from full configuration-interaction densities: Two-electron systems}}, + Volume = {130}, + Year = {2009}} + +@article{TeaCorHel-JCP-10b, + Author = {Andrew M. Teale and S. Coriani and Trygve Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {164112}, + Volume = {133}, + Year = {2010}} + +@article{TeaCorHel-JCP-10, + Author = {Andrew M. Teale and S. Coriani and Trygve Helgaker}, + Journal = {J. Chem. Phys.}, + Pages = {164115}, + Volume = {132}, + Year = {2010}} + +@article{TeaDepToz-JCP-08, + Author = {{A. M. Teale, F. De Proft, and D. J. Tozer}}, + Journal = {J. Chem. Phys.}, + Pages = {044110}, + Volume = {129}, + Year = {2008}} + +@article{TecGomEksVis-PCCP-11, + Author = {P. Tecmer and A. S. P. Gomes and U. Ekstr\"om and L. Visscher}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {6249}, + Volume = {13}, + Year = {2011}} + +@article{TelKvaSagEksTeaHel-PRA-12, + Author = {E. I. Tellgren and S. Kvaal and E. Sagvolden and U. Ekstr\"om and A. M. Teale and T. Helgaker}, + Journal = {Phys. Rev. A}, + Pages = {062506}, + Volume = {86}, + Year = {2012}} + +@article{TelSosRozChu-PRA-13, + Author = {D. A. Telnov and K. E. Sosnova and E. Rozenbaum and S.-I. Chu}, + Journal = {Phys. Rev. A}, + Pages = {053406}, + Volume = {87}, + Year = {2013}} + +@article{Tha-CPL-03, + Author = {A. J. Thakkar}, + Journal = {Chem. Phys. Lett.}, + Pages = {80}, + Volume = {381}, + Year = {2003}} + +@incollection{Tha-INC-87, + Address = {Dordrecht}, + Author = {A. J. Thakkar}, + Booktitle = {Density Matrices and Density Functionals}, + Editor = {R. M. Erdahl and V. H. 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Scheffler}, + Journal = {Phys. Rev. Lett.}, + Pages = {073005}, + Title = {{Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data}}, + Volume = {102}, + Year = {2009}} + +@article{TofSteDec-PRA-06, + Author = {D. Toffoli and M. Stener and P. Decleva}, + Journal = {Phys. Rev. A}, + Pages = {042704}, + Volume = {73}, + Year = {2006}} + +@article{ToiWoo-PRB-70, + Author = {F. Toigo and T. O. Woodruff}, + Journal = {Phys. Rev. B}, + Pages = {3958}, + Volume = {{2}}, + Year = {1970}} + +@article{ToiWoo-PRB-71, + Author = {F. Toigo and T. O. Woodruff}, + Journal = {Phys. Rev. B}, + Pages = {371}, + Volume = {{4}}, + Year = {1971}} + +@incollection{Tos-INC-99, + Address = {University of Oxford}, + Author = {M. P. Tosi}, + Booktitle = {Electron Correlation in the Solid State}, + Editor = {N. H. March}, + Publisher = {World Scientific Publishing Company}, + Title = {Many-Body Effects in Jellium}, + Year = {1999}} + +@incollection{TouAssUmr-INC-16, + Author = {J. Toulouse and R. Assaraf and C. J. Umrigar}, + Booktitle = {Electron Correlation in Molecules - ab initio Beyond Gaussian Quantum Chemistry}, + Doi = {10.1016/bs.aiq.2015.07.003}, + Editor = {P. E. Hoggan and T. Ozdogan}, + Pages = {285-314}, + Publisher = {Academic Press}, + Series = {Advances in Quantum Chemistry Vol. 73}, + Title = {Introduction to the Variational and Diffusion Monte Carlo Methods}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1016/bs.aiq.2015.07.003}} + +@article{TouAssUmr-JCP-07, + Author = {J. Toulouse and R. Assaraf and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {244112}, + Title = {{Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density}}, + Volume = {126}, + Year = {2007}} + +@incollection{TouCafReiHogUmr-INC-12, + Address = {Dordrecht Heidelberg London New York}, + Author = {J. Toulouse and M. Caffarel and P. Reinhardt and P. E. Hoggan and C. J. Umrigar}, + Booktitle = {Advances in the Theory of Quantum Systems in Chemistry and Physics}, + Editor = {P. E. Hoggan and J. Maruani and P. Piecuch and G. Delgado-Barrio and E. J. Br\"andas}, + Pages = {345-353}, + Publisher = {Springer}, + Series = {Progress in Theoretical Chemistry and Physics Vol. 22}, + Title = {Quantum Monte Carlo calculations of electronic excitation energies: The case of the singlet $n\to\pi^*$ (CO) transition in acrolein}, + Year = {2012}} + +@article{TouColSav-JCP-05, + Author = {J. Toulouse and F. Colonna and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {014110}, + Title = {Short-range exchange and correlation energy density functionals: Beyond the local-density approximation}, + Volume = {122}, + Year = {2005}} + +@article{TouColSav-MP-05, + Author = {Julien Toulouse and Francois Colonna and Andreas Savin}, + Journal = {Mol. Phys.}, + Pages = {2725}, + Title = {Exchange-correlation potentials and local energies per particle along non-linear adiabatic connections}, + Volume = {103}, + Year = {2005}} + +@article{TouColSav-PRA-04, + Author = {J. Toulouse and F. Colonna and A. Savin}, + Journal = {Phys. Rev. A}, + Keywords = {density functional theory; wave functions; exchange interactions (electron); electron correlations}, + Number = {6}, + Pages = {062505}, + Publisher = {APS}, + Title = {Long-range--short-range separation of the electron-electron interaction in density-functional theory}, + Volume = {70}, + Year = {2004}} + +@misc{TouGerJanSavAng-JJJ-XX-note, + Note = {For Ne$_{2}$ at equilibrium distance with aug-cc-pVQZ basis, the counterpoise correction on the interaction energy is 16 $\mu$H for RSH+RPAx and 62 $\mu$H for standard MP2.}} + +@article{TouGerJanSavAng-PRL-09, + Author = {J. Toulouse and I. C. Gerber and G. Jansen and A. Savin and J. G. \'Angy\'an}, + Journal = {Phys. Rev. Lett.}, + Pages = {096404}, + Title = {Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation}, + Volume = {102}, + Year = {2009}} + +@article{TouGorSav-IJQC-06, + Author = {J. Toulouse and P. Gori-Giorgi and A. Savin}, + Journal = {Int. J. Quantum Chem.}, + Pages = {2026}, + Title = {Scaling relations, virial theorem and energy densities for long-range and short-range density functionals}, + Volume = {106}, + Year = {2006}} + +@article{TouGorSav-TCA-05, + Author = {J. Toulouse and P. Gori-Giorgi and A. Savin}, + Date-Modified = {2019-04-07 14:55:33 +0200}, + Journal = {Theor. Chem. Acc.}, + Pages = {305}, + Title = {A short-range correlation energy density functional with multi-determinantal reference}, + Volume = {114}, + Year = {2005}} + +@misc{Tou-JJJ-XX, + Author = {S. Dubillard and E. Eliav and L. Visscher and R. Bast and T. Saue}, + Note = {unpublished}} + +@article{Tou-PRB-05, + Author = {Julien Toulouse}, + Journal = {Phys. Rev. B}, + Pages = {035117}, + Title = {Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction}, + Volume = {72}, + Year = {2005}} + +@article{TouRebGouDobSeaAng-JCP-13, + Author = {Julien Toulouse and Elisa Rebolini and Tim Gould and John F. Dobson and Prasenjit Seal and J\'anos G. \'Angy\'an}, + Journal = {J. Chem. Phys.