Interacting Quantum Atoms:  A Correlated Energy Decomposition Scheme Based on the Quantum Theory of Atoms in Molecules

Abstract

We make use of the Quantum Theory of Atoms in Molecules (QTAM) to partition the total energy of a many-electron system into intra- and interatomic terms, by explicitly computing both the one- and two-electron contributions. While the general scheme is formally equivalent to that by Bader et al., we focus on the separation and computation of the atomic self-energies and all the interaction terms. The partition is ultimately performed within the density matrices, in analogy with McWeeny's Theory of Electronic Separability, and then carried onto the energy. It is intimately linked with the atomistic picture of the chemical bond, not only allowing the separation of different two-body contributions (point-charge-like, multipolar, total Coulomb, exchange, correlation, ...) to the interaction between a pair of atoms but also including an effective many-body contribution to the binding (self-energy, formally one-body) due to the deformation of the atoms within the many-electron system as compared to the free atoms. Many qualitative ideas about the chemical bond can be quantified using this scheme.

An Interacting Quantum Atoms Analysis of the Metal–Metal Bond in [M2(CO)8]n Systems

“…The IQA methodology has been fully described in earlier studies, 39,42,[53][54][55] to which readers can refer for a more detailed explanation. Summarizing, within QTAIM the following one-and two-basin partitioning of the molecular energy is used:…”

“…In this respect, the Interacting Quantum Atoms (IQA) approach, 39 an energy decomposition method based on the QTAIM real space partitioning, may be the ideal tool. IQA has been previously used to obtain chemically relevant information and to shed light on many aspects relative to chemical bonding and binding in a wide variety of systems, [40][41][42][43][44][45][46] including different metal-organic compounds.…”

Two complementary molecular energy decomposition schemes: The Mayer and Ziegler–Rauk methods in comparison

“…[28][29][30][31][32][33] The two energy decomposition approaches discussed above, the fragment-based methods ͑such as Ziegler-Rauk and Kitaura-Morokuma͒ and the diatomic energy methods ͑such as Mayer's͒, tackle the question about the nature of the chemical bond from opposite ends. The Ziegler-Rauk and Kitaura-Morokuma methods focus on the energetic consequences of the bond formation process, whereas the Mayer approach separates the total energy of the final molecule in several contributions without using an explicit reference.…”

One- and two-center physical space partitioning of the energy in the density functional theory

“…For each atom or atomic pair, there is one such integration for calculating the Coulomb energy contribution and one for each pair of occupied molecular orbitals for the respective exchange energy component. Blanco et al 9 have extended the Hartree-Fock energy decomposition scheme of Ref. 10 to the post-Hartree-Fock case by partitioning the second order density matrix and introducing an efficient numerical quadrature algorithm for the two-center integrations.…”