In the construction of the original form of the four-electron interaction wavefunction in which we included cluster functions of one and two electrons, we outlined one particular approach to inclusion of correlation effects which uses cluster functions. This is certainly not the only such model. For example, we could have constructed a much simpler form (though a worse approximation) by constructing a separate wavefunction for each pairwise cluster function
and
etc. For each pair-correlated wavefunction, we could then construct an
energy equation. Each pair energy is determined independently of all
others, and the sum of the correlation energies for each would then be our
approximation to the total correlation energy. This method is referred to
as the independent pair approximation (IEPA) , and was developed by both
Sinanoglu[30] and
Nesbet[31] . The IEPA energy
expressions depend on the coefficients associated with each cluster
function, 
, but each set of coefficients is determined separately.
If, instead, we were to keep the pairwise interaction idea (i.e. retain the form of the pair-correlated wavefunctions (2.18), but now coupled the sets of equations that determine the coefficients -- after all, the correlation of each pair of electrons does depend on that of all other pairs -- we would obtain a more accurate assessment of the total correlation energy. This idea is at the heart of the coupled electron-pair approximation (CEPA) , and was developed by Meyer[32] . We will find that IEPA and CEPA will be useful for analysis of other, more complicated methods later on in these notes.