}, + Pages = {194106}, + Title = {Assessment of range-separated time-dependent density-functional theory for calculating $C_6$ dispersion coefficients}, + Volume = {138}, + Year = {2013}} + +@article{TouSavFla-IJQC-04, + Author = {J. Toulouse and A. Savin and H.-J. Flad}, + Journal = {Int. J. Quantum Chem.}, + Pages = {1047}, + Title = {Short-range exchange-correlation energy of a uniform electron gas with modified electron-electron interaction}, + Volume = {100}, + Year = {2004}} + +@misc{TouSav-JJJ-XX, + Author = {J. Toulouse and A. Savin}, + Title = {in preparation}} + +@article{TouSav-JMS-06, + Author = {Julien Toulouse and Andreas Savin}, + Journal = {J. Mol. Struct. (Theochem)}, + Pages = {147}, + Title = {Local density approximation for long-range or for short-range energy functionals?}, + Volume = {762}, + Year = {2006}} + +@article{TouShaBreAda-JCP-11, + Author = {J. Toulouse and K. Sharkas and E. Br\'emond and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {101102}, + Title = {Rationale for a new class of double-hybrid approximations in density-functional theory}, + Volume = {135}, + Year = {2011}} + +@phdthesis{Tou-THESIS-05, + Author = {J. Toulouse}, + Note = {tel.archives-ouvertes.fr/tel-00550772}, + School = {Universit\'e Pierre et Marie Curie (Paris 6)}, + Year = {2005}} + +@article{TouUmr-JCP-07, + Author = {J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {084102}, + Title = {{Optimization of quantum Monte Carlo wave functions by energy minimization}}, + Volume = {126}, + Year = {2007}} + +@article{TouUmr-JCP-08, + Author = {J. Toulouse and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {174101}, + Title = {{Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules}}, + Volume = {128}, + Year = {2008}} + +@misc{TouUmr-JJJ-XX, + Author = {J. Toulouse and C. J. Umrigar}, + Note = {unpublished}} + +@misc{TouZhuAngSav-JJJ-XX-note2, + Note = {In the context of density-functional theory RPA is usually derived from the Kohn-Sham reference, while in the context of many-body perturbation theory (see appendices) RPA is usually derived from the HF reference. Therefore, both PBE+RPA and HF+RPA are theoretically justified.}} + +@misc{TouZhuAngSav-JJJ-XX-note3, + Note = {The inverse of a 4-point function $\chi (1,2;1',2')$ is defined according to $\int d1'd2' \chi (1,2;1',2') \chi^{-1} (2',1';4,3) = \delta(1,3) \delta (2,4)$.}} + +@misc{TouZhuAngSav-JJJ-XX-note, + Note = {The short-range self-energy correction $\Delta \Sigma^\sr_\l$ is wrongly missing in Eq.~(11) of Ref.~\onlinecite{TouGerJanSavAng-PRL-09}. However, in practice, this term vanishes in the RPA or RPAx approximation so that the results of Ref.~\onlinecite{TouGerJanSavAng-PRL-09} are correct.}} + +@article{TouZhuAngSav-PRA-10, + Author = {Julien Toulouse and Wuming Zhu and J\'anos G. \'Angy\'an and Andreas Savin}, + Journal = {Phys. Rev. A}, + Pages = {032502}, + Title = {Range-separated density-functional theory with the random-phase approximation: Detailed formalism and illustrative applications}, + Volume = {82}, + Year = {2010}} + +@article{TouZhuSavJanAng-JCP-11, + Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angy\'an}, + Journal = {J. Chem. Phys.}, + Pages = {084119}, + Title = {Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions}, + Volume = {135}, + Year = {2011}} + +@misc{TouZhuSavJanAng-JJJ-XX, + Author = {J. Toulouse and W. Zhu and A. Savin and G. Jansen and J. G. \'Angyan}, + Note = {unpublished}} + +@misc{TouZhuSavJanAng-JJJ-XX-note, + Note = {In Ref.~\onlinecite{Hes-JCP-11}, AC-RPA, NRPA1, NRPA3, and NRPA4 refer to what we call here RPAx-I, RPAx-II, RPA-SO2, and RPA-SO1, respectively. In addition, NRPA2 corresponds to the variant of Fukuda {\it et al.}, i.e. $2E_{c,\RPAxII}-E_{c,\text{MP2}}$.}} + +@article{TowZupCau-CPC-96, + Author = {M. D. Towler and A. Zupan and M. Caus\'a}, + Journal = {Comp. Phys. Comm.}, + Pages = {181}, + Volume = {98}, + Year = {1996}} + +@article{TozHan-JCP-98, + Author = {D. J. Tozer and N. C. Handy}, + Journal = {J. Chem. Phys.}, + Pages = {10180}, + Volume = {109}, + Year = {1998}} + +@article{Tri-JPB-80, + Author = {H. P. Trivedi}, + Journal = {J. Phys. B}, + Pages = {839}, + Volume = {13}, + Year = {1980}} + +@article{Tru-CPL-98, + Author = {D. G. Truhlar}, + Journal = {Chem. Phys. Lett.}, + Pages = {45}, + Volume = {294}, + Year = {1998}} + +@article{TsuScu-JCP-11, + Author = {T. Tsuchimochi and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {064101}, + Volume = {134}, + Year = {2011}} + +@article{TsuScuSav-JCP-10, + Author = {T. Tsuchimochi and G. E. Scuseria and A. Savin}, + Journal = {J. Chem. Phys.}, + Pages = {024111}, + Volume = {132}, + Year = {2010}} + +@article{TsuSonSuzHir-JCP-10, + Author = {Takao Tsuneda and Jong-Won Song and Satoshi Suzuki and Kimihiko Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {174101}, + Volume = {133}, + Year = {2010}} + +@article{TsuSuzHir-JCP-99, + Author = {Takao Tsuneda and Toshihisa Suzumura and Kimihiko Hirao}, + Journal = {J. Chem. Phys.}, + Pages = {5656}, + Volume = {111}, + Year = {1999}} + +@article{UgaBoy-IJQC-85, + Author = {J. M. Ugalde and R. J. Boyd}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {439}, + Volume = {27}, + Year = {1985}} + +@book{Ull-BOOK-11, + Author = {Carsten A. Ullrich}, + Publisher = {OUP Oxford}, + Title = {Time-Dependent Density-Functional Theory: Concepts and Applications}, + Year = {2011}} + +@article{UllKoh-PRL-01, + Author = {C. A. Ullrich and W. Kohn}, + Journal = {Phys. Rev. Lett.}, + Pages = {093001}, + Volume = {87}, + Year = {2001}} + +@article{UmrFil-PRL-05, + Author = {C. J. Umrigar and C. Filippi}, + Journal = {Phys. Rev. Lett.}, + Pages = {150201}, + Title = {{Energy and variance optimization of many-body wave functions}}, + Volume = {94}, + Year = {2005}} + +@misc{UmrFil-PRL-05-note, + Note = {The convergence in 2 iterations, mentioned near the end of Ref.~\onlinecite{UmrFil-PRL-05} was obtained using the correlated sampling adjustment of $a_\diag$ and the TU Hessian.}} + +@incollection{UmrGon-INC-93, + Address = {Singapore}, + Author = {C. J. Umrigar and X. Gonze}, + Booktitle = {High Performance Computing and its Application to the Physical Sciences, Proceedings of the Mardi Gras '93 Conference}, + Editor = {D. A. Browne {\it et al.}}, + Publisher = {World Scientific}, + Year = {1993}} + +@article{UmrGon-PRA-94, + Author = {C. J. Umrigar and X. Gonze}, + Journal = {Phys. Rev. A}, + Pages = {3827}, + Volume = {50}, + Year = {1994}} + +@article{Umr-IJQC-89, + Author = {C. J. Umrigar}, + Journal = {Int. J. Quantum Chem.