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Manuscript/G2-srDFT.bib
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@ -1,13 +1,98 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2019-04-07 14:04:11 +0200
%% Created for Pierre-Francois Loos at 2019-04-07 14:40:55 +0200
%% Saved with string encoding Unicode (UTF-8)
@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. Sonnenberg and M. Hada and M. Ehara and K. Toyota and R. Fukuda and J. Hasegawa and M. Ishida and T. Nakajima and Y. Honda and O. Kitao and H. Nakai and T. Vreven and Montgomery, {Jr.}, J. A. and J. E. Peralta and F. Ogliaro and M. Bearpark and J. J. Heyd and E. Brothers and K. N. Kudin and V. N. Staroverov and R. Kobayashi and J. Normand and K. Raghavachari and A. Rendell and J. C. Burant and S. S. Iyengar and J. Tomasi and M. Cossi and N. Rega and J. M. Millam and M. Klene and J. E. Knox and J. B. Cross and V. Bakken and C. Adamo and J. Jaramillo and R. Gomperts and R. E. Stratmann and O. Yazyev and A. J. Austin and R. Cammi and C. Pomelli and J. W. Ochterski and R. L. Martin and K. Morokuma and V. G. Zakrzewski and G. A. Voth and P. Salvador and J. J. Dannenberg and S. Dapprich and A. D. Daniels and O. Farkas and J. B. Foresman and J. V. Ortiz and J. Cioslowski and D. J. Fox},
Date-Added = {2019-04-07 14:01:06 +0200},
@ -17,7 +102,7 @@
Year = 2009}
@article{HauJanScu-JCP-09,
Author = {R. Haunschild and B. G. Janesko and G. E. Scuseria},
Author = {R. Haunschild and B. G. Janesko and G. E. Scuseria},
Date-Added = {2019-04-07 13:56:11 +0200},
Date-Modified = {2019-04-07 13:57:34 +0200},
Doi = {10.1063/1.3247288},
@ -25,7 +110,8 @@
Pages = {154112},
Title = {Local hybrids as a perturbation to global hybrid functionals},
Volume = {131},
Year = {2009}}
Year = {2009},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3247288}}
@article{SceGarCafLoo-JCTC-18,
Author = {A. Scemama and Y. Garniron and M. Caffarel and P. F. Loos},
@ -69,18 +155,20 @@
@article{KonBisVal-CR-12,
Author = {L. Kong and F. A. Bischo and E. F. Valeev},
Date-Added = {2019-04-03 21:44:11 +0200},
Date-Modified = {2019-04-03 21:44:25 +0200},
Date-Modified = {2019-04-07 14:36:39 +0200},
Journal = {Chem. 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 = {2019-04-03 21:43:44 +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}}
@ -151,18 +239,20 @@
@article{TenNog-WIREs-12,
Author = {S. Ten-no and J. Noga},
Date-Added = {2019-04-03 21:40:52 +0200},
Date-Modified = {2019-04-03 21:41:22 +0200},
Date-Modified = {2019-04-07 14:35:25 +0200},
Journal = {WIREs Comput. Mol. Sci.},
Pages = {114},
Title = {Explicitly correlated electronic structure theory from R12/F12 ansatze},
Volume = {2},
Year = {2012}}
@article{Ten-TCA-12,
Author = {S. Ten-no},
Date-Added = {2019-04-03 21:40:52 +0200},
Date-Modified = {2019-04-03 21:41:01 +0200},
Date-Modified = {2019-04-07 14:34:33 +0200},
Journal = {Theor. Chem. Acc.},
Pages = {1070},
Title = {Explicitly correlated wave functions: summary and perspective},
Volume = {131},
Year = {2012}}
@ -205,18 +295,20 @@
@article{TewKloNeiHat-PCCP-07,
Author = {D. P. Tew and W. Klopper and C. Neiss and C. Hattig},
Date-Added = {2019-04-03 21:38:34 +0200},
Date-Modified = {2019-04-03 21:38:49 +0200},
Date-Modified = {2019-04-07 14:39:25 +0200},
Journal = {Phys. Chem. Chem. Phys.},
Pages = {1921},
Title = {Quintuple-{{$\zeta$}} quality coupled-cluster correlation energies with triple-{{$\zeta$}} basis sets},
Volume = {9},
Year = {2007}}
@article{NogKut-JCP-94,
Author = {J. Noga and W. Kutzelnigg},
Date-Added = {2019-04-03 21:37:47 +0200},
Date-Modified = {2019-04-03 21:37:55 +0200},
Date-Modified = {2019-04-07 14:32:34 +0200},
Journal = {J. Chem. Phys.},
Pages = {7738},
Title = {Coupled cluster theory that takes care of the correlation cusp by inclusion of linear terms in the interelectronic coordinates},
Volume = {101},
Year = {1994}}
@ -250,18 +342,20 @@
@article{KutKlo-JCP-91,
Author = {W. Kutzelnigg and W. Klopper},
