Self-consistent one-electron equation for many-electron systems and its general application to ground and excited states
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Self-consistent one-electron equation for many-electron systems and its general application to ground and excited states Chol Jonga Faculty of Physics, Kim Chaek University of Technology, Yonggwang Street, Pyongyang, Democratic People’s Republic of Korea Received: 10 July 2020 / Accepted: 28 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 oneelectron 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.
1 Introduction The ab initio calculation for many-electron systems sets up the extremely demanding tasks which involve the explicit expression of exchange and correlation, and the calculation for excited states in a way applicable to all stationary states. The main purpose of the manyparticle theory in non-relativistic quantum mechanics is to study the properties of solutions of the Schrödinger equation describing the characteristics of many-body interactions including the exchange and correlation effects. The key problems of ab initio calculations for manyparticle systems involve how to exclude the self-interaction, how to include the exchange and correlation effects and how to reduce the many-particle problem to a one-particle one. By these criteria, we review the several approaches to ab initio calculations. The complexity of many-electron problems is due to the interaction operator represented by two-particle
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variables. It makes it impossible to use the variable separation method to solve the Schrödinger equation for many-body systems. The first approa
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