Maximum-Overlap Orbitals, an Energy Variational Principle, and Perturbation Theory

The maximum-overlap orbitals first proposed by Brenig, in which the overlap between the true wave function and a Slater determinant is maximized, is shown to be equivalent to L\"owdin's exact self-consistent-field theory. By defining an energy functional and varying it, some points in L\"owdin's theory are clarified. The ground-state energy is expanded in perturbation theory, and it is pointed out that some diagrams could become divergent. In order to eliminate these diagrams, Bogoliubov's principle of compensation of dangerous diagrams (PCDD) is extended to finite fermion systems. In these systems, the PCDD states that the sum of all the diagrams leading from the vacuum to a single particle-hole state must be set equal to zero. This condition is the Brillouin-Brueckner condition, which is also obtained from the other methods. The form of the PCDD obtained here is different from another form that leads to L\"owdin's natural orbitals, and the difference is discussed.