From 0490f035c8877e23e013616927e4c25fb2d54e9a Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Sun, 7 Apr 2019 14:05:34 +0200 Subject: [PATCH] 2 extra comments --- Manuscript/G2-srDFT.bib | 113 +++++++++++++++++++++++++++------------- Manuscript/G2-srDFT.tex | 23 ++++---- 2 files changed, 90 insertions(+), 46 deletions(-) diff --git a/Manuscript/G2-srDFT.bib b/Manuscript/G2-srDFT.bib index 80832c0..e8ecea7 100644 --- a/Manuscript/G2-srDFT.bib +++ b/Manuscript/G2-srDFT.bib @@ -1,13 +1,53 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2019-04-03 22:18:33 +0200 +%% Created for Pierre-Francois Loos at 2019-04-07 14:04:11 +0200 %% Saved with string encoding Unicode (UTF-8) +@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}, + Date-Modified = {2019-04-07 14:01:12 +0200}, + Note = {\uppercase{G}aussian Inc. Wallingford CT}, + Title = {Gaussian~09 \uppercase{R}evision {D}.01}, + Year = 2009} + +@article{HauJanScu-JCP-09, + 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}, + Journal = {J. Chem. Phys.}, + Pages = {154112}, + Title = {Local hybrids as a perturbation to global hybrid functionals}, + Volume = {131}, + Year = {2009}} + +@article{SceGarCafLoo-JCTC-18, + Author = {A. Scemama and Y. Garniron and M. Caffarel and P. F. Loos}, + Date-Added = {2019-04-07 13:55:03 +0200}, + Date-Modified = {2019-04-07 13:55:23 +0200}, + Doi = {10.1021/acs.jctc.7b01250}, + Journal = {J. Chem. 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. Csonka}, Date-Added = {2019-04-03 22:17:53 +0200}, @@ -6886,8 +6926,9 @@ @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.}, - Note = {doi: 10.1002/wcms.1257}, Pages = {410}, Title = {The uniform electron gas}, Volume = {6}, @@ -11882,13 +11923,12 @@ @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}, - Eprint = {https://doi.org/10.1063/1.5082638}, - Journal = {The Journal of Chemical Physics}, + 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}, - Url = {https://doi.org/10.1063/1.5082638}, Volume = {150}, Year = {2019}, Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}} @@ -11941,27 +11981,24 @@ @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}, - Eprint = {https://doi.org/10.1021/acs.jctc.8b01205}, - Journal = {Journal of Chemical Theory and Computation}, + Journal = {J. Chem. Theory Comput.}, Number = {3}, Pages = {1939-1956}, Title = {Reference Energies for Double Excitations}, - Url = {https://doi.org/10.1021/acs.jctc.8b01205}, 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}, - Eprint = {https://doi.org/10.1021/acs.jctc.8b00406}, - Journal = {Journal of Chemical Theory and Computation}, - Note = {PMID: 29966098}, + Journal = {J. Chem. Theory Comput.}, Number = {8}, Pages = {4360-4379}, Title = {A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks}, - Url = {https://doi.org/10.1021/acs.jctc.8b00406}, Volume = {14}, Year = {2018}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} @@ -11992,30 +12029,32 @@ Bdsk-Url-1 = {https://doi.org/10.1063/1.4992127}} @article{GorSav-PRA-06, - title = {Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence}, - author = {Gori-Giorgi, Paola and Savin, Andreas}, - journal = {Phys. Rev. A}, - volume = {73}, - issue = {3}, - pages = {032506}, - numpages = {9}, - year = {2006}, - month = {Mar}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevA.73.032506}, - url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506} -} + 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{HalHelJorKloKocOls-CPL-98, - title = "Basis-set convergence in correlated calculations on Ne, N2, and H2O", - journal = "Chemical Physics Letters", - volume = "286", - number = "3", - pages = "243 - 252", - year = "1998", - issn = "0009-2614", - doi = "https://doi.org/10.1016/S0009-2614(98)00111-0", - url = "http://www.sciencedirect.com/science/article/pii/S0009261498001110", - author = "Asger Halkier and Trygve Helgaker and Poul Jørgensen and Wim Klopper and Henrik Koch and Jeppe Olsen and Angela K. Wilson", - 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." -} + 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}, + Doi = {https://doi.org/10.1016/S0009-2614(98)00111-0}, + Issn = {0009-2614}, + Journal = {Chemical Physics Letters}, + 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}} diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index 0350580..ec6732b 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -60,7 +60,9 @@ \newcommand{\lr}{\text{lr}} \newcommand{\sr}{\text{sr}} -\newcommand{\Nel}{N} +\newcommand{\Ne}{N} +\newcommand{\Nb}{N_{\Bas}} +\newcommand{\Ng}{N_\text{grid}} \newcommand{\n}[2]{n_{#1}^{#2}} \newcommand{\Ec}{E_\text{c}} @@ -170,7 +172,7 @@ We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} fo %================================================================= %\subsection{Correcting the basis set error of a general WFT model} %================================================================= -Let us assume we have both the energy $\E{\modX}{\Bas}$ and density $\n{\modY}{\Bas}$ of a $\Nel$-electron system described by two methods $\modX$ and $\modY$ (potentially identical) in an incomplete basis set $\Bas$. +Let us assume we have both the energy $\E{\modX}{\Bas}$ and density $\n{\modY}{\Bas}$ of a $\Ne$-electron system described by two methods $\modX$ and $\modY$ (potentially identical) in an incomplete basis set $\Bas$. According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that $\E{\modX}{\Bas}$ and $\n{\modY}{\Bas}$ are reasonable approximations of the \titou{FCI} energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be written as \begin{equation} \label{eq:e0basis} @@ -186,7 +188,7 @@ where - \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_{i