}, + Pages = {217}, + Volume = {{23}}, + Year = {1989}} + +@incollection{Umr-INC-99, + Address = {Dordrecht}, + Author = {C. J. Umrigar}, + Booktitle = {Quantum Monte Carlo Methods in Physics and Chemistry}, + Editor = {M. P. Nightingale and C. J. Umrigar}, + Pages = {129}, + Publisher = {Kluwer}, + Series = {NATO ASI Ser. C 525}, + Year = {1999}} + +@article{UmrNigRun-JCP-93, + Author = {C. J. Umrigar and M. P. Nightingale and K. J. Runge}, + Journal = {J. Chem. Phys.}, + Pages = {2865}, + Title = {{A diffusion Monte Carlo algorithm with very small time-step errors}}, + Volume = {99}, + Year = {1993}} + +@article{Umr-PRL-93, + Author = {C. J. Umrigar}, + Journal = {Phys. Rev. Lett.}, + Pages = {408}, + Title = {{Accelerated Metropolis method}}, + Volume = {71}, + Year = {1993}} + +@incollection{UmrSavGon-INC-98, + Author = {Umrigar, C.J. and Savin, A. and Gonze, Xavier}, + Booktitle = {Electronic Density Functional Theory}, + Doi = {10.1007/978-1-4899-0316-7_12}, + Editor = {Dobson, John F. and Vignale, Giovanni and Das, Mukunda P.}, + Pages = {167-176}, + Publisher = {Springer US}, + Title = {Are Unoccupied Kohn-Sham Eigenvalues Related to Excitation Energies?}, + Year = {1998}, + Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4899-0316-7_12}} + +@article{UmrTouFilSorHen-PRL-07, + Author = {C. J. Umrigar and J. Toulouse and C. Filippi and S. Sorella and R. G. Hennig}, + Journal = {Phys. Rev. Lett.}, + Pages = {110201}, + Title = {Alleviation of the Fermion-sign problem by optimization of many-body wave functions}, + Volume = {98}, + Year = {2007}} + +@misc{Umr-UNP-XXb, + Author = {C. J. Umrigar}, + Note = {unpublished}} + +@misc{Umr-UNP-XX, + Author = {C. J. Umrigar}, + Note = {unpublished}} + +@misc{Umr-UNP-XX_fr, + Author = {C. J. Umrigar}, + Note = {non publi{\'e}}} + +@incollection{UmrWilWil-INC-88, + Address = {Berlin}, + Author = {C. J. Umrigar and K. G. Wilson and J. W. Wilkins}, + Booktitle = {Computer Simulation Studies in Condensed Matter Physics: Recent Developments}, + Editor = {D. P. Landau and K. K. Mon and H. B. Sch\"uttler}, + Publisher = {Springer}, + Year = {1988}} + +@article{UmrWilWil-PRL-88, + Author = {C. J. Umrigar and K. G. Wilson and J. W. Wilkins}, + Journal = {Phys. Rev. Lett.}, + Pages = {1719}, + Title = {{Optimized trial wave functions for quantum Monte Carlo calculations}}, + Volume = {60}, + Year = {1988}} + +@article{UtsIch-PRB-80a, + Author = {K. Utsumi and S. Ichimaru}, + Journal = {Phys. Rev. B}, + Pages = {1522}, + Volume = {{22}}, + Year = {1980}} + +@article{UtsIch-PRB-80, + Author = {K. Utsumi and S. Ichimaru}, + Journal = {Phys. Rev. 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B}, + Pages = {045113}, + Volume = {{69}}, + Year = {2004}} + +@article{VosWilNus-CJP-80, + Author = {S. J. Vosko and L. Wilk and M. Nusair}, + Journal = {Can. J. Phys.}, + Pages = {1200}, + Volume = {{58}}, + Year = {1980}} + +@article{VrbDepRot-JCP-88, + Author = {J. Vrbik and M. F. DePasquale and S. M. Rothstein}, + Journal = {J. Chem. Phys.}, + Pages = {3784}, + Volume = {88}, + Year = {1988}} + +@article{VutCamGurHutparPatPetSpaDoyGabDem-JPB-10, + Author = {A. C. Vutha and W. C. Campbell and Y. V. Gurevich and N. R. Hutzler and M. Parsons and D. Patterson and E. Petrik and B. Spaun and J. M. Doyle and G. Gabrielse and D. DeMille}, + Journal = {J. Phys. B}, + Pages = {074007}, + Volume = {43}, + Year = {2010}} + +@article{VydScu-JCP-06, + Author = {O. A. Vydrov and G. E. Scuseria}, + Journal = {J. Chem. Phys.}, + Pages = {234109}, + Volume = {125}, + Year = {2006}} + +@article{VydScuPer-JCP-07, + Author = {Vydrov, O. A. and Scuseria, G. E. and Perdew, J. P.}, + Journal = {J. Chem. Phys.}, + Pages = {154109}, + Title = {Tests of functionals for systems with fractional electron number}, + Volume = {126}, + Year = {2007}} + +@article{VydVoo-JCP-09, + Author = {O. A. Vydrov and T. van Voorhis}, + Journal = {J. Chem. Phys.}, + Pages = {104105}, + Volume = {130}, + Year = {2009}} + +@article{VydVoo-JCP-10b, + Author = {O. A. Vydrov and T. V. Voorhis}, + Journal = {J. Chem. Phys.}, + Pages = {244103}, + Title = {{Nonlocal van der Waals density functional: The simpler the better}}, + Volume = {133}, + Year = {2010}} + +@article{VydVoo-PRL-09, + Author = {O. A. Vydrov and T. van Voorhis}, + Journal = {Phys. Rev. Lett.}, + Pages = {063004}, + Volume = {103}, + Year = {2009}} + +@article{Wal-TFS-45, + Author = {A. D. Walsh}, + Journal = {Trans. Faraday Soc.}, + Pages = {498}, + Volume = {41}, + Year = {1945}} + +@article{WanGauWul-JCP-08, + Author = {{F. Wang, J. Gauss, and C. van W\"ullen}}, + Journal = {J. Chem. Phys.}, + Pages = {064113}, + Volume = {129}, + Year = {2008}} + +@article{WanPer-PRB-91, + Author = {Y. Wang and J.P. Perdew}, + Journal = {Phys. Rev. B}, + Pages = {13298}, + Volume = {{44}}, + Year = {1991}} + +@article{WanSch-JCP-96, + Author = {S. G. Wang and W. H. E. Schwarz}, + Journal = {J. Chem. Phys.}, + Pages = {4641}, + Volume = {{105}}, + Year = {1996}} + +@article{WanSchSmi-PRA-00, + Author = {J. Wang and H. L. Schmider and V. H. Smith}, + Journal = {Phys. Rev. A}, + Pages = {016501}, + Volume = {62}, + Year = {2000}} + +@article{WanSmi-IJQC-94, + Author = {J. Wang and V. H. Smith}, + Journal = {Int. J. Quantum. Chem.}, + Pages = {147}, + Volume = {49}, + Year = {1994}} + +@article{WanTriSmi-JCP-92, + Author = {J. Wang and A. N. Tripathi and V. H. Smith}, + Journal = {J. Chem. Phys.}, + Pages = {9188}, + Volume = {97}, + Year = {1992}} + +@article{WanTriSmi-JCP-94, + Author = {J. Wang and A. N. Tripathi and V. H. Smith}, + Journal = {J. Chem. Phys.}, + Pages = {4842}, + Volume = {101}, + Year = {1994}} + +@article{WanZie-JCP-04, + Author = {F. Wang and T. Ziegler}, + Journal = {J. Chem. Phys.}, + Pages = {12191}, + Volume = {121}, + Year = {2004}} + +@article{WasBur-PRL-05, + Author = {A. Wasserman and K. Burke}, + Journal = {Phys. Rev. Lett.}, + Pages = {163006}, + Volume = {95}, + Year = {2005}} + +@article{WasMaiBur-PRL-03, + Author = {A. Wasserman and N. T. Maitra and K. Burke}, + Journal = {Phys. Rev. Lett.}, + Pages = {263001}, + Volume = {91}, + Year = {2003}} + +@article{WatKamYamUdaMul-MP-04, + Author = {Noboru Watanabe and Yohei Kamata and Kota Yamauchi and Yasuo Udagawa and Thomas M\"uller}, + Journal = {Mol. Phys.}, + Pages = {649}, + Volume = {102}, + Year = {2004}} + +@article{WeiDelGor-JCP-08, + Author = {M. Weimer and F. Della Sala and A. G\"orling}, + Journal = {J. Chem. Phys.