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saving work in appendix B

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Pierre-Francois Loos 2020-08-19 09:45:42 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -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?}
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\bibliography{rsdft-cipsi-qmc}
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