Appendix
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@ 1143,7 +1143,7 @@ The context is rather different within KSDFT.


Indeed, mainstream density functionals have distinct functional forms to take


into account correlation effects of samespin and oppositespin electron pairs.


Therefore, KS determinants corresponding to different values of $m_s$ lead to different total energies.


Consequently, in the context of RSDFT, the determinant expansions is impacted by this spurious effect, as opposed to FCI.


Consequently, in the context of RSDFT, the determinant expansion is impacted by this spurious effect, as opposed to FCI.




In this Appendix, we investigate the impact of the spin contamination on the FNDMC energy


originating from the shortrange density functional. We have


@ 1162,7 +1162,12 @@ $2$ m\hartree{}, is obtained for $\mu=0$, but this bias decreases quickly


below $1$ m\hartree{} when $\mu$ increases. As expected, with $\mu=\infty$


we observe a perfect spininvariance of the energy (within the error bars), and the bias is not


noticeable for $\mu=5$~bohr$^{1}$.


\titou{T2: what do you conclude from this section? What value of $m_s$ do you use to compute the atoms?}




Hence, at the FNDMC level the error due to the lack of


spininvariance with RSDFTCIPSI trial wave functions is below the


chemical accuracy, and is not expected to be problematic for the


comparison of energies of systems with different spin quantum numbers


as in atomization energies.




%%% TABLE IV %%%


\begin{table}



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