}, + Pages = {144109}, + Title = {Multiconfiguration optimized effective potential method for a density-functional treatment of static correlation}, + Volume = {128}, + Year = {2008}} + +@article{WenBer-JCTC-11, + Author = {Shuhao Wen and Gregory J. O. Beran}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3733}, + Volume = {7}, + Year = {2011}} + +@article{WerKno-JCP-88, + Author = {H.-J. Werner and P. J. Knowles}, + Journal = {J. Chem. 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Phys.}, + Number = {13}, + Pages = {134108}, + Title = {Relations between coordinate and potential scaling in the high-density limit}, + Volume = {122}, + Year = {2005}} + +@article{WilMouDun-JMS-96, + Author = {A. K. Wilson and T. v. Mourik and T. H. Dunning}, + Journal = {J. Mol. Struct.}, + Pages = {339}, + Volume = {388}, + Year = {1996}} + +@article{WilWooPetDun-JCP-99, + Author = {A.K. Wilson and D.E. Woon and K.A. Peterson and T.H.Dunning}, + Journal = {J. Chem. Phys.}, + Pages = {7667}, + Volume = {110}, + Year = {1999}} + +@article{WodJanRagCor-JPCA-08, + Author = {{M. D. Wodrich, D. F. Jana, P. v. R. Schleyer, and C. Corminboeuf}}, + Journal = {J. Phys. Chem. A}, + Pages = {11495}, + Volume = {112}, + Year = {2008}} + +@article{Wol-PRL-89, + Author = {Wolff, U.}, + Doi = {10.1103/PhysRevLett.62.361}, + Issue = {4}, + Journal = {Phys. Rev. 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Phys.}, + Keywords = {density functional theory; variational techniques; electron affinity; negative ions}, + Number = {6}, + Pages = {2978-2990}, + Publisher = {AIP}, + Title = {Density-functional theory calculations with correct long-range potentials}, + Url = {http://link.aip.org/link/?JCP/119/2978/1}, + Volume = {119}, + Year = {2003}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/119/2978/1}} + +@article{WuCheVoo-JCP-07, + Author = {{Q. Wu, C.-L. Cheng, and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {164119}, + Title = {Configuration interaction based on constrained density functional theory: A multireference method}, + Volume = {127}, + Year = {2007}} + +@article{WuKadVoo-JCP-09, + Author = {{Q. Wu, B. Kaduk, and T. Van Voorhis}}, + Journal = {J. Chem. Phys.}, + Pages = {034109}, + Volume = {130}, + Year = {2009}} + +@incollection{Wul-INC-10, + Address = {Netherlands}, + Author = {{C. van W\"ullen}}, + Booktitle = {Relativistic Methods for Chemists, Challenges and Advances in Computational Chemistry and Physics 10}, + Editor = {M. Barysz and Y. Ishikawa}, + Pages = {191-214}, + Publisher = {Springer}, + Title = {RELATIVISTIC DENSITY FUNCTIONAL THEORY}, + Year = {2010}} + +@article{WuSha-CPL-99, + Author = {W. Wu and S. Shaik}, + Journal = {Chem. Phys. Lett.}, + Pages = {37}, + Volume = {301}, + Year = {1999}} + +@article{WuShaHib-xx, + Author = {P. Su and J. Wu. and J. Gu and W. Wu and S. Shaik and P. C. Hiberty}, + Journal = {J. Chem. Theory Comput.}, + Pages = {121}, + Volume = {7}, + Year = {2011}} + +@article{WuSonCaoZhaSha-JPCA-02, + Author = {W. Wu and L. Song and Z. Cao and Q. Zhang and S. Shaik}, + Journal = {J. Phys. Chem. A}, + Pages = {2721}, + Volume = {106}, + Year = {2002}} + +@article{WuVarNayLotSco-JCP-01, + Author = {X. Wu and M. C. Vargas and S. Nayak and V. Lotrich and G. Scoles}, + Journal = {J. Chem. Phys.}, + Pages = {8748}, + Volume = {115}, + Year = {2001}} + +@article{WuWuMo-IJQC-98, + Author = {W. Wu and A. Wu and Y. Mo and M. Lin and Q. Zhang}, + Journal = {Int. J. Quantum Chem.}, + Pages = {287}, + Volume = {67}, + Year = {1998}} + +@article{WuYan-JCP-02, + Author = {Q. Wu and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {515}, + Volume = {116}, + Year = {2002}} + +@article{WuYan-JCP-03, + Author = {Qin Wu and Weitao Yang}, + Journal = {J. Chem. Phys.}, + Number = {6}, + Pages = {2498-2509}, + Title = {A direct optimization method for calculating density functionals and exchange--correlation potentials from electron densities}, + Volume = {118}, + Year = {2003}} + +@article{xantheas:8054, + Author = {Sotiris S. Xantheas and Gregory J. Atchity and Stephen T. Elbert and Klaus Ruedenberg}, + Journal = {The Journal of Chemical Physics}, + Keywords = {OZONE; ELECTRONIC STRUCTURE; POTENTIAL ENERGY; SELF–CONSISTENT FIELD; CONFIGURATION INTERACTION; POTENTIAL ENERGY SURFACES; QUANTUM CHEMISTRY}, + Number = {12}, + Pages = {8054-8069}, + Publisher = {AIP}, + Title = {Potential energy surfaces of ozone. I}, + Url = {http://link.aip.org/link/?JCP/94/8054/1}, + Volume = {94}, + Year = {1991}, + Bdsk-Url-1 = {http://link.aip.org/link/?JCP/94/8054/1}} + +@article{YamKocTen-JCP-07, + Author = {D. Yamaki and H. Koch and S. Ten-no}, + Journal = {J. Chem. Phys.}, + Pages = {144104}, + Volume = {127}, + Year = {2007}} + +@article{YamNakUkaTakYam-IJQC-06, + Author = {S. Yamanaka and K. Nakata and T. Ukai and T. Takada and K. Yamaguchi}, + Journal = {Int. J. Quantum Chem.}, + Pages = {3312}, + Title = {Multireference Density Functional Theory With Orbital-Dependent Correlation Corrections}, + Volume = {106}, + Year = {2006}} + +@article{YanAyeWu-PRL-04, + Author = {Weitao Yang and Paul W. Ayers and Qin Wu}, + Journal = {Phys. Rev. Lett.}, + Pages = {146404}, + Volume = {92}, + Year = {2003}} + +@article{YanCohMor-JCP-12, + Author = {Weitao Yang and Aron J. Cohen and Paula Mori-S\'anchez}, + Journal = {J. Chem. Phys.}, + Pages = {204111}, + Volume = {136}, + Year = {2012}} + +@article{YanHarHan-MP-05, + Author = {T. Yanai and R. J. Harrison and N. C. Handy}, + Journal = {Mol. Phys.}, + Pages = {413}, + Volume = {103}, + Year = {2005}} + +@article{Yan-JCP-98, + Author = {W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {10107}, + Title = {Generalized adiabatic connection in density functional theory}, + Volume = {{109}}, + Year = {1998}} + +@article{YanMorCoh-JCP-13, + Author = {W. Yang and P. Mori-S{\'a}nchez and A. J. Cohen}, + Journal = {J. Chem. Phys.}, + Pages = {104114}, + Volume = {139}, + Year = {2013}} + +@article{YanPerKur-PRB-00, + Author = {Yan, Z. and Perdew, J. P. and Kurth, S.}, + Journal = {Phys. Rev. B.}, + Pages = {16430-16439}, + Title = {Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes}, + Volume = {61}, + Year = {2000}} + +@article{YanTewHan-CPL-04, + Author = {Takeshi Yanai and David P. Tew and Nicholas C. Handy}, + Journal = {Chem. Phys. Lett.}, + Pages = {51}, + Volume = {393}, + Year = {2004}} + +@article{YanWu-PRL-02, + Author = {Weitao Yang and Qin Wu}, + Journal = {Phys. Rev. Lett.}, + Pages = {143002}, + Title = {Direct Method for Optimized Effective Potentials in Density-Functional Theory}, + Volume = {89}, + Year = {2002}} + +@article{YanZhaAye-PRL-00, + Author = {Weitao Yang and Yingkai Zhang and Paul W. Ayers}, + Journal = {Phys. Rev. Lett.