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@ 531,14 +531,14 @@ starting from $\mu=0$ (\ie, the KS determinant),


the FNDMC 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 FNDMC error raises until it reaches the $\mu=\infty$ limit (\ie, the FCI wave function).


For instance, with respect to the fixednode energy associated with the srPBE/VDZBFD trial wave function at $\mu=\infty$,


For instance, with respect to the fixednode energy associated with the RSDFTCIPSI(srPBE/VDZBFD) trial wave function at $\mu=\infty$,


one can obtain a lowering of the FNDMC energy of $2.6 \pm 0.7$~m\hartree{}


with an optimal value of $\mu=1.75$~bohr$^{1}$.


This lowering in FNDMC energy is to be compared with the $3.2 \pm


0.7$~m\hartree{} gain in FNDMC energy between the KS wave function ($\mu=0$)


and the FCI wave function ($\mu=\infty$). When the basis set is improved, the


gain in FNDMC 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 FNDMC energies with respect


to those obtained with srPBE, even if the


@ 547,7 +547,7 @@ tens of m\hartree{}.


Accordingly, all the RSDFT 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/VDZBFD level, while the FCI wave function contains $200\,521$ determinants (see Table \ref{tab:h2odmc}). Even at the srPBE/VTZBFD 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 RSDFTCIPSI(srPBE/VDZBFD) level, while the FCI wave function contains $200\,521$ determinants (see Table \ref{tab:h2odmc}). Even at the RSDFTCIPSI(srPBE/VTZBFD) level, we observe a reduction by a factor two in the number of determinants between the optimal $\mu$ value and $\mu = \infty$.


The takehome message of this first numerical study is that RSDFTCIPSI trial wave functions can yield a lower fixednode energy with more compact multideterminant expansion as compared to FCI.


This is a key result of the present study.





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