loos/srDFT_G2
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

two-electron integrals

Browse Source
This commit is contained in:
Julien Toulouse 2019-04-19 15:57:16 +02:00
parent 40a24bebd3
commit e8ad26aa33
1 changed files with 3 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
Manuscript/G2-srDFT.tex
View File

@ -244,13 +244,13 @@ where
\n{2}{}(\br{1},\br{2})
= \sum_{pqrs \in \Bas} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
\end{equation}
and $\Gam{pq}{rs} =\mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{p_\uparrow}\ai{q_\downarrow}}{\wf{}{\Bas}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor (respectively), $\SO{p}{}$ is a molecular orbital (MO),
and $\Gam{pq}{rs} =\mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{p_\uparrow}\ai{q_\downarrow}}{\wf{}{\Bas}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor, respectively, $\SO{p}{}$ is a (real-valued) molecular orbital (MO),
\begin{equation}
\label{eq:fbasis}
\f{\Bas}{}(\br{1},\br{2})
= \sum_{pqrstu \in \Bas} \SO{p}{1} \SO{q}{2} \V{pq}{rs} \Gam{rs}{tu} \SO{t}{1} \SO{u}{2},
\end{equation}
and $\V{pq}{rs}$ are the usual two-electron Coulomb integrals.
and $\V{pq}{rs}=\langle pq | rs \rangle$ are the usual two-electron Coulomb integrals.
With such a definition, $\W{\Bas}{}(\br{1},\br{2})$ satisfies (see Appendix A of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18})
\begin{equation}
\label{eq:int_eq_wee}