Generalized product expansions for pair‐correlated wavefunctions

A correlated wavefunction in the form of a linear combination of generalized products is proposed for describing electron correlation in N‐electron systems. The generalized product configurations are group functional products describing the correlated behavior of a pair of electrons in an N‐2‐electron independent particle sea. The linear expansion includes terms for all possible pairs and thus includes correlation effects for every pair of electrons. The structure of the wavefunction is given, the matrix elements of the Hamiltonian are determined, and some of the variational equations determining the optimal total wavefunction are discussed. The relation between second‐order Nesbet‐Bethe‐Goldstone calculations and the pair at a time CI method of Sinanoğlu and the pair‐correlated wavefunction developed here is discussed, and a method is given for obtaining a complete generalized product wavefunction from these type independent pair approximations.