Charge overlap effects and the validity of the multipole results for first-order molecule-molecule interaction energies. Formalism and an application to H₂-H₂

Abstract

For the interaction of two molecules, the first-order coulomb energy, Ee(1), is expressed as a sum of non-expanded partial wave components which exhibit the orientation dependence of the energy explicitly. By comparing these non-expanded results with the analogous multipolar results for the first-order energy, the effects of charge overlap on the multipole representation of the energy can be investigated as a function of intermoleeular separation and orientation, and the validity of the multip01e results for Ee (1) assessed. The interaction of two ground-state hydrogen molecules is considered as a specific example of this approach for studying the validity of the multipole expansion as a representation of molecular first-order Coulomb energies. All calculations are presented as a function of four molecular wave functions of varying degrees of sophistication in order to assess the sensitivity of (1) the representation of charge overlap effects and (2) the calculated quadrupole and hexadecapole moments of H 2 with respect to the quality of the molecular wave function. The first-order partial wave energies, through partial wave indices la=19=2, are used to discuss the validity of severely truncated multipole expansions of the first-order interaction energy to represent the total and the orientation dependent part of the Coulomb energy for the H2-H2 interaction. The importance of first-order charge overlap effects for the interaction of more complicated molecules is also discussed briefly.

Intermolecular interactions

“…Calculations have been performed 169 ' 173 " 176 for H*, H 2 , He 2 , He, and H. The validity of the multipole expansion for the Coulomb energy in the first order has been discussed by Kin-Chue Ng et a?. 177 in the case of the H 2 -H 2 system.…”

Method for Slater-Type Density Fitting for Intermolecular Electrostatic Interactions with Charge Overlap. I. The Model

“…Charge overlap has been studied before. Pioneering work on atoms and small molecules were done by Ng et al using the bipolar expansion. − Also, in early work on the convergence of the one-center multipole expansion, the charge overlap has been discussed. , The use of several distributed centers in the expansion practically reduces some of the limitations of the one-center multipole expansion. − Still, the charge overlap is not properly accounted for, and the missing term in such a model has to be heuristically modeled through some other term in the force field. There is a wealth of methods available nowadays for the construction of distributed charges or multipoles, and all lack charge overlap. , Standard quantum chemical calculations generate diffuse densities, described in terms of several Gaussian functions.…”

Atom–atom partitioning of intramolecular and intermolecular Coulomb energy

“…Hättig and Hess 28 have proposed a simpler method to derive the T l A m A l B m B double-tensor and listed the explicit formulas for Lр6 or l A ϩl B р5. Alternative expansions of r AB Ϫ1 have been discussed before, 1 such as the exact bipolar expansion of Buehler and Hirshfelder, 29,30 but the question is if they offer any advantage in our framework is open.…”