A multipolar approach to the interatomic covalent interaction energy

Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities ρA(r) and ρB(r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1-2 pairs) albeit it works reasonably well most times for 1- n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l1+l2=2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.