scemama/RSDFT-CIPSI-QMC
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Merge branch 'master' of https://git.irsamc.ups-tlse.fr/scemama/RSDFT-CIPSI-QMC

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Emmanuel Giner 2020-08-17 10:55:56 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -20,6 +20,7 @@
\newcommand{\alert}[1]{\textcolor{red}{#1}}
\definecolor{darkgreen}{HTML}{009900}
\usepackage[normalem]{ulem}
\newcommand{\trashtoto}[1]{\textcolor{blue}{\sout{#1}}}
\newcommand{\toto}[1]{\textcolor{blue}{#1}}
\newcommand{\manu}[1]{\textcolor{green}{#1}}
\newcommand{\trashAS}[1]{\textcolor{blue}{\sout{#1}}}
@ -119,7 +120,7 @@ Moreover, because of the approximate nature of the xc functional, although the r
Diffusion Monte Carlo (DMC), which belongs to the family of stochastic methods, is yet another numerical scheme to obtain
the exact solution of the Schr\"odinger equation with a different
constraint. \cite{Foulkes_2001,Austin_2012,Needs_2020}
In DMC, solution is imposed to have the same nodes (or zeroes)
In DMC, the solution is imposed to have the same nodes (or zeroes)
as a given (approximate) antisymmetric trial wave function. \cite{Reynolds_1982,Ceperley_1991}
Within this so-called fixed-node (FN) approximation,
the FN-DMC energy associated with a given trial wave function is an upper
@ -170,7 +171,7 @@ 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 coupled cluster.\cite{Dubecky_2014,Grossman_2002}
This approach obviously fails in the presence of strong correlation, like in
transition metal complexes, low-spin open-shell systems, and covalent bond breaking situations which cannot be even qualitatively described by a single electronic configuration.
transition metal complexes, low-spin open-shell systems, and covalent bond breaking situations which cannot be \trashtoto{even} qualitatively described by a single electronic configuration.
In such cases or when very high accuracy is required, a viable alternative is to consider the FN-DMC method as a
``post-FCI'' method. A multi-determinant trial wave function is then produced by
approaching FCI with a SCI method such as the \emph{configuration interaction using a perturbative