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Pierre-Francois Loos 2020-01-24 15:11:04 +01:00
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Manuscript/srDFT_SC.tex
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@ -188,7 +188,7 @@
\newcommand{\denmodelr}[0]{\den_{\model}^\Bas ({\bf r})}
\newcommand{\denfci}[0]{\den_{\psifci}}
\newcommand{\denFCI}[0]{\den^{\Bas}_{\text{FCI}}}
\newcommand{\denbas}[0]{{P}^{\Bas}(\den)}
\newcommand{\denbas}[0]{\alert{{P}^{\Bas}(\den)}}
\newcommand{\denhf}[0]{\den_{\text{HF}}^\Bas}
\newcommand{\denrfci}[0]{\denr_{\psifci}}
\newcommand{\dencipsir}[0]{{n}_{\text{CIPSI}}^\Bas({\bf r})}
@ -437,7 +437,7 @@ which is again fundamental to guarantee the correct behavior of the theory in th
\subsubsection{Frozen-core approximation}
\label{sec:FC}
As all WFT calculations in this work are performed within the frozen-core approximation, we use a ``valence-only'' (or no-core) version of the various quantities needed for the complementary functional introduced in Ref.~\onlinecite{LooPraSceTouGin-JCPL-19}. We partition the basis set as $\Bas = \Cor \bigcup \BasFC$, where $\Cor$ and $\BasFC$ are the sets of core and valence (\ie, no-core) orbitals, respectively, and define the valence-only local range-separation function as
As all WFT calculations in this work are performed within the frozen-core approximation, we use a \alert{``valence-only'' (or no-core) version} of the various quantities needed for the complementary functional introduced in Ref.~\onlinecite{LooPraSceTouGin-JCPL-19}. We partition the basis set as $\Bas = \Cor \bigcup \BasFC$, where $\Cor$ and $\BasFC$ are the sets of core and valence (\ie, no-core) orbitals, respectively, and define the valence-only local range-separation function as
\begin{equation}
\label{eq:def_mur_val}
\murpsival = \frac{\sqrt{\pi}}{2} \wbasiscoalval{},
@ -708,7 +708,7 @@ Regarding the complementary functional, we first perform full-valence CASSCF cal
Also, as the frozen-core approximation is used in all our selected CI calculations, we use the corresponding valence-only complementary functionals (see Subsec.~\ref{sec:FC}). Therefore, all density-related quantities exclude any contribution from the $1s$ core orbitals, and the range-separation function follows the definition given in Eq.~\eqref{eq:def_mur_val}.
\alert{It should be stressed that the computational cost of the basis-set correction (see Appendix~\ref{app:computational}) is negligible compared to the cost the selected-CI calculations}.
\alert{It should be stressed that the computational cost of the basis-set correction (see Appendix~\ref{app:computational}) is negligible compared to the cost the selected CI calculations}.
%We thus believe that this approach is a significant step towards the routine calculation of near-CBS energetic quantities in strongly correlated systems.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -906,7 +906,7 @@ So, $f(\bfr{},\bfr{})$ is a local intensive quantity.
As a consequence, the local range-separation function of the supersystem $\text{A}+\text{B}$ is
\begin{equation}
\label{eq:def_murAB}
\mu_{\text{A}+\text{B}}(\bfr{}) = \frac{\sqrt{\pi}}{2} \frac{f_{\text{A}}(\bfr{},\bfr{}) + f_{\text{B}}(\bfr{},\bfr{})}{n_{2,\text{A}}(\br{}) + n_{2,\text{B}}(\br{})},
\alert{\mu_{\text{A}+\text{B}}(\bfr{}) = \frac{\sqrt{\pi}}{2} \frac{f_{\text{A}}(\bfr{},\bfr{}) + f_{\text{B}}(\bfr{},\bfr{})}{n_{2,\text{A}}(\br{}) + n_{2,\text{B}}(\br{})},}
\end{equation}
which gives
\begin{equation}