modif 1st paragraph of intro
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\newcommand{\Ndet}{N_{\text{det}}}


\newcommand{\hartree}{$E_h$}




\newcommand{\LCT}{Laboratoire de Chimie Théorique (UMR 7616), Sorbonne Université, CNRS, Paris, France}


\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}


\newcommand{\ANL}{Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, IL 60439, United States}


\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, France}


\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}






\begin{document}




\title{Enabling high accuracy diffusion Monte Carlo calculations with


rangeseparated density functional theory and selected configuration interaction}


\title{Taming the fixednode error in diffusion Monte Carlo via range separation}


%\title{Enabling high accuracy diffusion Monte Carlo calculations with


% rangeseparated density functional theory and selected configuration interaction}




\author{Anthony Scemama}


\affiliation{\LCPQ}


@ 55,32 +56,27 @@


\section{Introduction}


\label{sec:intro}




The full configuration interaction (FCI) method within a finite atomic


basis set leads to an approximate solution of the Schrödinger


equation.


This solution is the eigenpair of an approximate Hamiltonian, which is


the projection of the exact Hamiltonian onto the finite basis of all


possible Slater determinants.


The FCI wave function can be interpreted as the constrained solution of the


true Hamiltonian, where the solution is forced to span the space


provided by the basis.


At the complete basis set (CBS) limit, the constraint vanishes and the


exact solution is obtained.


Hence the FCI method enables a systematic improvement of the


calculations by improving the quality of the basis set.


Nevertheless, its exponential scaling with the number of electrons and


with the size of the basis is prohibitive for large systems.


In recent years, the introduction of new algorithms\cite{Booth_2009}


and the


revival\cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016}


Within a finite oneelectron basis, full configuration interaction (FCI)


delivers only an approximate solution of the Schr\"odinger equation.


This solution is the eigenpair of an approximate Hamiltonian defined as


the projection of the exact Hamiltonian onto the finite manyelectron basis of


all possible Slater determinants generated within this finite oneelectron basis.


The FCI wave function can be interpreted as a constrained solution of the


true Hamiltonian forced to span the restricted space provided by the oneelectron basis.


In the complete basis set (CBS) limit, the constraint is lifted and the


exact solution is recovered.


Hence, the accuracy of a FCI calculation can be systematically improved by increasing the size of the oneelectron basis set.


Nevertheless, its exponential scaling with the number of electrons and with the size of the basis is prohibitive for most chemical systems.


In recent years, the introduction of new algorithms \cite{Booth_2009} and the


revival \cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016}


of selected configuration interaction (sCI)


methods\cite{Bender_1969,Huron_1973,Buenker_1974} pushed the limits of


the sizes of the systems that could be computed at the FCI level, but


the scaling remains exponential unless some bias is introduced leading


to a loss of size consistency.


methods \cite{Bender_1969,Huron_1973,Buenker_1974} pushed the limits of


the sizes of the systems that could be computed at the FCI level.


However, the scaling remains exponential unless some bias is introduced leading


to a loss of size consistency. % CITE CIPSI 3CLASS AND INITIATOR APPROXIMATION.




The Diffusion Monte Carlo (DMC) method is a numerical scheme to obtain


the exact solution of the Schrödinger equation with an additional


Diffusion Monte Carlo (DMC) is a numerical scheme to obtain


the exact solution of the Schr\"odinger equation with a different


constraint, imposing the solution to have the same nodal hypersurface


as a given trial wave function.


Within this socalled \emph{fixednode} (FN) approximation,



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