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2nd screening of Sec IV done

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Pierre-Francois Loos 2020-08-18 10:42:39 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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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 FN-DMC 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 VDZ-BFD basis. Within this set of determinants,
we solve the self-consistent equations of RS-DFT [see Eq.~\eqref{rs-dft-eigen-equation}]
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 two-body 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:jast-eN} and \eqref{eq:jast-ee}, $r_{iA}$ 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 Jastrow-correlated determinants $e^J D_i$: