Eigenvalue equations from the field of theoretical chemistry and correlation calculations

TL;DR

This paper explores eigenvalue equations and their applications in theoretical chemistry, focusing on multi-electron densities, energy estimations, and fundamental theorems, with analytical evaluations relevant to ground state energies and electron correlation.

Contribution

It introduces new eigenvalue equations and analytical methods connecting electronic structure theories with correlation calculations in quantum chemistry.

Findings

Derived equations relating multi-electron densities to energy estimations

Analytical evaluation of Coulomb integrals for multi-electron operators

Insights into ground state energy and correlation energy calculations

Abstract

Many equations have been introduced and derived by the author indicated in the title in relation to multi-electron densities between the Hohenberg-Kohn theorems and variational principle, conversion of the non-relativistic electronic Schrodinger equation to scaling correct moment functional of ground state one-electron density to estimate ground state electronic energy, participation of electron-electron repulsion energy operator in the non-relativistic electronic Schrodinger equation via the coupling strength parameter along with generalizing the Hund rule, the emblematic theorems virial-, Moller-Plesset-, Hohenberg-Kohn-, Koopmans-, Brillouin theorem and configuration interactions formalism, and with analytic evaluation of Coulomb integrals for one, two and three-electron operators, as well as focusing on ground state electronic energy, correlation energy and zero point energy of stationer molecular systems.