2nd screening of Sec IV done
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@ 495,7 +495,7 @@ The first question we would like to address is the quality of the


nodes of the wave function $\Psi^{\mu}$ obtained for intermediate values of the


range separation parameter (\ie, $0 < \mu < +\infty$).


For this purpose, we consider a weakly correlated molecular system, namely the water


molecule \titou{at its experimental geometry. \cite{Caffarel_2016}}


molecule at its experimental geometry. \cite{Caffarel_2016}


We then generate trial wave functions $\Psi^\mu$ for multiple values of


$\mu$, and compute the associated FNDMC energy keeping fixed all the


parameters impacting the nodal surface, such as the CI coefficients and the molecular orbitals.


@ 583,7 +583,7 @@ To do so, we have made the following numerical experiment.


First, we extract the 200 determinants with the largest weights in the FCI wave


function out of a large CIPSI calculation obtained with the VDZBFD basis. Within this set of determinants,


we solve the selfconsistent equations of RSDFT [see Eq.~\eqref{rsdfteigenequation}]


for different values of $\mu$ \titou{using the srPBE functional}. This gives the CI expansions $\Psi^\mu$.


for different values of $\mu$ using the srPBE functional. This gives the CI expansions $\Psi^\mu$.


Then, within the same set of determinants we optimize the CI coefficients $c_I$ [see Eq.~\eqref{eq:Slater}] in the presence of


a simple one and twobody Jastrow factor $e^J$ with $J = J_\text{eN} + J_\text{ee}$ and


\begin{subequations}


@ 601,7 +601,7 @@ where the sum over $i < j$ loops over all unique electron pairs.


In Eqs.~\eqref{eq:jasteN} and \eqref{eq:jastee}, $r_{iA}$ is the distance between the $i$th electron and the $A$th nucleus while $r_{ij}$ is the interlectronic distance between electrons $i$ and $j$.


The parameters $a=1/2$


and $b=0.89$ were fixed, and the parameters $\gamma_{\text{O}}=1.15$ and $\gamma_{\text{H}}=0.35$


were obtained by energy minimization of a single \titou{HF?} determinant.


were obtained by energy minimization of a single determinant.


The optimal CI expansion $\Psi^J$ is obtained by sampling the matrix elements


of the Hamiltonian ($\mathbf{H}$) and the overlap ($\mathbf{S}$), in the


basis of Jastrowcorrelated determinants $e^J D_i$:



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