Introduction to Determinant CI

As we have already pointed out, the size of the CI space can be reduced significantly by including only those N-electron basis functions which have the same value of the quantum number S as the desired approximate wavefunction (cf. sections 4.1 and 4.4). Thus it would seem that one should always prefer CSF's to Slater determinants when performing a CI. However, certain computational advantages arise from using determinants, as we will discuss in the next few sections. Many modern algorithms for performing large CI's (i.e. more than single and double excitations) use determinants as the N-electron basis.

Handy's  1980 paper ``Multi-Root Configuration Interaction Calculations'' [29] represented a major advance in determinant-based CI, even though the paper was more concerned with how integrals and CI coefficients are stored than with the computational advantages of determinants over CSF's. Handy used the Cooper-Nesbet method for performing the CI iteration; the CI coefficients are updated according to the formula

$$\delta c_i = \frac{r_i}{(E - H_{ii})}$$ (tex2html_deferredtex2html_deferred6.tex2html_deferred1c_i = r_i(E - H_ii) )

where the ${\bf r}$ vector is defined as

$$r_i = \sum_j (H_{ij} - E \delta_{ij}) c_j$$ (tex2html_deferredtex2html_deferred6.tex2html_deferred2 r_i = _j (H_ij - E _ij) c_j )

Handy realized that, if determinants are used as basis functions, and particularly if these determinants are expressed as ``alpha strings''  and ``beta strings,''  then H_ij (and thus ${\bf r}$) could be evaluated very efficiently. In order to understand Handy's reasoning, we must first define alpha and beta strings.