Self-consistent one-electron equation including exchange and correlation in terms of equivalent function and phase norm: calculation for ground and excited states in a unified way

TL;DR

This paper introduces a novel one-electron equation that analytically incorporates exchange and correlation effects using the concepts of equivalent function and phase norm, enabling unified calculations of ground and excited states.

Contribution

It proposes a new analytical one-electron equation based on equivalent function and phase norm, effectively including exchange and correlation effects without additional empirical terms.

Findings

Successfully derives a one-electron equation including exchange and correlation

Provides a unified framework for calculating ground and excited states

Embodies electronic correlation physically through phase norm

Abstract

We present an alternative one-electron equation for resolving many-electron problem to one-electron approximation and including the exchange and correlation effects in an analytical way, thereby fulfilling the requirements for ab initio calculation. To derive one-electron equation, we accept a new notion of equivalent function suggestive of the pseudo wavefunction. As a result, we reduce many-electron equation to one-electron including the exchange effect in an analytical method. Moreover we accept the notion of phase norm for two electrons to resolve the electronic correlation problem. The phase norm is used to specify the electron-approachable limit between particles. We take into consideration the electronic correlation with the help of a correlation-hole function in terms of the phase norm, by which multiplying the integrand of the operator term representing the interaction between electrons. Using the phase norm leads to analytical consideration of the electronic correlation without employing in a factitious way the additional term pertaining to correlation, so it embodies the physical essence of electronic correlation. The derived equation becomes an one-electron equation which does not include an additional term pertaining to the exchange and correlation, but takes into consideration the exchange and correlation effects in a rigorous ab initio way.