ORBITAL SELF-CONSISTENT-FIELD THEORY .2. NATURAL ORBITAL HAMILTONIAN

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. © 1969 The American Physical Society.