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Pierre-Francois Loos 2019-04-24 16:08:31 +02:00
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Manuscript/G2-srDFT.tex
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@ -388,7 +388,8 @@ Defining $\nFC{\modZ}{\Bas}$ as the FC (i.e.~valence-only) one-electron density
%\subsection{Computational considerations} %\subsection{Computational considerations}
%================================================================= %=================================================================
The most computationally intensive task of the present approach is the evaluation of $\W{}{\Bas}(\br{},\br{})$ at each quadrature grid point. The most computationally intensive task of the present approach is the evaluation of $\W{}{\Bas}(\br{},\br{})$ at each quadrature grid point.
Yet embarrassingly parallel, this step scales, in the general case (i.e.~$\wf{}{\Bas}$ is a multi-determinant expansion), as $\Ng \Nb^4$ (where $\Nb$ is the number of basis functions in $\Bas$) but is reduced to $\order*{ \Ng \Ne^2 \Nb^2}$ when $\wf{}{\Bas}$ is a single Slater determinant. \titou{In the general case (i.e.~$\wf{}{\Bas}$ is a multi-determinant expansion), we compute this embarrassingly parallel step in $\order*{\Ng \Nb^4}$ computational cost with a memory requirement of $\order*{ \Ng \Nb^2}$, where $\Nb$ is the number of basis functions in $\Bas$.
The computational cost can be reduced to $\order*{ \Ng \Ne^2 \Nb^2}$ when $\wf{}{\Bas}$ is a single Slater determinant.}
As shown in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, this choice for $\wf{}{\Bas}$ already provides, for weakly correlated systems, a quantitative representation of the incompleteness of $\Bas$. As shown in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, this choice for $\wf{}{\Bas}$ already provides, for weakly correlated systems, a quantitative representation of the incompleteness of $\Bas$.
Hence, we will stick to this choice throughout the present study. Hence, we will stick to this choice throughout the present study.
In our current implementation, the computational bottleneck is the four-index transformation to get the two-electron integrals in the MO basis which appear in Eqs.~\eqref{eq:n2basis} and \eqref{eq:fbasis}. In our current implementation, the computational bottleneck is the four-index transformation to get the two-electron integrals in the MO basis which appear in Eqs.~\eqref{eq:n2basis} and \eqref{eq:fbasis}.