From 565bf6cf41a68f66168d1140064f289aaa841b6c Mon Sep 17 00:00:00 2001
From: PierreFrancois Loos
Date: Wed, 19 Aug 2020 09:45:42 +0200
Subject: [PATCH] saving work in appendix B

Manuscript/rsdftcipsiqmc.tex  9 ++++
1 file changed, 4 insertions(+), 5 deletions()
diff git a/Manuscript/rsdftcipsiqmc.tex b/Manuscript/rsdftcipsiqmc.tex
index 438465d..2da2ddc 100644
 a/Manuscript/rsdftcipsiqmc.tex
+++ b/Manuscript/rsdftcipsiqmc.tex
@@ 1112,7 +1112,7 @@ twice the statistical error bars).
Closedshell molecules often dissociate into openshell
fragments. To get reliable atomization energies, it is important to
have a theory which is of comparable quality for open and
closedshell systems. A good test is to check that all the components
+closedshell 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 oppositespin pairs.\cite{Tenno_2004}
Again, when pseudopotentials are employed, this tiny error is transferred
to the FNDMC energy unless the DLA is enforced.
The context is rather different within DFT.
+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.
@@ 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 fixednode 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 spininvariance 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 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?}
%%% 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?}

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