Natural, Brueckner, and SCF Orbitals for Alternant Systems

Abstract

It is shown that natural orbitals, Brueckner orbitals, and SCF orbitals have pairing properties for alternant systems, where alternant systems are defined as systems with polyelectronic Hamiltonians fulfilling a certain commutation relation with the pairing operator. For an alternant system, the sum of the occupation numbers for two paired natural orbitals is equal to 1. The eigenvectors of the spinless density operator and of the resultant spin-density operator have properties similar to the properties of corresponding quantities in the one-electron approximation. This is shown to be partly true even for the density operator of the second order. The conditions sufficient and necessary for the existence of alternant properties for a group of electrons in a molecule are formulated. A concept of contraction of an operator is introduced, which allows unique formulation of the density operators, Hartree—Fock effective Hamiltonians and other quantities in second quantization formalism.