Chemical descriptors, convexity and structure of density matrices in molecular systems

TL;DR

This paper explores how environmental interactions can smooth out discontinuities in chemical descriptors derived from electron density matrices, enabling well-defined higher-order derivatives in molecular systems.

Contribution

It introduces a grand-canonical framework that incorporates environmental effects, ensuring the continuity of density matrix derivatives for improved chemical descriptor definitions.

Findings

Environmental interactions suppress discontinuities in density matrix derivatives.

Grand-canonical formulation provides a coherent structure for density matrices.

Higher-order derivatives of chemical descriptors become well-defined.

Abstract

The electron energy and density matrices in molecular systems are convex in respect of the number of particles. So that, the chemical descriptors based on their derivatives present the hamper of discontinuities for isolated systems and consequently higher order derivatives are undefined. The introduction of the interaction between the physical domain with an environment induces a coherent structure for the density matrix in the grand-canonical formulation suppressing the discontinuities leading to the proper definitions of the descriptors.