Orbital Self-Consistent-Field Theory. III. Hamiltonian for the Natural Orbitals of Multiconfigurational Wave Functions

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Abstract
A self-consistent-field Hamiltonian which determines the natural orbitals of a multiconfigurational wave function, is derived. The advantage of using natural orbitals in multiconfigurational wave functions is that one can then determine the Langrangian multipliers once and for all. The Hamiltonian is valid for almost all of the proposed multiconfigurational wave functions, including those for which self-consistent-field equations have not been previously given. The Hamiltonian is derived by combining the results of Parts I and II of this series of studies. It is derived in such a way that it contains explicitly electronic Coulomb and exchange operators. This has the advantage that the coupling operators which appear in the Hamiltonian, depend only on that part of the two-electron density matrix which describes the correlation between the electrons. The practical question of how to use the derived equation is discussed in a brief, general way.