Full CI Algorithm

Next: Bibliography Up: Determinant-Based CI Previous: Olsen's Full CI Equations

Full CI Algorithm

It is easy to vectorize the formation of $\sigma _1$ since each element $\sigma_1(I_{\alpha}, I_{\beta})$ can be written as independent of $I_{\alpha}$ apart from multiplication by a factor $C(I_{\alpha}, J_{\beta})$ . The vectorized algorithm for the evaluation of $\sigma _1$ , adapted from reference [16], appears in Figure 5. An analogous algorithm can be used to obtain $\sigma_2$ . However, we can also obtain $\sigma_2$ for M_s = 0 states by

$\begin{displaymath} \sigma_2(I_{\alpha}, I_{\beta}) = (-1)^{S} \sigma_1(I_{\beta}, I_{\alpha}) \end{displaymath}$

(tex2html_deferredtex2html_deferred6.tex2html_deferred29 _2(I_, I_) = (-1)^S _1(I_, I_) )

as proven by Olsen and co-workers [16].

**Figure:** Vectorized Algorithm for $\sigma _1$ .
$\begin{figure}\par\begin{verse} loop over $I_{\beta}$\space \\ \hspace{0.4in} S... ..._{\alpha}$\space \\ end loop over $I_{\beta}$\space \\ \end{verse}\end{figure}$

A fairly straightforward algorithm for evaluating $\sigma _3$ is presented in Figure 6. The vectorized algorithm for the evaluation of $\sigma _3$ is presented in Figure 7. This algorithm makes use of a gather and scatter operation to avoid indirect addressing.

**Figure:** Simple Algorithm for $\sigma _3$ .
$\begin{figure}\par\begin{verse} loop over $I_{\alpha}$\space \\ \hspace{0.4in} ... ...gn}(kl) (ij\vert kl) C(J_{\alpha}, J_{\beta})$\space \\ \end{verse}\end{figure}$

**Figure:** Vectorized Algorithm for $\sigma _3$ .
$\begin{figure}\par\begin{verse} loop over $kl$\space \\ \hspace{0.4in} set up $... ...nd loop over $I_{\beta}$\space \\ end loop over $kl$\end{verse}\par\end{figure}$

For M_s=0, an improvement to the $\sigma _3$ algorithm can be made by utilizing an identity similar to equation (6.31). The ijklth component of $\sigma _3$ is related to the klijth component via

$\begin{displaymath}\sigma_3^{ijkl}(I_{\alpha}, I_{\beta}) = (-1)^{S} \sigma_1^{klij}(I_{\beta}, I_{\alpha}) \end{displaymath}$

(tex2html_deferredtex2html_deferred6.tex2html_deferred30_3^ijkl(I_, I_) = (-1)^S _1^klij(I_, I_) )

Next: Bibliography Up: Determinant-Based CI Previous: Olsen's Full CI Equations

C. David Sherrill
2000-04-18