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
where the 
vector is defined as
Handy realized that, if determinants are used as basis functions, and
particularly if these determinants are expressed as
``alpha strings'' and
``beta strings,''
then 
(and thus ) could be
evaluated very efficiently. In order to understand Handy's reasoning, we
must first define alpha and beta strings.