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As we have already pointed out, the size of the CI space can be reduced
significantly by including only those Nelectron 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
Nelectron basis.
Handy's
1980 paper ``MultiRoot Configuration Interaction Calculations''
[29] represented a major advance in determinantbased 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 CooperNesbet method for
performing the CI iteration; the CI coefficients are updated according to
the formula

(tex2html_deferredtex2html_deferred6.tex2html_deferred1c_i = r_i(E  H_ii)
) 
where the
vector is defined as

(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 )
could be
evaluated very efficiently. In order to understand Handy's reasoning, we
must first define alpha and beta strings.
Next: Alpha and Beta Strings
Up: DeterminantBased CI
Previous: DeterminantBased CI
C. David Sherrill
20000418