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RSDFT-CIPSI-QMC
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OK with IVA

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Pierre-Francois Loos 2020-08-20 12:04:34 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -531,14 +531,14 @@ starting from $\mu=0$ (\ie, the KS determinant),
the FN-DMC error is reduced continuously until it reaches a minimum
for an optimal value of $\mu$ (which is obviously basis set and functional dependent),
and then the FN-DMC error raises until it reaches the $\mu=\infty$ limit (\ie, the FCI wave function).
For instance, with respect to the fixed-node energy associated with the srPBE/VDZ-BFD trial wave function at $\mu=\infty$,
For instance, with respect to the fixed-node energy associated with the RS-DFT-CIPSI(srPBE/VDZ-BFD) trial wave function at $\mu=\infty$,
one can obtain a lowering of the FN-DMC energy of $2.6 \pm 0.7$~m\hartree{}
with an optimal value of $\mu=1.75$~bohr$^{-1}$.
This lowering in FN-DMC energy is to be compared with the $3.2 \pm
0.7$~m\hartree{} gain in FN-DMC energy between the KS wave function ($\mu=0$)
and the FCI wave function ($\mu=\infty$). When the basis set is improved, the
gain in FN-DMC energy with respect to the FCI trial wave function is reduced,
and the optimal value of $\mu$ is slightly shifted towards large $\mu$.
and the optimal value of $\mu$ is slightly shifted towards large $\mu$ as expected.
Last but not least, the nodes of the wave functions $\Psi^\mu$ obtained with the srLDA
functional give very similar FN-DMC energies with respect
to those obtained with srPBE, even if the
@ -547,7 +547,7 @@ tens of m\hartree{}.
Accordingly, all the RS-DFT calculations are performed with the srPBE functional in the remaining of this paper.
Another important aspect here is the compactness of the trial wave functions $\Psi^\mu$:
at $\mu=1.75$~bohr$^{-1}$, $\Psi^{\mu}$ has \textit{only} $54\,540$ determinants at the srPBE/VDZ-BFD level, while the FCI wave function contains $200\,521$ determinants (see Table \ref{tab:h2o-dmc}). Even at the srPBE/VTZ-BFD level, we observe a reduction by a factor two in the number of determinants between the optimal $\mu$ value and $\mu = \infty$.
at $\mu=1.75$~bohr$^{-1}$, $\Psi^{\mu}$ has \textit{only} $54\,540$ determinants at the RS-DFT-CIPSI(srPBE/VDZ-BFD) level, while the FCI wave function contains $200\,521$ determinants (see Table \ref{tab:h2o-dmc}). Even at the RS-DFT-CIPSI(srPBE/VTZ-BFD) level, we observe a reduction by a factor two in the number of determinants between the optimal $\mu$ value and $\mu = \infty$.
The take-home message of this first numerical study is that RS-DFT-CIPSI trial wave functions can yield a lower fixed-node energy with more compact multi-determinant expansion as compared to FCI.
This is a key result of the present study.