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