On the coupling operator method

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Abstract
The coupling operator method in the general SCF theory is discussed in terms of the projection operator property of the density operator. The advantage of using the density operator is that one can put the arbitrariness of the general SCF orbitals in evidence. We showed how to put the fundamental condition for the optimum orbitals of the general SCF theory into a more general and useful form. The essential point of the coupling operator is how the variational conditions are included as the projections onto the intermanifolds. By using the arbitrariness of the manifold, we indicate how a modified SCF theory is developed, where by choosing an appropriate operator one can get any desired modified orbitals and their associated orbital energies under orbital transformations. The Appendix contains an extension of Koopmans' theorem as an application of the modified SCF theory. Finally the effective Hamiltonian is derived which is valid for almost all of the proposed SCF theory.