saving work in appendix B
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@ 706,7 +706,7 @@ and therefore that the operators that produced these wave functions (\ie, $H^\mu


Considering the form of $\hat{H}^\mu[n]$ [see Eq.~\eqref{H_mu}],


one can notice that the differences with respect to the usual bare Hamiltonian come


from the nondivergent twobody interaction $\hat{W}_{\text{ee}}^{\text{lr},\mu}$


and the effective onebody potential $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n]$ which is the functional derivative of the Hartreeexchangecorrelation functional.


and the effective onebody potential $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n]$ which is the functional derivative of the Hartreeexchangecorrelation functional.


The roles of these two terms are therefore very different: with respect


to the exact groundstate wave function $\Psi$, the nondivergent twobody interaction


increases the probability to find electrons at short distances in $\Psi^\mu$,


@ 716,11 +716,11 @@ This is clearly what has been observed in


Fig.~\ref{fig:densities}.


Regarding now the transcorrelated Hamiltonian $e^{J}He^J$, as pointed out by Tenno,\cite{Tenno_2000}


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


can be nondivergent when a proper Jastrow factor is chosen, \ie, the Jastrow factor must fulfill the socalled electronelectron cusp conditions. \cite{Kato_1957,Pack_1966}


\titou{T2: I think we are missing the point here that the onebody Jastrow mimics the effective onebody potential which makes the onebody density fixed.


The twobody Jastrow makes the interaction nondivergent like the nondivergent twobody interaction in RSDFT.


Therefore, the onebody terms take care of the onebody properties and the twobody terms take care of the twobody properties. QED.}


Therefore, one can understand the similarity between the eigenfunctions of $H^\mu$ and the SlaterJastrow optimization:


can be nondivergent when a proper twobody Jastrow factor $J_\text{ee}$ is chosen, \ie, the Jastrow factor must fulfill the socalled electronelectron cusp conditions. \cite{Kato_1957,Pack_1966}


There is therefore a clear parallel between $\hat{W}_{\text{ee}}^{\text{lr},\mu}$ in RSDFT and $J_\text{ee}$ in FNDMC.


Moreover, the onebody Jastrow term $J_\text{eN}$ ensures that the onebody density remain unchanged when the CI coefficients are reoptmized in the presence of $J_\text{ee}$.


There is then a second clear parallel between $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n]$ in RSDFT and $J_\text{eN}$ in FNDMC.


Thus, one can understand the similarity between the eigenfunctions of $H^\mu$ and the SlaterJastrow optimization:


they both deal with an effective nondivergent interaction but still


produce a reasonable onebody density.




@ 828,7 +828,9 @@ described by a single determinant. Therefore, the atomization energies


calculated at the DFT level are relatively accurate, even when


the basis set is small. The introduction of exact exchange (B3LYP and


PBE0) make the results more sensitive to the basis set, and reduce the


accuracy. Thanks to the singlereference character of these systems,


accuracy. Note that, due to the approximate nature of the xc functionals,


the MAEs associated with KSDFT atomization energies do not converge towards zero and remain altered even in the CBS limit.


Thanks to the singlereference character of these systems,


the CCSD(T) energy is an excellent estimate of the FCI energy, as


shown by the very good agreement of the MAE, MSE and RMSE of CCSDT(T)


and FCI energies.


@ 842,7 +844,7 @@ This significant imbalance at the VDZBFD level affects the nodal


surfaces, because although the FNDMC energies obtained with nearFCI


trial wave functions are much lower than the singledeterminant FNDMC


energies, the MAE obtained with FCI ($7.38\pm1.08$ kcal/mol) is


larger than the \titou{singledeterminant} MAE ($4.61\pm 0.34$ kcal/mol).


larger than the \titou{singledeterminant} MAE ($4.61\pm0.34$ kcal/mol).


Using the FCI trial wave function the MSE is equal to the


negative MAE which confirms that the atomization energies are systematically


underestimated. This confirms that some of the basis set



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