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Appendix

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Anthony Scemama 2020-08-23 14:40:12 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -1143,7 +1143,7 @@ The context is rather different within KS-DFT.
Indeed, mainstream density functionals have distinct functional forms to take
into account correlation effects of same-spin and opposite-spin electron pairs.
Therefore, KS determinants corresponding to different values of $m_s$ lead to different total energies.
Consequently, in the context of RS-DFT, the determinant expansions is impacted by this spurious effect, as opposed to FCI.
Consequently, in the context of RS-DFT, 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 FN-DMC energy
originating from the short-range 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 spin-invariance 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 FN-DMC level the error due to the lack of
spin-invariance with RS-DFT-CIPSI 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}