Group Product Functions and the Basis Orbitals

We suppose that the complex contains n electrons which we divide into two subsets, labelled M and L, n = Am + Al. We write a trial wavefunction 0 to be used in Eq. (2-2) in the group product form  

The n-electron Hamiltonian H in the fixed nucleus approximation may be written as 

Under these conditions it is a simple matter to show that the expectation value of if for a function of the form (3-1) may be written in separable form. 

The Coulomb and exchange operators, J and K respectively, are defined by the formulae. 

An exactly similar criterion obtained by interchanging the roles of M and L, and m, , applies to the optimum L group wavefunctions. This is a well-defined optimization problem which may be solved iteratively starting from some reasonable guess for the group functions, and its solution already gives us a good treatment of electron correlation. 

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