From 565bf6cf41a68f66168d1140064f289aaa841b6c Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 19 Aug 2020 09:45:42 +0200 Subject: [PATCH] saving work in appendix B --- Manuscript/rsdft-cipsi-qmc.tex | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/Manuscript/rsdft-cipsi-qmc.tex b/Manuscript/rsdft-cipsi-qmc.tex index 438465d..2da2ddc 100644 --- a/Manuscript/rsdft-cipsi-qmc.tex +++ b/Manuscript/rsdft-cipsi-qmc.tex @@ -1112,7 +1112,7 @@ twice the statistical error bars). Closed-shell molecules often dissociate into open-shell fragments. To get reliable atomization energies, it is important to have a theory which is of comparable quality for open- and -closed-shell systems. A good test is to check that all the components +closed-shell systems. A good check is to make sure that all the components of a spin multiplet are degenerate, as expected from exact solutions. FCI wave functions have this property and yield degenerate energies with @@ -1124,7 +1124,7 @@ for the opposite-spin pairs.\cite{Tenno_2004} Again, when pseudopotentials are employed, this tiny error is transferred to the FN-DMC energy unless the DLA is enforced. -The context is rather different within DFT. +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. @@ -1142,11 +1142,12 @@ The results are reported in Table~\ref{tab:spin}. Although the energy obtained with $m_s=0$ is higher than the one obtained with $m_s=1$, the bias is relatively small, \ie, more than one order of magnitude smaller than the energy gained by reducing the fixed-node error going from the single -determinant to the FCI trial wave function. The largest bias, close to +determinant to the FCI trial wave function. The largest spin-invariance error, close to $2$ 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?} %%% TABLE IV %%% \begin{table} @@ -1170,8 +1171,6 @@ noticeable for $\mu=5$~bohr$^{-1}$. \end{table} %%% %%% %%% %%% -\titou{T2: what do you conclude from this section? What value of $m_s$ do you use to compute the atoms?} - %%%%%%%%%%%%%%%%%%%%%%%%%%%% \bibliography{rsdft-cipsi-qmc} %%%%%%%%%%%%%%%%%%%%%%%%%%%%