Date-Added = {2019-04-03 21:35:04 +0200},
Date-Modified = {2019-04-03 21:35:52 +0200},
Date-Modified = {2019-04-07 14:31:15 +0200},
Journal = {J. Chem. Phys.},
Pages = {1985},
Title = {Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory},
Volume = {94},
Year = {1991}}
@article{Kut-TCA-85,
Author = {W. Kutzelnigg},
Date-Added = {2019-04-03 21:34:30 +0200},
Date-Modified = {2019-04-03 21:34:37 +0200},
Date-Modified = {2019-04-07 14:30:33 +0200},
Journal = {Theor. Chim. Acta},
Pages = {445},
Title = {r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l},
Volume = {68},
Year = {1985}}
@ -1475,8 +1569,10 @@
@article{BooCleThoAla-JCP-11,
Author = {G. H. Booth and D. Cleland and A. J. W. Thom and A. Alavi},
Date-Modified = {2019-04-07 14:11:52 +0200},
Journal = {J. Chem. Phys.},
Pages = {084104},
Title = {Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods},
Volume = {135},
Year = {2011}}
@ -6932,7 +7028,8 @@
Pages = {410},
Title = {The uniform electron gas},
Volume = {6},
Year = {2016}}
Year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1002/wcms.1257}}
@article{LopGov-JCTC-11,
Author = {K. Lopata and N. Govind},

9
Manuscript/G2-srDFT.tex
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@ -139,8 +139,8 @@ WFT is attractive as it exists a well-defined path for systematic improvement.
For example, the coupled cluster (CC) family of methods offers a powerful WFT approach for the description of weakly correlated systems and is well regarded as the gold standard of quantum chemistry.
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 pricey.
One of the most fundamental drawback 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}
who proposed, to palliate this, to introduce explicitly the interelectronic distance $r_{12} = \abs{\br{1} - \br{2}}$ as a basis function. \cite{Kut-TCA-85, KutKlo-JCP-91, TerKloKut-JCP-91, KloKut-JCP-91, KloRohKut-CPL-91, NogKut-JCP-94}
This undesirable feature was put into light by Kutzelnigg more than thirty years ago. \cite{Kut-TCA-85}
To palliate this, in the Hylleraas' footsteps, \cite{Hyl-ZP-29} Kutzelnigg proposed to introduce explicitly the interelectronic distance $r_{12} = \abs{\br{1} - \br{2}}$ as a basis function. \cite{Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94}
The resulting F12 methods yields 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, it is advertised that 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.
@ -158,6 +158,9 @@ Using accurate and rigorous WFT methods, some of us have developed radical gener
In that respect range-separated DFT (RS-DFT) is particularly promising as it allows to perform multi-configurational DFT calculations within a rigorous mathematical framework.
Range-separated hybrids, i.e.~single-determinant approximations of RS-DFT, correct for the wrong long-range behavior of the usual hybrid approximations thanks to the inclusion of the long-range part of the Hartree-Fock (HF) exchange.
Other basis set corrections are cool too, \cite{TorVal-JCP-09, KonVal-JCP-10, KonVal-JCP-11, BooCleAlaTew-JCP-2012, IrmHumGru-arXiv-2019, IrmGru-arXiv-2019} but not as cool as ours.
%The present manuscript is organized as follows.
Unless otherwise stated, atomic used are used.
@ -675,7 +678,7 @@ Defining $\n{\wf{}{\Bas}}{\Val}$ as the valence one-electron density, the valenc
%\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5).
In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.
\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 test set, whereas \ce{C2} already contains a non-negligible amount of strong correlation.
\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 test set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11}
In a second time, we compute the entire atomization energies of the G2 test sets composed by 55 molecules.
%The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$.
As a method $\modX$ we employ either $\CCSDT$ or $\exFCI$.