Fast density-matrix based partitioning of the energy over the atoms in a molecule consistent with the Hirshfeld-I partitioning of the electron density

TL;DR

This paper introduces a fast, density-matrix based method for partitioning molecular energy into atomic contributions consistent with Hirshfeld-I density partitioning, offering computational efficiency over traditional integral-based methods.

Contribution

The authors develop a novel, efficient approach to partition molecular energies at the Hartree-Fock level using a density matrix framework aligned with Hirshfeld-I partitioning, avoiding complex numerical integrations.

Findings

Method is computationally efficient for small to medium molecules.

Partitioned energies are fully consistent with the electron density partitioning.

Approach outperforms traditional integral-based methods in speed.

Abstract

For the Hirshfeld-I atom-in-molecule model, associated single-atom energies and interaction energies at the Hartree-Fock level are determined efficiently in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix. Starting from the Hirshfeld-I atom-in-molecule model for the electron density, the molecular one-electron density matrix is partitioned with a previously introduced double-atom scheme [Vanfleteren D. et al., J Chem Phys 2010, 132, 164111]. Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. Since the Hartree-Fock energy can be expressed solely in terms of the one-electron density matrix, the partitioning of the latter over the atoms in the molecule leads naturally to a corresponding partitioning of the Hartree-Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared to other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions.