Self-consistent one-electron equation for many-electron systems and its general application to ground and excited states

Abstract

The present status of ab initio calculations for electronic states requires the further development of the quantum many-body theory which mainly targets the improvement of the fundamental equation in the sense of completely non-empirical, i.e., true ab initio theory. In compliance with this requirement, we present an alternative self-consistent one-electron equation different from both the Hartree–Fock equation and the Kohn–Sham equation, but essentially the improvement and unification of them. This equation includes the exchange and correlation effect in an ab initio way based on the quantum principles. To derive a one-electron equation including the exchange effect in an explicit way in terms of antisymmetric wavefunctions, we introduce a new concept called the equivalent function. Moreover, to treat the electronic correlation in a first-principle way, we introduce another new concept referred to as the phase norm which specifies the mutual-electron-approachable limit in terms of phase space. The derived equation becomes a self-consistent one-electron equation which satisfies the main requirements for ab initio calculations. This equation offers a big advantage of calculating electronic states of many-electron systems in a unified way commonly applicable to all stationary state problems, irrespective of ground or excited states, without recourse to the approaches based on the Hartree–Fock or the density functional theory.