merging figures
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@ 365,7 +365,6 @@ to standard WFT and $\Psi^\mu$ is the FCI wave function.




%%% FIG 1 %%%


\begin{figure*}


\centering


\includegraphics[width=0.7\linewidth]{algorithm.pdf}


\caption{Algorithm showing the generation of the RSDFT wave


function $\Psi^{\mu}$ starting from $\Psi^{(0)}$.


@ 459,7 +458,6 @@ stochastic reconfiguration algorithm developed by Assaraf \textit{et al.},


\begin{table}


\caption{FNDMC energy $\EDMC$ (in \hartree{}) and number of determinants $\Ndet$ in \ce{H2O} for various trial wave functions $\Psi^{\mu}$ obtained with the srPBE density functional.}


\label{tab:h2odmc}


\centering


\begin{ruledtabular}


\begin{tabular}{crlrl}


& \multicolumn{2}{c}{VDZBFD} & \multicolumn{2}{c}{VTZBFD} \\


@ 485,7 +483,6 @@ stochastic reconfiguration algorithm developed by Assaraf \textit{et al.},




%%% FIG 2 %%%


\begin{figure}


\centering


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


\caption{FNDMC energy of \ce{H2O} as a function


of $\mu$ for various levels of theory to generate


@ 619,39 +616,29 @@ and solving Eq.~\eqref{eq:cij}.\cite{Nightingale_2001}




We can easily compare $\Psi^\mu$ and $\Psi^J$ as they are developed


on the same set of Slater determinants.


In Fig.~\ref{fig:overlap}, we plot the overlaps


$\braket*{\Psi^J}{\Psi^\mu}$ obtained for water as a function of $\mu$


and, in Fig.~\ref{fig:dmc_small}, the FNDMC energy of the wave function


$\Psi^\mu$ as a function of $\mu$ together with that of $\Psi^J$.


In Fig.~\ref{fig:overlap}, we plot the overlap


$\braket*{\Psi^J}{\Psi^\mu}$ obtained for water as a function of $\mu$ (left graph)


as well as the FNDMC energy of the wave function


$\Psi^\mu$ as a function of $\mu$ together with that of $\Psi^J$ (right graph).




%%% FIG 3 %%%


\begin{figure}


\centering


\begin{figure*}


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


\caption{Overlap between $\Psi^\mu$ and $\Psi^J$ as a function of $\mu$ for \ce{H2O}.


\includegraphics[width=\columnwidth]{h2o200dmc.pdf}


\caption{Left: Overlap between $\Psi^\mu$ and $\Psi^J$ as a function of $\mu$ for \ce{H2O}.


Right: FNDMC energy of $\Psi^\mu$ (red curve) as a function of $\mu$, together with


the FNDMC energy of $\Psi^J$ (blue line) for \ce{H2O}.


The width of the lines represent the statistical error bars.


For these two trial wave functions, the CI expansion consists of the 200 most important


determinants of the FCI expansion obtained with the VDZBFD basis (see Sec.~\ref{sec:rsdftj} for more details).}


\label{fig:overlap}


\end{figure}


%%% %%% %%% %%%




%%% FIG 4 %%%


\begin{figure}


\includegraphics[width=\columnwidth]{h2o200dmc.pdf}


\caption{


FNDMC energies of $\Psi^\mu$ (red curve) as a function of $\mu$, together with


the FNDMC energy of $\Psi^J$ (blue line) for \ce{H2O}. The width of the lines


represent the statistical error bars.


For these two trial wave functions, the CI expansion consists of the 200 most important


determinants of the FCI expansion obtained with the VDZBFD basis (see Sec.~\ref{sec:rsdftj} for more details).}


\label{fig:dmc_small}


\end{figure}


\end{figure*}


%%% %%% %%% %%%




As evidenced by Fig.~\ref{fig:overlap}, there is a clear maximum overlap between the two trial wave functions at $\mu=1$~bohr$^{1}$, which


coincides with the minimum of the FNDMC energy of $\Psi^\mu$ (see Fig.~\ref{fig:dmc_small}).


coincides with the minimum of the FNDMC energy of $\Psi^\mu$.


Also, it is interesting to notice that the FNDMC energy of $\Psi^J$ is compatible


with that of $\Psi^\mu$ for $0.5 < \mu < 1$~bohr$^{1}$, as shown by the overlap between the red and blue bands in Fig.~\ref{fig:dmc_small}.


with that of $\Psi^\mu$ for $0.5 < \mu < 1$~bohr$^{1}$, as shown by the overlap between the red and blue bands.


This confirms that introducing shortrange correlation with DFT has


an impact on the CI coefficients similar to a Jastrow factor.


This is yet another key result of the present study.


@ 660,7 +647,7 @@ This is yet another key result of the present study.


\begin{table}


\caption{\ce{H2O}, doublezeta basis set. Integrated ontop pair density $\expval{ P }$


for $\Psi^J$ and $\Psi^\mu$ with different values of $\mu$.


\titou{Please remove table and merge data in the Fig. 5.}}


\titou{Please remove table and merge data in Fig. 5.}}


\label{tab:table_on_top}


\begin{ruledtabular}


\begin{tabular}{cc}


@ 680,28 +667,16 @@ This is yet another key result of the present study.


\end{table}


%%% %%% %%% %%%




%%% FIG 5 %%%


\begin{figure}


%%% FIG 4 %%%


\begin{figure*}


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


\caption{Oneelectron density $n(\br)$ along


the \ce{OH} axis of \ce{H2O} as a function of $\mu$ for $\Psi^J$ (dashed curve) and $\Psi^\mu$.


For these two trial wave functions, the CI expansion consists of the 200 most important


determinants of the FCI expansion obtained with the VDZBFD basis (see Sec.~\ref{sec:rsdftj} for more details).}


\label{fig:n1}


\end{figure}


%%% %%% %%% %%%






%%% FIG 6 %%%


\begin{figure}


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


\caption{Ontop pair


density $n_2(\br,\br)$ along the \ce{OH} axis of \ce{H2O} as a function of $\mu$


for $\Psi^J$ (dashed curve) and $\Psi^\mu$.


\caption{Oneelectron density $n(\br)$ (left) and ontop pair


density $n_2(\br,\br)$ (right) along the \ce{OH} axis of \ce{H2O} as a function of $\mu$ for $\Psi^J$ (dashed curve) and $\Psi^\mu$.


For these two trial wave functions, the CI expansion consists of the 200 most important


determinants of the FCI expansion obtained with the VDZBFD basis (see Sec.~\ref{sec:rsdftj} for more details).}


\label{fig:n2}


\end{figure}


\label{fig:densities}


\end{figure*}


%%% %%% %%% %%%




In order to refine the comparison between $\Psi^\mu$ and $\Psi^J$, we


@ 714,9 +689,9 @@ report in Table~\ref{tab:table_on_top} the integrated ontop pair density


where $n_2(\br_1,\br_2)$ is the twobody density [normalized to $\Nelec(\Nelec1)$]


obtained for both $\Psi^\mu$ and $\Psi^J$.


Then, in order to have a pictorial representation of both the ontop


pair density and the density, we report in Figs.~\ref{fig:n1} and \ref{fig:n2}


pair density and the density, we report in Fig.~\ref{fig:densities}


the plots of the total density $n(\br)$ and ontop pair density


$n_2(\br,\br)$ along one of these \ce{OH} axis of the water molecule.


$n_2(\br,\br)$ along one of the \ce{OH} axis of the water molecule.




From these data, one can clearly notice several trends.


First, from Table~\ref{tab:table_on_top}, we can observe that the overall


@ 733,7 +708,7 @@ $\Psi^{\mu=0.5}$, and at a large distance the ontop pair density is


the closest to $\mu=\infty$. The integrated ontop pair density


obtained with $\Psi^J$ lies between the values obtained with


$\mu=0.5$ and $\mu=1$~bohr$^{1}$, consistently with the FNDMC energies


and the overlap curve depicted in Figs.~\ref{fig:overlap} and \ref{fig:dmc_small}


and the overlap curve depicted in Fig.~\ref{fig:overlap}.




These data suggest that the wave functions $\Psi^{0.5 \le \mu \le 1}$ and $\Psi^J$ are close,


and therefore that the operators that produced these wave functions (\ie, $H^\mu[n]$ and $e^{J}He^J$) contain similar physics.


@ 747,7 +722,7 @@ increases the probability to find electrons at short distances in $\Psi^\mu$,


while the effective onebody potential $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n_{\Psi^{\mu}}]$,


provided that it is exact, maintains the exact onebody density.


This is clearly what has been observed from


Figs.~\ref{fig:n1} and \ref{fig:n2}.


Fig.~\ref{fig:densities}.


Regarding now the transcorrelated Hamiltonian $e^{J}He^J$, as pointed out by Tenno,\cite{Tenno2000Nov}


the effective twobody interaction induced by the presence of a Jastrow factor


can be nondivergent when a proper Jastrow factor is chosen.


@ 1075,7 +1050,7 @@ extrapolated FCI energies. The same comment applies to


$\mu=0.5$~bohr$^{1}$ with the quadruplezeta basis set.






%%% FIG 7 %%%


%%% FIG 5 %%%


\begin{figure*}


\centering


\includegraphics[width=\textwidth]{g2dmc.pdf}


@ 1101,7 +1076,7 @@ $\mu$. Although the FNDMC energies are higher, the numbers show that


they are more consistent from one system to another, giving improved


cancellations of errors.




%%% FIG 8 %%%


%%% FIG 6 %%%


\begin{figure*}


\centering


\includegraphics[width=\textwidth]{g2ndet.pdf}



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