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%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% 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) %% 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, @article{Perdew_1996,
Author = {John P. Perdew and Matthias Ernzerhof and Kieron Burke}, Author = {John P. Perdew and Matthias Ernzerhof and Kieron Burke},
Date-Added = {2020-08-20 10:26:11 +0200}, Date-Added = {2020-08-20 10:26:11 +0200},
@ -41,7 +83,8 @@
Pages = {785}, Pages = {785},
Title = {Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density}, Title = {Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density},
Volume = {37}, Volume = {37},
Year = {1988}} Year = {1988},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.37.785}}
@article{Becke_1993, @article{Becke_1993,
Author = {A. D. Becke}, Author = {A. D. Becke},
@ -52,7 +95,8 @@
Pages = {5648}, Pages = {5648},
Title = {Densityfunctional thermochemistry. III. The role of exact exchange}, Title = {Densityfunctional thermochemistry. III. The role of exact exchange},
Volume = {98}, Volume = {98},
Year = {1993}} Year = {1993},
Bdsk-Url-1 = {https://doi.org/10.1063/1.464913}}
@article{Tubman_2016, @article{Tubman_2016,
Author = {Tubman, Norm M. and Lee, Joonho and Takeshita, Tyler Y. and {Head-Gordon}, Martin and Whaley, K. Birgitta}, Author = {Tubman, Norm M. and Lee, Joonho and Takeshita, Tyler Y. and {Head-Gordon}, Martin and Whaley, K. Birgitta},

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@ -177,7 +177,7 @@ determinant. This feature is in part responsible for the success of
DFT and coupled cluster (CC) theory. DFT and coupled cluster (CC) theory.
Likewise, DMC with a single-determinant trial wave function can be used as a 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 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 In single-determinant DMC calculations, the only degree of freedom available to
reduce the fixed-node error are the molecular orbitals with which the reduce the fixed-node error are the molecular orbitals with which the
Slater determinant is built. 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-, pseudopotentials \cite{Burkatzki_2007,Burkatzki_2008} with the associated double-,
triple-, and quadruple-$\zeta$ basis sets (VXZ-BFD). triple-, and quadruple-$\zeta$ basis sets (VXZ-BFD).
The small-core BFD pseudopotentials include scalar relativistic effects. 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. \emph{Gaussian09},\cite{g16} using the unrestricted formalism for open-shell systems.
The CIPSI calculations have been performed with \emph{Quantum 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.} solution would have been the PBE single determinant.}
For comparison, we have computed the energies of all the atoms and 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 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) 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}. with respect to the NIST reference values as explained in Sec.~\ref{sec:comp-details}.
For FCI (RS-DFT-CIPSI, $\mu=\infty$) we have For FCI (RS-DFT-CIPSI, $\mu=\infty$) we have