R scripts and data
This commit is contained in:
parent
7739286953
commit
8a1677edc5
5012
Data/RSDFTCIPSI.org
5012
Data/RSDFTCIPSI.org
File diff suppressed because it is too large
Load Diff
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
@ 23,7 +23,7 @@


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






\begin{document}


\begin{document}




\title{Enabling high accuracy diffusion Monte Carlo calculations with


rangeseparated density functional theory and selected configuration interaction}


@ 50,7 +50,7 @@


\section{Introduction}


\label{sec:intro}




The full configuration interaction (FCI) method \eg{within an incomplete basis set}


The full configuration interaction (FCI) method \eg{within an incomplete basis set}


leads to the exact solution of the Schrödinger equation with an approximate Hamiltonian


\eg{which consists in the exact one projected onto } \sout{expressed in} a finite basis of Slater determinants.


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


@ 76,7 +76,7 @@ The Diffusion Monte Carlo (DMC) method is a numerical scheme to obtain


the exact solution of the Schrödinger equation with an additional


constraint, imposing the solution to have the same nodal hypersurface


as a given trial wave function. This approximation, known as the


\emph{fixednode} approximation, \eg{is variational with respect to the nodes of the trial wave function: the DMC energy obtained with a given trial wave function is an upper bound to the exact energy, and the latter is recovered only }


\emph{fixednode} approximation, \eg{is variational with respect to the nodes of the trial wave function: the DMC energy obtained with a given trial wave function is an upper bound to the exact energy, and the latter is recovered only }


when the nodes of the trial wave function coincide with the nodes of the exact wave function\sout{, the exact energy and wave function are obtained}.


The DMC method is attractive because its scaling is polynomial with


the number of electrons and with the size of the trial wave


@ 95,7 +95,7 @@ systems.


As it has been shown by many studies\cite{Per_2012}, the nodal surfaces obtained with the


KS determinant are in general better than those obtained with


the HF determinant, and of comparable quality


to those obtained with a Slater determinant built with NO.\cite{Wang_2019}


to those obtained with a Slater determinant built with NO.\cite{Wang_2019}




However, the fixednode approximation is much more difficult to


control than the finitebasis approximation, as it is not possible


@ 131,25 +131,25 @@ factor.\cite{Giner_2016,Dash_2018,Dash_2019}


\begin{enumerate}


\item Total energies and nodal quality:


\begin{itemize}


\item Factual stuffs: KS occupied orbitals closer to NOs than HF


\item Factual stuffs: KS occupied orbitals closer to NOs than HF


\item Even if exact functional, complete basis set, still approximated nodes for KS


\item KS > exponentially fast convergence (as HF) with basis because of non divergence of effective KS potential (citer le papier de Gill)


\item KS > exponentially fast convergence (as HF) with basis because of non divergence of effective KS potential (citer le papier de Gill)


\item With correlation consistent basis set, FCI nodes (which include correlation) are better than KS


\item With FCI, good limit at CBS ==> exact energy


\item But slow convergence with basis set because of divergence of the ee interaction not well represented in atom centered basis set


\item Exponential increase of number of Slater determinants


\item Exponential increase of number of Slater determinants


\item Cite papierS RSDFT: there exists an hybrid scheme combining fast convergence wr to basis set (non divergent basis set) and short expansion in SCI (cite papier Ferté)


\item Question: does such a scheme provide better nodal quality ?


\item In RSDFT we cannot optimize energy with $\mu$ , but in FNDMC


\item In RSDFT we cannot optimize energy with $\mu$ , but in FNDMC


\item Factual stuffs: with optimal $\mu$, lower FNDMC energy than HF/KS/FCI


\begin{itemize}


\item less determinants $\Rightarrow$ large systems


\item only one parameter to optimize $\Rightarrow$ deterministic


\item $\Rightarrow$ reproducible


\item $\Rightarrow$ reproducible


\end{itemize}


\item with the optimal $\mu$:


\begin{itemize}


\item Direct optimization of FNDMC with one parameter


\item Direct optimization of FNDMC with one parameter


\item Do we improve energy differences ?


