Phase-amplitude functional theory -- new ab initio calculation method for large size systems

TL;DR

This paper introduces a novel ab initio calculation method for large systems based on phase-amplitude functional theory, transforming the Schrödinger equation into a functional of phase and amplitude variables.

Contribution

It develops a new theoretical framework that simplifies large system calculations by expressing energies and wavefunctions through phase and amplitude functions.

Findings

Derivation of equations for phase and amplitude variables.

Expression of kinetic and Coulomb energies in terms of these variables.

Formulation of one-electron wavefunctions using the new variables.

Abstract

New method for ab initio calculations of the properties of large size system based on phase-amplitude functional is presented. It is shown that Schrodinger equation for many electrons complex system including large size molecules, or clusters and also periodic systems could be translated into functional of two variables, attributed to many electron wavefunctions: phase and the amplitude (i.e. square root of total electron density). The equations for the phase and the amplitude are derived. The kinetic and Coulomb interaction energy are expressed in function of these variables. The equations for one-electron wavefunctions, necessary for the energy spectrum are derived using these two variables.