Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

TL;DR

This paper introduces a novel Hilbert-space based method for partitioning the molecular one-electron density matrix using orthogonal projectors, enhancing the interpretation of atomic and bond contributions in molecules.

Contribution

It extends atomic weight functions to orthogonal projection operators in Hilbert space, enabling a more interpretable analysis of bonds and atomic charges in molecules.

Findings

Strong correlation between atomic charges and Hirshfeld-I charges

Method successfully applied to diverse molecules

Provides clearer bond contribution interpretation

Abstract

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.