}, + Pages = {5172}, + Volume = {84}, + Year = {2000}} + +@article{Yar-CPL-81, + Author = {D. R. Yarkony}, + Journal = {Chem. Phys. Lett.}, + Pages = {634}, + Volume = {77}, + Year = {1981}} + +@article{Yas-PRL-02, + Author = {Koji Yasuda}, + Eid = {053001}, + Journal = {Physical Review Letters}, + Keywords = {density functional theory; electron density; electron correlations; Schrodinger equation; scaling phenomena; electron gas}, + Number = {5}, + Numpages = {4}, + Pages = {053001}, + Publisher = {APS}, + Title = {Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory}, + Url = {http://link.aps.org/abstract/PRL/v88/e053001}, + Volume = {88}, + Year = {2002}, + Bdsk-Url-1 = {http://link.aps.org/abstract/PRL/v88/e053001}} + +@article{YeaJor-JCP-79, + Author = {D. L. Yeager and P. J{\o}rgensen}, + Journal = {J. Chem. Phys.}, + Pages = {755}, + Volume = {{71}}, + Year = {1979}} + +@article{YinSuCheShaWu-JCTC-12, + Author = {F. Ying and P. Su and Z. Chen and S. Shaik and W. Wu}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1608}, + Volume = {8}, + Year = {2012}} + +@article{Yu-IJQC-13, + Author = {F. Yu}, + Journal = {Int. J. Quantum Chem.}, + Pages = {2355}, + Volume = {113}, + Year = {2013}} + +@article{ZahLeaGor-JCP-13, + Author = {F. Zahariev and S. S. Leang and M. S. Gordon}, + Journal = {J. Chem. Phys.}, + Pages = {244108}, + Volume = {138}, + Year = {2013}} + +@book{ZalPapMezLes-BOOK-11, + Address = {Netherlands}, + Editor = {R. Zalesny and M. G. Papadopoulos and P. G. Mezey and J. Leszczynski}, + Publisher = {Springer}, + Series = {Challenges and Advances in Computational Chemistry and Physics Vol. 13}, + Title = {Linear-Scaling Techniques in Computational Chemistry and Physics}, + Year = {2011}} + +@article{ZanSov-PRA-80, + Author = {A. Zangwill and P. Soven}, + Journal = {Phys. Rev. A}, + Pages = {1561}, + Volume = {21}, + Year = {1980}} + +@article{ZarKoh-PRB-76, + Author = {E. Zaremba and W. Kohn}, + Journal = {Phys. Rev. B}, + Pages = {2270}, + Volume = {13}, + Year = {1976}} + +@article{ZecGorMorBac-PRB-04, + Author = {Lorenzo Zecca and Paola Gori-Giorgi and Saverio Moroni and Giovanni B. Bachelet}, + Journal = {Phys. Rev. B}, + Keywords = {density functional theory; Monte Carlo methods; ground states; electron gas; electron density; electron correlations}, + Number = {20}, + Pages = {205127}, + Publisher = {APS}, + Title = {Local density functional for the short-range part of the electron-electron interaction}, + Volume = {70}, + Year = {2004}} + +@article{ZeiMea-MP-77, + Author = {G. D. Zeiss and W. J. Meath}, + Journal = {Mol. Phys.}, + Pages = {1155}, + Volume = {33}, + Year = {1977}} + +@article{ZhaBur-PRA-04, + Author = {F. Zhang and K. Burke}, + Journal = {Phys. Rev. A}, + Pages = {052510}, + Volume = {69}, + Year = {2004}} + +@article{ZhaLuoXu-JCP-10b, + Author = {I. Y. Zhang and Y. Luo and X. Xu}, + Journal = {J. Chem. Phys.}, + Pages = {104105}, + Volume = {133}, + Year = {2010}} + +@article{ZhaLuoXu-JCP-10, + Author = {I. Y. Zhang and Y. Luo and X. Xu}, + Journal = {J. Chem. Phys.}, + Pages = {194105}, + Volume = {132}, + Year = {2010}} + +@article{ZhaLynTru-JPCA-04, + Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar}, + Journal = {J. Phys. Chem. A}, + Pages = {4786}, + Volume = {108}, + Year = {2004}} + +@article{ZhaLynTru-PCCP-05, + Author = {Y. Zhao and B. J. Lynch and D. G. Truhlar}, + Journal = {Phys. Chem. Chem. Phys.}, + Pages = {43}, + Volume = {7}, + Year = {2005}} + +@article{ZhaPar-PRA-92, + Author = {Q. Zhao and R. G. Parr}, + Journal = {Phys. Rev. A.}, + Pages = {2337}, + Volume = {{46}}, + Year = {1992}} + +@article{ZhaSchTru-JCTC-06, + Author = {Y. Zhao and N. E. Schultz and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {364}, + Volume = {2}, + Year = {2006}} + +@article{ZhaSteYan-JCP-13, + Abstract = {We present a dynamical second-order kernel for the Bethe-Salpeter equation to calculate electronic excitation energies. The derivation takes explicitly the functional derivative of the exact second-order self energy with respect to the one-particle Green's function. It includes naturally a frequency dependence, going beyond the adiabatic approximation. Perturbative calculations under the Tamm-Dancoff approximation, using the configuration interaction singles (CIS) eigenvectors, reveal an appreciable improvement over CIS, time-dependent Hartree-Fock, and adiabatic time-dependent density functional theory results. The perturbative results also compare well with equation-of-motion coupled-cluster and experimental results.}, + Author = {Zhang, Du and Steinmann, Stephan N and Yang, Weitao}, + Journal = {J. Chem. Phys.}, + Month = oct, + Number = {15}, + Pages = {154109}, + Pmid = {24160502}, + Publisher = {American Institute of Physics}, + Title = {{Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation.}}, + Volume = {139}, + Year = {2013}} + +@article{ZhaSuBreAdaXu-JCP-12, + Author = {I. Y. Zhang and N. Q. Su and E. A. G. Br\'emond and C. Adamo}, + Journal = {J. Chem. Phys.}, + Pages = {174103}, + Volume = {136}, + Year = {2012}} + +@article{ZhaTru-JCTC-07, + Author = {Y. Zhao and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {289}, + Title = {Density Functionals for Noncovalent Interaction Energies of Biological Importance}, + Volume = {3}, + Year = {2007}} + +@article{ZhaTru-TCA-08, + Author = {Y. Zhao and D. G. Truhlar}, + Journal = {Theor. Chem. Acc.}, + Pages = {215}, + Volume = {120}, + Year = {2008}} + +@article{ZhaWuXu-CC-10, + Author = {I. Y. Zhang and J. Wu and X. Xu}, + Journal = {Chem. Commun.}, + Pages = {3057}, + Volume = {46}, + Year = {2010}} + +@article{ZhaXuGod-PNAS-09, + Author = {{Y. Zhang, X. Xu and W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {4963}, + Volume = {106}, + Year = {2009}} + +@article{ZhaXuGod-PNAS-09_fr, + Author = {{Y. Zhang, X. Xu et W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {4963}, + Volume = {106}, + Year = {2009}} + +@article{ZhaXu-IRPC-11, + Author = {I. Y. Zhang and X. Xu}, + Journal = {Int. Rev. Phys. Chem.}, + Pages = {115}, + Volume = {30}, + Year = {2011}} + +@article{ZhaXu-JPCL-13, + Author = {I. Y. Zhang and X. Xu}, + Journal = {J. Phys. Chem. Lett.}, + Pages = {1669}, + Volume = {4}, + Year = {2013}} + +@article{ZhaXuJunGod-PNAS-11, + Author = {{I. Y. Zhang, X. Xu, Y. Jung, and W. A. Goddard III}}, + Journal = {Proc. Natl. Acad. Sci. U.S.A.}, + Pages = {19896}, + Volume = {108}, + Year = {2011}} + +@article{ZhaYan-JCP-98, + Author = {Y. Zhang and W. Yang}, + Journal = {J. Chem. Phys.