diff --git a/Manuscript/rsdft-cipsi-qmc.bib b/Manuscript/rsdft-cipsi-qmc.bib index 8a576c9..891ba10 100644 --- a/Manuscript/rsdft-cipsi-qmc.bib +++ b/Manuscript/rsdft-cipsi-qmc.bib @@ -1,13 +1,55 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-08-20 10:30:22 +0200 +%% Created for Pierre-Francois Loos at 2020-08-20 13:13:29 +0200 %% Saved with string encoding Unicode (UTF-8) +@article{Scuseria_1989, + Author = {G. E. Scuseria and H. F. Schaefer III}, + Date-Added = {2020-08-20 13:12:34 +0200}, + Date-Modified = {2020-08-20 13:13:25 +0200}, + Doi = {10.1063/1.455827}, + Journal = {J. Chem. Phys.}, + Pages = {3700-3703}, + Title = {Is coupled cluster singles and doubles (CCSD) more computationally intensive than quadratic configuration-interaction (QCISD)?}, + Volume = {90}, + Year = {1989}} + +@article{Scuseria_1988, + Author = {G. E. Scuseria, C. L. Janssen, and H. F. Schaefer III}, + Date-Added = {2020-08-20 13:11:43 +0200}, + Date-Modified = {2020-08-20 13:12:29 +0200}, + Doi = {10.1063/1.455269}, + Journal = {J. Chem. Phys.}, + Pages = {7382--7387}, + Title = {An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations}, + Volume = {89}, + Year = {1988}} + +@article{Cizek_1969, + Author = {J. Cizek}, + Date-Added = {2020-08-20 13:07:49 +0200}, + Date-Modified = {2020-08-20 13:10:49 +0200}, + Doi = {10.1002/9780470143599}, + Journal = {Adv. Chem. Phys.}, + Pages = {35}, + Volume = {14}} + +@article{Purvis_1982, + Author = {G. D. Purvis III and R. J. Bartlett}, + Date-Added = {2020-08-20 13:06:17 +0200}, + Date-Modified = {2020-08-20 13:07:06 +0200}, + Doi = {10.1063/1.443164}, + Journal = {J. Chem. Phys.}, + Pages = {1910--1918}, + Title = {A full coupled-cluster singles and doubles model - the inclusion of disconnected triples}, + Volume = {76}, + Year = {1982}} + @article{Perdew_1996, Author = {John P. Perdew and Matthias Ernzerhof and Kieron Burke}, Date-Added = {2020-08-20 10:26:11 +0200}, @@ -41,7 +83,8 @@ Pages = {785}, Title = {Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density}, Volume = {37}, - Year = {1988}} + Year = {1988}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.37.785}} @article{Becke_1993, Author = {A. D. Becke}, @@ -52,7 +95,8 @@ Pages = {5648}, Title = {Density‐functional thermochemistry. III. The role of exact exchange}, Volume = {98}, - Year = {1993}} + Year = {1993}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.464913}} @article{Tubman_2016, Author = {Tubman, Norm M. and Lee, Joonho and Takeshita, Tyler Y. and {Head-Gordon}, Martin and Whaley, K. Birgitta}, diff --git a/Manuscript/rsdft-cipsi-qmc.tex b/Manuscript/rsdft-cipsi-qmc.tex index 3b5e3ce..2354860 100644 --- a/Manuscript/rsdft-cipsi-qmc.tex +++ b/Manuscript/rsdft-cipsi-qmc.tex @@ -177,7 +177,7 @@ determinant. This feature is in part responsible for the success of DFT and coupled cluster (CC) theory. Likewise, DMC with a single-determinant trial wave function can be used as a single-reference post-Hartree-Fock method for weakly correlated systems, with an accuracy comparable -to CCSD(T), \cite{Dubecky_2014,Grossman_2002} the gold standard of WFT for ground state energies. +to CCSD(T), \cite{Dubecky_2014,Grossman_2002} the gold standard of WFT for ground state energies. \cite{Cizek_1969,Purvis_1982} In single-determinant DMC calculations, the only degree of freedom available to reduce the fixed-node error are the molecular orbitals with which the Slater determinant is built. @@ -434,7 +434,7 @@ All calculations have been performed using Burkatzki-Filippi-Dolg (BFD) pseudopotentials \cite{Burkatzki_2007,Burkatzki_2008} with the associated double-, triple-, and quadruple-$\zeta$ basis sets (VXZ-BFD). The small-core BFD pseudopotentials include scalar relativistic effects. -Coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] and KS-DFT energies have been computed with +Coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] \cite{Scuseria_1988,Scuseria_1989} and KS-DFT energies have been computed with \emph{Gaussian09},\cite{g16} using the unrestricted formalism for open-shell systems. The CIPSI calculations have been performed with \emph{Quantum @@ -832,7 +832,7 @@ have converged to the KS orbitals with $\mu=0$, and the solution would have been the PBE single determinant.} For comparison, we have computed the energies of all the atoms and molecules at the KS-DFT level with various semi-local and hybrid density functionals [PBE, \cite{PerBurErn-PRL-96} BLYP, \cite{Becke_1988,Lee_1988} PBE0, \cite{Perdew_1996} and B3LYP \cite{Becke_1993}], and at -the CCSD(T) level. Table~\ref{tab:mad} gives the corresponding mean +the CCSD(T) level. \cite{Cizek_1969,Purvis_1982,Scuseria_1988,Scuseria_1989} Table~\ref{tab:mad} gives the corresponding mean absolute errors (MAEs), mean signed errors (MSEs), and root mean square errors (RMSEs) with respect to the NIST reference values as explained in Sec.~\ref{sec:comp-details}. For FCI (RS-DFT-CIPSI, $\mu=\infty$) we have