diff --git a/Manuscript/rsdft-cipsi-qmc.tex b/Manuscript/rsdft-cipsi-qmc.tex index 668ceff..c45b08a 100644 --- a/Manuscript/rsdft-cipsi-qmc.tex +++ b/Manuscript/rsdft-cipsi-qmc.tex @@ -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}