}, + Pages = {2604}, + Volume = {109}, + Year = {1998}} + +@article{ZheZhaTru-JCTC-07, + Author = {J. Zheng and Y. Zhao and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {569}, + Volume = {3}, + Year = {2007}} + +@article{ZheZhaTru-JCTC-09, + Author = {J. Zheng and Y. Zhao and D. G. Truhlar}, + Journal = {J. Chem. Theory Comput.}, + Pages = {808}, + Volume = {5}, + Year = {2009}} + +@article{ZhoChu-PRA-09, + Author = {Z. Zhou and S.-I. Chu}, + Journal = {Phys. Rev. A}, + Pages = {053412}, + Volume = {79}, + Year = {2009}} + +@article{ZhuTouSavAng-JCP-10, + Author = {Wuming Zhu and Julien Toulouse and Andreas Savin and J\'anos G. \'Angy\'an}, + Journal = {J. Chem. Phys.}, + Pages = {244108}, + Title = {Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions}, + Volume = {132}, + Year = {2010}} + +@misc{ZhuTouSavAng-JJJ-XX, + Author = {W. Zhu and J. Toulouse and A. Savin and J. G. \'Angy\'an}, + Note = {unpublished}} + +@article{ZieCio-PA-05, + Author = {P. Ziesche and J. Cioslowski}, + Journal = {Physica A}, + Year = {to appear}} + +@article{Zie-JPC-80, + Author = {P. Ziesche}, + Journal = {J. Phys. C}, + Pages = {3625}, + Volume = {13}, + Year = {1980}} + +@article{ZieSetKryAutWan-JCP-09, + Author = {T. Ziegler and M. Seth and M. Krykunov and J. Autschbach and F. Wang}, + Journal = {J. Chem. Phys.}, + Pages = {154102}, + Volume = {130}, + Year = {2009}} + +@article{ZimParKou-JCP-04, + Author = {U. Zimmerli and M. Parrinello and P. Koumoutsakos}, + Journal = {J. Chem. Phys.}, + Pages = {2693}, + Volume = {120}, + Year = {2004}} + +@article{ZimTouZhaMusUmr-JCP-09, + Author = {P. M. Zimmerman and J. Toulouse and Z. Zhang and C. B. Musgrave and C. J. Umrigar}, + Journal = {J. Chem. Phys.}, + Pages = {124103}, + Title = {Excited states of methylene from quantum Monte Carlo}, + Volume = {131}, + Year = {2009}} + +@article{ZucPodMosJezSza-JCP-08, + Author = {P. S. Zuchowski and R. Podeszwa and R. Moszynski and B. Jeziorski and K. Szalewicz}, + Journal = {J. Chem. Phys.}, + Pages = {084101}, + Title = {{Symmetry-adapted perturbation theory utilizing density functional description of monomers for high-spin open-shell complexes}}, + Volume = {129}, + Year = {2008}} + +@article{FerGinTou-JCP-18, + Author = {Fert{\'e},Anthony and Giner,Emmanuel and Toulouse,Julien}, + Date-Modified = {2019-04-07 14:03:44 +0200}, + Doi = {10.1063/1.5082638}, + Journal = {J. Chem. Phys.}, + Number = {8}, + Pages = {084103}, + Title = {Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density}, + Volume = {150}, + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}} + +@article{GoriSav-PRA-06, + Author = {Gori-Giorgi, Paola and Savin, Andreas}, + Doi = {10.1103/PhysRevA.73.032506}, + Issue = {3}, + Journal = {Phys. Rev. A}, + Month = {Mar}, + Numpages = {9}, + Pages = {032506}, + Publisher = {American Physical Society}, + Title = {Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.73.032506}} + +@article{PazMorGorBac-PRB-06, + Author = {Paziani, Simone and Moroni, Saverio and Gori-Giorgi, Paola and Bachelet, Giovanni B.}, + Date-Modified = {2019-04-07 14:56:44 +0200}, + Doi = {10.1103/PhysRevB.73.155111}, + Issue = {15}, + Journal = {Phys. Rev. B}, + Month = {Apr}, + Numpages = {9}, + Pages = {155111}, + Publisher = {American Physical Society}, + Title = {Local-spin-density functional for multideterminant density functional theory}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.73.155111}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.73.155111}} + +@article{GinTewGarAla-JCTC-18, + Author = {Giner, Emmanuel and Tew, David P. and Garniron, Yann and Alavi, Ali}, + Doi = {10.1021/acs.jctc.8b00591}, + Eprint = {https://doi.org/10.1021/acs.jctc.8b00591}, + Journal = {Journal of Chemical Theory and Computation}, + Note = {PMID: 30347156}, + Number = {12}, + Pages = {6240-6252}, + Title = {Interplay between Electronic Correlation and Metal--Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes}, + Url = {https://doi.org/10.1021/acs.jctc.8b00591}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}} + +@article{LooBogSceCafJAc-JCTC-19, + Author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis}, + Date-Modified = {2019-04-07 14:02:34 +0200}, + Doi = {10.1021/acs.jctc.8b01205}, + Journal = {J. Chem. Theory Comput.}, + Number = {3}, + Pages = {1939-1956}, + Title = {Reference Energies for Double Excitations}, + Volume = {15}, + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01205}} + +@article{LooSceBloGarCafJac-JCTC-18, + Author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Blondel, Aymeric and Garniron, Yann and Caffarel, Michel and Jacquemin, Denis}, + Date-Modified = {2019-04-07 14:03:07 +0200}, + Doi = {10.1021/acs.jctc.8b00406}, + Journal = {J. Chem. Theory Comput.}, + Number = {8}, + Pages = {4360-4379}, + Title = {A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} + +@article{HolUmrSha-JCP-17, + Author = {Holmes,Adam A. and Umrigar,C. J. and Sharma,Sandeep}, + Doi = {10.1063/1.4998614}, + Eprint = {https://doi.org/10.1063/1.4998614}, + Journal = {J. Chem. Phys.}, + Number = {16}, + Pages = {164111}, + Title = {Excited states using semistochastic heat-bath configuration interaction}, + Url = {https://doi.org/10.1063/1.4998614}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4998614}} + +@article{stochastic_pt_yan, + Author = {Yann Garniron and Anthony Scemama and Pierre-Fran{\c c}ois Loos and Michel Caffarel}, + Doi = {10.1063/1.4992127}, + Journal = {J. Chem. Phys.}, + Number = {3}, + Pages = {034101}, + Title = {Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory}, + Url = {https://doi.org/10.1063/1.4992127}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4992127}} + +@article{GorSav-PRA-06, + Author = {Gori-Giorgi, Paola and Savin, Andreas}, + Doi = {10.1103/PhysRevA.73.032506}, + Issue = {3}, + Journal = {Phys. Rev. A}, + Month = {Mar}, + Numpages = {9}, + Pages = {032506}, + Publisher = {American Physical Society}, + Title = {Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence}, + Url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.73.032506}} + +@article{HalHelJorKloKocOlsWil-CPL-98, + Abstract = {Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.