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

Abstract

For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree-Fock level are efficiently determined 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 (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren 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. As the Hartree-Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads 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 with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions.

A viewpoint on population analyses

“…Vantfleteren [47], and Mayer [48] have also suggested an energy decomposition scheme. Extensions have also been made to transform basis set into sets into eigenfunctions of other relevant operators, as in the energy density operator [49].…”

Computing Accurate Net Atomic Charges, Atomic Spin Moments, and Effective Bond Orders in Complex Materials

“…3. Projection using the same atomic weights used to partition rr ð Þ into overlapping atoms, 46,53,[56][57][58] The above projectors and similar ones can be expressed in matrix form and diagonalized to obtain ''bonding orbitals''. [10][11][12]46,50,[53][54][55]58,59,71,72 This allows one to identify the occupancies and shapes of independent bonding modes between atom pairs.…”

A reference‐free stockholder partitioning method based on the force on electrons

“…Inspired by Nalewajski and Parr's realization that Hirshfeld's stockholder partitioning can be derived from the principles of information theory, the last decade has seen a proliferation of population analysis approaches . These methods are mostly based on partitioning the electron density, though other quantities (e.g., the local hardness and the one‐electron reduced density matrix) have also been considered …”