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Size-consistency

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Anthony Scemama 2020-08-01 13:49:47 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -586,32 +586,34 @@ are computed analytically and the computational cost of the
pseudo-potential is dramatically reduced (for more detail, see
Ref.~\onlinecite{Scemama_2015}).
In this section, we make a numerical verification that the produced
wave functions are size-consistent. We have computed the energy of the
dissocited fluorine dimer, where the two atoms are at a distance of 50~\AA.
We expect that the energy of this system is equal to twice the energy
of the fluorine atom.
%\begin{squeezetable}
\begin{table}
\caption{FN-DMC Energies of the fluorine atom and the dissociated fluorine
dimer, and size-consistency error.}
\label{tab:size-cons}
\begin{ruledtabular}
\begin{tabular}{clll}
\begin{tabular}{cccc}
$\mu$ & F & Dissociated F$_2$ & Size-consistency error \\
\hline
0.00 & $-24.188\,7(3)$ & $-48.377\,7(3)$ & $0.000\,3(4)$ \\
0.25 & $-24.188\,7(3)$ & $-48.377\,2(4)$ & $0.000\,2(5)$ \\
0.50 & $-24.188\,8(1)$ & $-48.376\,8(4)$ & $0.000\,2(4)$ \\
% 1.00 & $-24.189\,7(1)$ & $-48.37 \, ( )$ & $0.00 \, (9)$ \\
2.00 & $-24.194\,1(3)$ & $-48.388\,4(4)$ & $0.000\,2(5)$ \\
5.00 & $-24.194\,7(4)$ & $-48.388\,5(7)$ & $0.000\,9(8)$ \\
$\infty$ & $-24.193\,5(2)$ & $-48.386\,9(4)$ & $0.000\,1(5)$ \\
0.00 & $-24.188\,7(3)$ & $-48.377\,7(3)$ & $-0.000\,3(4)$ \\
0.25 & $-24.188\,7(3)$ & $-48.377\,2(4)$ & $+0.000\,2(5)$ \\
0.50 & $-24.188\,8(1)$ & $-48.376\,9(4)$ & $+0.000\,7(4)$ \\
1.00 & $-24.189\,7(1)$ & $-48.380\,2(4)$ & $-0.000\,8(4)$ \\
2.00 & $-24.194\,1(3)$ & $-48.388\,4(4)$ & $-0.000\,2(5)$ \\
5.00 & $-24.194\,7(4)$ & $-48.388\,5(7)$ & $+0.000\,9(8)$ \\
$\infty$ & $-24.193\,5(2)$ & $-48.386\,9(4)$ & $+0.000\,1(5)$ \\
\end{tabular}
\end{ruledtabular}
\end{table}
In this section, we make a numerical verification that the produced
wave functions are size-consistent. We have computed the energy of the
dissocited fluorine dimer, where the two atoms are at a distance of 50~\AA.
We expect that the energy of this system is equal to twice the energy
of the fluorine atom.
The data in table~\ref{tab:size-cons} shows that the proposed scheme
provides size-consistent FN-DMC energies for all values of $\mu$.
\subsection{Spin-invariance}