Lower bounds to eigenvalues of one-electron Hamiltonians

TL;DR

This paper introduces a method for deriving lower bounds on eigenvalues of one-electron Hamiltonians, utilizing operator sum bounds, molecular symmetry, and Temple's inequality to improve accuracy for molecular property analysis.

Contribution

The paper presents a novel approach combining operator sum bounds, symmetry considerations, and Temple's inequality to estimate lower eigenvalue bounds of electronic Hamiltonians.

Findings

Effective lower bounds for eigenvalues of one-electron Hamiltonians.

Improved bounds achieved by incorporating molecular symmetry.

Potential applications in molecular property studies.

Abstract

A method for computing lower bounds to eigenvalues of sums of lower semibounded self-adjoint operators is presented. We apply the method to one-electron Hamiltonians. To improve the lower bounds we consider symmetry of molecules and use Temple's inequality. These methods would be useful in estimating eigenvalues of electronic Hamiltonians needed for studies of properties of molecules.