On the analyticity of electronic reduced densities for molecules

TL;DR

This paper proves that the reduced densities and current densities of a bound electronic state in molecules are real analytic functions away from collisions, enhancing understanding of molecular electronic structure.

Contribution

It establishes the real analyticity of reduced densities and current densities for molecular bound states, a novel mathematical result in quantum chemistry.

Findings

Reduced densities are real analytic away from collisions.

Reduced current density is also real analytic.

Supports mathematical understanding of molecular electronic structures.

Abstract

We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions and fixed nuclei. Away from appropriate collisions, we prove the real analyticity of all the reduced densities and density matrices, that are associated to this bound state. We provide a similar result for the associated reduced current density.Published: J. Math. Phys. 63, 013509 (2022); https://doi.org/10.1063/5.0056488