title: A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank.
abstract: A finite field method for calculating spherical tensor molecular polarizability tensors α(lm;l'm') = ∂Δ(lm)/∂ϕ(l'm')* by numerical derivatives of induced molecular multipole Δ(lm) with respect to gradients of electrostatic potential ϕ(l'm')* is described for arbitrary multipole ranks l and l'. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water using the following ab initio methods: Hartree-Fock (HF), Becke three-parameter Lee-Yang-Parr exchange-correlation functional (B3LYP), Møller-Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields.
authors.affiliation: University of North Carolina, Department of Chemistry, Chapel Hill, North Carolina 27599, USA.
authors.forename: Dennis M
authors.initials: DM
authors.lastname: Elking
authors.forename: Lalith
authors.initials: L
authors.lastname: Perera
authors.forename: Robert
authors.initials: R
authors.lastname: Duke
authors.forename: Thomas
authors.initials: T
authors.lastname: Darden
authors.forename: Lee G
authors.initials: LG
authors.lastname: Pedersen
mesh_terms: D004583:Electrons; D008722:Methods; D008958:Models, Molecular; D008962:Models, Theoretical; D055672:Static Electricity