}, + Author = {Asger Halkier and Trygve Helgaker and Poul J{\o}rgensen and Wim Klopper and Henrik Koch and Jeppe Olsen and Angela K. Wilson}, + Date-Modified = {2019-04-07 14:59:22 +0200}, + Doi = {https://doi.org/10.1016/S0009-2614(98)00111-0}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Number = {3}, + Pages = {243 - 252}, + Title = {Basis-set convergence in correlated calculations on Ne, N2, and H2O}, + Url = {http://www.sciencedirect.com/science/article/pii/S0009261498001110}, + Volume = {286}, + Year = {1998}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261498001110}, + Bdsk-Url-2 = {https://doi.org/10.1016/S0009-2614(98)00111-0}} + +@article{DasHer-JCC-17, + Author = {Dasgupta, Saswata and Herbert, John M.}, + Doi = {10.1002/jcc.24761}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.24761}, + Journal = {J. Comput. Chem.}, + Number = {12}, + Pages = {869-882}, + Title = {Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3}, + Volume = {38}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1002/jcc.24761}} + +@article{Tenno-CPL-04, + Abstract = {We employ the Slater-type function as a geminal basis function to incorporate the inter-electron distance in explicitly correlated theory. It is shown that the use of the Slater-type geminals confers numerical and computational advantages over the previous explicitly correlated methods. The performance of the resulting method is examined in some benchmark calculations at the second order M{\o}ller--Plesset perturbation theory. The results reveal that the Slater-type function is promising compared to the ordinary Gaussian-type geminals and linear r12 function.}, + Author = {Seiichiro Ten-no}, + Doi = {https://doi.org/10.1016/j.cplett.2004.09.041}, + Issn = {0009-2614}, + Journal = {Chem. Phys. Lett.}, + Number = {1}, + Pages = {56 - 61}, + Title = {Initiation of explicitly correlated Slater-type geminal theory}, + Url = {http://www.sciencedirect.com/science/article/pii/S000926140401379X}, + Volume = {398}, + Year = {2004}, + Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S000926140401379X}, + Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2004.09.041}} diff --git a/JPCL_revision/G2-srDFT.tex b/JPCL_revision/G2-srDFT.tex new file mode 100644 index 0000000..e67ec7f --- /dev/null +++ b/JPCL_revision/G2-srDFT.tex @@ -0,0 +1,525 @@ +\documentclass[aip,jcp,preprint,noshowkeys]{revtex4-1} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,xspace,wrapfig} +\usepackage{mathpazo,libertine} + +\usepackage{natbib} +\bibliographystyle{achemso} +\AtBeginDocument{\nocite{achemso-control}} + +\newcommand{\alert}[1]{\textcolor{red}{#1}} +\definecolor{darkgreen}{HTML}{009900} +\usepackage[normalem]{ulem} +\newcommand{\titou}[1]{\textcolor{red}{#1}} +\newcommand{\juju}[1]{\textcolor{purple}{#1}} +\newcommand{\manu}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\toto}[1]{\textcolor{brown}{#1}} +\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} +\newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}} +\newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}} +\newcommand{\trashAS}[1]{\textcolor{brown}{\sout{#1}}} +\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}} +\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}} +\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} +\newcommand{\AS}[1]{\toto{(\underline{\bf TOTO}: #1)}} + +\usepackage{hyperref} +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, + citecolor=blue +} +\newcommand{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\SI}{\textcolor{blue}{supporting information}} +\newcommand{\QP}{\textsc{quantum package}} + +% second quantized operators +\newcommand{\ai}[1]{\hat{a}_{#1}} +\newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\InAA}[1]{#1 \AA} +\newcommand{\kcal}{kcal/mol} + +% methods +\newcommand{\D}{\text{D}} +\newcommand{\T}{\text{T}} +\newcommand{\Q}{\text{Q}} +\newcommand{\X}{\text{X}} +\newcommand{\UEG}{\text{UEG}} +\newcommand{\HF}{\text{HF}} +\newcommand{\ROHF}{\text{ROHF}} +\newcommand{\LDA}{\text{LDA}} +\newcommand{\PBE}{\text{PBE}} +\newcommand{\FCI}{\text{FCI}} +\newcommand{\CBS}{\text{CBS}} +\newcommand{\exFCI}{\text{exFCI}} +\newcommand{\CCSDT}{\text{CCSD(T)}} +\newcommand{\lr}{\text{lr}} +\newcommand{\sr}{\text{sr}} + +\newcommand{\Ne}{N} +\newcommand{\NeUp}{\Ne^{\uparrow}} +\newcommand{\NeDw}{\Ne^{\downarrow}} +\newcommand{\Nb}{N_{\Bas}} +\newcommand{\Ng}{N_\text{grid}} +\newcommand{\nocca}{n_{\text{occ}^{\alpha}}} +\newcommand{\noccb}{n_{\text{occ}^{\beta}}} + +\newcommand{\n}[2]{n_{#1}^{#2}} +\newcommand{\Ec}{E_\text{c}} +\newcommand{\E}[2]{E_{#1}^{#2}} +\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}} +\newcommand{\bEc}[1]{\Bar{E}_\text{c,md}^{#1}} +\newcommand{\e}[2]{\varepsilon_{#1}^{#2}} +\newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}} +\newcommand{\bec}[1]{\Bar{e}^{#1}} +\newcommand{\wf}[2]{\Psi_{#1}^{#2}} +\newcommand{\W}[2]{W_{#1}^{#2}} +\newcommand{\w}[2]{w_{#1}^{#2}} +\newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}} +\newcommand{\rsmu}[2]{\mu_{#1}^{#2}} +\newcommand{\V}[2]{V_{#1}^{#2}} +\newcommand{\SO}[2]{\phi_{#1}(\br{#2})} + +\newcommand{\modY}{Y} +\newcommand{\modZ}{Z} + +% basis sets +\newcommand{\Bas}{\mathcal{B}} +\newcommand{\BasFC}{\mathcal{A}} +\newcommand{\FC}{\text{FC}} +\newcommand{\occ}{\text{occ}} +\newcommand{\virt}{\text{virt}} +\newcommand{\val}{\text{val}} +\newcommand{\Cor}{\mathcal{C}} + +% operators +\newcommand{\hT}{\Hat{T}} +\newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}} +\newcommand{\updw}{\uparrow\downarrow} +\newcommand{\f}[2]{f_{#1}^{#2}} +\newcommand{\Gam}[2]{\Gamma_{#1}^{#2}} + +% coordinates +\newcommand{\br}[1]{\mathbf{r}_{#1}} +\newcommand{\dbr}[1]{d\br{#1}} + +\newcommand{\ra}{\rightarrow} + +% frozen core +\newcommand{\WFC}[2]{\widetilde{W}_{#1}^{#2}} +\newcommand{\fFC}[2]{\widetilde{f}_{#1}^{#2}} +\newcommand{\rsmuFC}[2]{\widetilde{\mu}_{#1}^{#2}} +\newcommand{\nFC}[2]{\widetilde{n}_{#1}^{#2}} + + +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Sorbonne Universit\'e, CNRS, Paris, France} +\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France} + + +\begin{document} + +\title{A Density-Based Basis-Set Correction For Wave Function Theory} + +\author{Pierre-Fran\c{c}ois Loos} +\email{loos@irsamc.ups-tlse.fr} +\affiliation{\LCPQ} +\author{Bath\'elemy Pradines} +\affiliation{\LCT} +\affiliation{\ISCD} +\author{Anthony Scemama} +\affiliation{\LCPQ} +\author{Julien Toulouse} +\email{toulouse@lct.jussieu.fr} +\affiliation{\LCT} +\author{Emmanuel Giner} +\email{emmanuel.giner@lct.jussieu.fr} +\affiliation{\LCT} + +\begin{abstract} +\begin{wrapfigure}[7]{o}[-1.2cm]{0.4\linewidth} + \centering + \includegraphics[width=\linewidth]{TOC} +\end{wrapfigure} +We report a universal density-based basis-set incompleteness correction that can be applied to any wave function method. +The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error. +Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ that automatically adapts to the spatial non-homogeneity of the basis-set incompleteness error. +As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets. +\end{abstract} + +\maketitle + +%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Introduction} +%%%%%%%%%%%%%%%%%%%%%%%% +Contemporary quantum chemistry has developed in two directions --- wave function theory (WFT) \cite{Pop-RMP-99} and density-functional theory (DFT). \cite{Koh-RMP-99} +Although both spring from the same Schr\"odinger equation, each of these philosophies has its own \textit{pros} and \textit{cons}. + +WFT is attractive as it exists a well-defined path for systematic improvement as well as powerful tools, such as perturbation theory, to guide the development of new WFT \textit{ans\"atze}. +The coupled cluster (CC) family of methods is a typical example of the WFT philosophy and is well regarded as the gold standard of quantum chemistry for weakly correlated systems. +By increasing the excitation degree of the CC expansion, one can systematically converge, for a given basis set, to the exact, full configuration interaction (FCI) limit, although the computational cost associated with such improvement is usually high. +One of the most fundamental drawbacks of conventional WFT methods is the slow convergence of energies and properties with respect to the size of the one-electron basis set. +This undesirable feature was put into light by Kutzelnigg more than thirty years ago. \cite{Kut-TCA-85} +To palliate this, following Hylleraas' footsteps, \cite{Hyl-ZP-29} Kutzelnigg proposed to introduce explicitly the interelectronic distance $r_{12} = \abs{\br{1} - \br{2}}$ to properly describe the electronic wave function around the coalescence of two electrons. \cite{Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94} +The resulting F12 methods yield a prominent improvement of the energy convergence, and achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12, GruHirOhnTen-JCP-17, MaWer-WIREs-18} +For example, at the CCSD(T) level, one can obtain quintuple-$\zeta$ quality correlation energies with a triple-$\zeta$ basis, \cite{TewKloNeiHat-PCCP-07} although computational overheads are introduced by the large auxiliary basis used to resolve three- and four-electron integrals. \cite{BarLoo-JCP-17} +To reduce further the computational cost and/or ease the transferability of the F12 correction, approximated and/or universal schemes have recently emerged. \cite{TorVal-JCP-09, KonVal-JCP-10, KonVal-JCP-11, BooCleAlaTew-JCP-2012, IrmHumGru-arXiv-2019, IrmGru-arXiv-2019} + +Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. \cite{KohSha-PR-65} +The attractiveness of DFT originates from its very favorable accuracy/cost ratio as it often provides reasonably accurate energies and properties at a relatively low computational cost. +Thanks to this, KS-DFT \cite{HohKoh-PR-64, KohSha-PR-65} has become the workhorse of electronic structure calculations for atoms, molecules and solids. \cite{ParYan-BOOK-89} +Although there is no clear way on how to systematically improve density-functional approximations, \cite{Bec-JCP-14} climbing Perdew's ladder of DFT is potentially the most satisfactory way forward. \cite{PerSch-AIPCP-01, PerRuzTaoStaScuCso-JCP-05} +In the context of the present work, one of the interesting feature of density-based methods is their much faster convergence with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15} + +Progress toward unifying WFT and DFT are on-going. +In particular, range-separated DFT (RS-DFT) (see Ref.~\onlinecite{TouColSav-PRA-04} and references therein) rigorously combines these two approaches via a decomposition of the electron-electron (e-e) interaction into a non-divergent long-range part and a (complementary) short-range part treated with WFT and DFT, respectively. +As the WFT method is relieved from describing the short-range part of the correlation hole around the e-e coalescence points, the convergence with respect to the one-electron basis set is greatly improved. \cite{FraMusLupTou-JCP-15} +Therefore, a number of approximate RS-DFT schemes have been developed within single-reference \cite{AngGerSavTou-PRA-05, GolWerSto-PCCP-05, TouGerJanSavAng-PRL-09,JanHenScu-JCP-09, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15} or multi-reference \cite{LeiStoWerSav-CPL-97, FroTouJen-JCP-07, FroCimJen-PRA-10, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-18} WFT approaches. +Very recently, a major step forward has been taken by some of the present authors thanks to the development of a density-based basis-set correction for WFT methods. \cite{GinPraFerAssSavTou-JCP-18} +The present work proposes an extension of this new methodological development alongside the first numerical tests on molecular systems. + +%%%%%%%%%%%%%%%%%%%%%%%% +%\section{Theory} +%%%%%%%%%%%%%%%%%%%%%%%% +The present basis-set correction relies on the RS-DFT formalism to capture the missing part of the short-range correlation effects, a consequence of the incompleteness of the one-electron basis set. +Here, we only provide the main working equations. +We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} for a more formal derivation. + +Let us assume we have both the energy $\E{\modY}{\Bas}$ and density $\n{\modZ}{\Bas}$ of a $\Ne$-electron system described by two methods $\modY$ and $\modZ$ (potentially identical) in an incomplete basis set $\Bas$. +According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that $\E{\modY}{\Bas}$ and $\n{\modZ}{\Bas}$ are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as +\begin{equation} + \label{eq:e0basis} + \E{}{} + \approx \E{\modY}{\Bas} + + \bE{}{\Bas}[\n{\modZ}{\Bas}], +\end{equation} +where +\begin{equation} + \label{eq:E_funcbasis} + \bE{}{\Bas}[\n{}{}] + = \min_{\wf{}{} \to \n{}{}} \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}} + - \min_{\wf{}{\Bas} \to \n{}{}} \mel*{\wf{}{\Bas}}{\hT + \hWee{}}{\wf{}{\Bas}} +\end{equation} +is the basis-dependent complementary density functional, $\hT$ is the kinetic operator and $\hWee{} = \sum_{il000;ztnFOQoq8N{hw+H+1jPXzsO6<^2k&Qs3PCb?LGTH{ywI*2>w~W zeoXzKJ^c8)y%qY#)cwbj{=@XouaDM0ra* zWSlOv`xv)&lKYo_MrbQ+E%l=_<|$24qUzBFdrmhk#iyeB!y8SA@V7CIW3J;zq2C2G z^MNPP+zAuLoOsNgE0N4S5rz~NJ3>GI!W5fYh^w-TTvO=p3X%3QRhlQR=WdzUG4${>FtaQ1xp8R1VzHENa{3zuGKS3OjTeJ!y2d^7kMneyVW zOMNmh0%I6(^S73=uC1BIJw67ETkQ13m#sYKN6-_c2BeNYb8HmZ^C?O&m8vglj1EWd8ws z#+{7(WQ6)8chZhpOGaBlLdhE&T})&-M|)BWb$r^lZuKdIWR$A+I@^3}k|J6$iW}F1 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