The Direct Determination of Natural Orbitals and Natural Expansion Coefficients of Many Electron Wave Functions. I. Natural Orbitals in the Geminal Product Approximation

摘要

The approximation of a many particle wave function as an antisymmetrized product of strongly orthogonal geminals (APSG) (geminal means two electron function) is analized in terms of its natural expansion. APSG wave functions have very simple and interesting properties. The 'generating spin geminals' (GSG) are automatically natural spin geminals (NSG) of the system with occupation number 1 (in the Lowdin normalization); 1 is the upper bound for the eigenvalues of the 2 particle density matrix for wave functions of this type. The natural spin orbitals 'NSO' of the GSG are automatically NSO of the total wave function and of all the NSG. A generalized 'paired orbital function' is defined in terms of its natural expansion. It contains the APSG type as well as the BardeenCooper-Schrieffer (BCS)-functions as special cases. Integrodifferential equations determining the NSO and their expansion coefficients for an APSG function are derived for the special case of a singlet state by minimizing the total electronic energy. An iterative resolution procedure is proposed. (Author)