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


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.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The article aims at the improvement of the fundamental equation for the calculation of electronic states in the sense of completely non-empirical, i.e., true ab initio theory. The proposed self-consistent one-electron equation different from both the Hartree-Fock equation and the Kohn-Sham equation includes the exchange and correlation effect in an ab initio way based on the quantum principles, and 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.]


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This work was supported partially from the Committee of Education, Democratic People’s Republic of Korea, under the project entitled “Ab Initio Calculation: Exchange-Correlation Effects and Excited States.” We thank Profs. Chol-Jun Yu and Hak-Chol Pak from Kim Il Sung University for advice and help. We are grateful to Prof. Il-Yong Kang from Kim Chaek University of Technology for information and comment.

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Correspondence to Chol Jong.

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Jong, C. Self-consistent one-electron equation for many-electron systems and its general application to ground and excited states. Eur. Phys. J. Plus 135, 746 (2020).

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