Orbital Self-Consistent-Field Theory. II. Natural Orbital Hamiltonian

Abstract

A constrained energy extremal principle for natural orbitals and natural spin orbitals is demonstrated. The extremal principle is used to derive a one-electron Hamiltonian for the natural spin orbitals of a system of $N$ electrons. The natural spin-orbital Hamiltonian depends on the one- and two-body density matrices, and is thus of the self-consistent-field type. Whether or not the natural spin-orbital Hamiltonian will be of any practical significance in the determination of exact or accurate natural spin orbitals depends upon finding a practical solution to the $N$-representability problem.