\item system dependent


\item basis set dependent: $\mu \rightarrow \infty$ when $\mathcal{B}\rightarrow \text{CBS}$


@ 162,7 +162,7 @@ factor.\cite{Giner_2016,Dash_2018,Dash_2019}


\section{Combining rangeseparated DFT with CIPSI}


\label{sec:rsdftcipsi}




Starting from a HartreeFock determinant in a small basis set,


Starting from a HartreeFock determinant in a small basis set,


we have seen that we can systematically improve the trial wave


function in two directions. The first one is by increasing the


size of the atomic basis set, and the second one is by


@ 342,11 +342,11 @@ takes the form




It is possible to use DFT for shortrange interactions and CIPSI for


the longrange. This scheme has been recently


implemented.\cite{GinPraFerAssSavTouJCP18}


implemented.\cite{GinPraFerAssSavTouJCP18}




\begin{figure}[h]


\centering


\includegraphics[width=\columnwidth]{algorithm.pdf}


\includegraphics[width=\columnwidth]{algorithm.pdf}


\caption{Algorithm showing the generation of the RSDFTCIPSI wave


function}


\end{figure}


@ 386,7 +386,7 @@ implemented.\cite{GinPraFerAssSavTouJCP18}




\begin{figure}[h]


\centering


\includegraphics[width=\columnwidth]{h2odmc.pdf}


\includegraphics[width=\columnwidth]{h2odmc.pdf}


\caption{Fixednode energies of the water molecule with variable


values of $\mu$.}


\label{fig:h2odmc}


@ 563,6 +563,8 @@ of the RSDFTCIPSI trial wave functions for energy differences.


& & 1/4 & 5.55 \\


& & 1/2 & 13.42 \\


& & 1 & 17.07 \\


& & 2 & 19.20 \\


& & 5 & 22.93 \\


& & $\infty$ & 23.62 \\


& VTZBFD & 0 & 6.31 \\


& & 1/4 & 4.58 \\


@ 573,10 +575,12 @@ of the RSDFTCIPSI trial wave functions for energy differences.


& & 1/2 & 6.35 \\


\hline


DMC/RSDFTCIPSI & VDZBFD & 0 & 5.07 $\pm$ 0.44 \\


& & 1/4 & 4.04 $\pm$ 0.37 \\


& & 1/2 & 3.74 $\pm$ 0.35 \\


& & 1 & 5.42 $\pm$ 0.29 \\


& & $\infty$ & 7.38 $\pm$ 1.08 \\


& & 1/4 & 4.04 $\pm$ 0.37 \\


& & 1/2 & 3.74 $\pm$ 0.35 \\


& & 1 & 5.42 $\pm$ 0.29 \\


& & 2 & 5.98 $\pm$ 0.83 \\


& & 5 & 6.68 $\pm$ 1.07 \\


& & $\infty$ & 7.38 $\pm$ 1.08 \\


& VTZBFD & 0 & 3.52 $\pm$ 0.19 \\


& & 1/4 & 3.39 $\pm$ 0.77 \\


& & 1/2 & 2.46 $\pm$ 0.18 \\


@ 593,21 +597,21 @@ of the RSDFTCIPSI trial wave functions for energy differences.




\begin{figure}[h]


\centering


\includegraphics[width=\columnwidth]{g2dmcdz.pdf}


\includegraphics[width=\columnwidth]{g2dmcdz.pdf}


\caption{Histogram of the errors in atomization energies with the doublezeta basis set.}


\label{fig:g2dmcdz}


\end{figure}




\begin{figure}[h]


\centering


\includegraphics[width=\columnwidth]{g2dmctz.pdf}


\includegraphics[width=\columnwidth]{g2dmctz.pdf}


\caption{Histogram of the errors in atomization energies with the triplezeta basis set.}


\label{fig:g2dmctz}


\end{figure}




\begin{figure}[h]


\centering


\includegraphics[width=\columnwidth]{g2dmcqz.pdf}


\includegraphics[width=\columnwidth]{g2dmcqz.pdf}


\caption{Histogram of the errors in atomization energies with the quadruplezeta basis set.}


\label{fig:g2dmcqz}


\end{figure}



Loading…
Reference in New Issue
Block a user