Following the development given by reference [29], we consider a reference determinant of the form
where 
is a one-electron occupied eigenstate of a zeroth-order
Hamiltonian. For example, 
could simply be an SCF wavefunction,
whose component one-electron states are molecular orbitals arising from the
Hartree-Fock calculation. Improve
by including a two-electron function for the correlation between
electrons in states and 
, such that
where 
is the two-electron function (as yet undefined). We may
have chosen, instead, to consider the correlation effects of electrons in
states 
and 
But, let's be more intelligent about this, and correlate all possible pairwise combinations of electrons in our four-electron system
There is no reason, however, that our discussion should be limited to pairs only. We could, just as easily consider the construction of three-electron functions with the purpose of correlating the motions of three electrons at a time (in addition to our pairwise-correlated function)
We could continue on through n-tuple (four, in this case) cluster
functions, until we've obtained the exact wavefunction (within our
specified basis). However, we assume here that only clusters of ``modest
size'' are important in defining an acceptable wavefunction. We also
should include single-electron ``cluster functions'' 
to take into
account the possibility of adjusting the one-electron basis for correlation
effects (that is, to account for changes in the molecular orbitals as
cluster functions are added). Therefore, we develop a four-electron
wavefunction which includes all clusters of one and two electrons
We must now determine an analytic form for the cluster functions (as well as a more compact notation!).
