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

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.