Distributed atomic polarizabilities from electron density. 1. Motivations and Theory

In this paper, the distributed atomic polarizabilities computed within the Quantum Theory of Atoms in Molecules are discussed. Methods are presented to calculate and visualize symmetric atomic polarizability tensors, with proved additivity to molecular polarizabilities. The analysis of QTAIM bond polarizabilities is also presented for some simple molecules and potential applications in material science are anticipated. Introduction The response of electron density to an electric field is fundamental to understand, among the others, the behavior of molecules in chemical reactions, the solvation properties, the recognition processes and spectroscopic properties. As a matter of facts, the (hyper)polarizabilities tensors determine the soft ("orbital controlled") assembly and reactivity of molecules, the intensities of Raman scattering and many other optical processes. For this reason, measuring or calculating the molecular (hyper)polarizabilities is of fundamental importance, especially when dealing with material science. If the material is a crystalline solid, the properties are regulated by the electric susceptibilities, which are related, for molecular based materials, to the molecular (hyper)polarizabilities tensors through lattice summation. Quantum chemistry allows to calculate (hyper)polarizabilities of molecules and crystals, by derivation of the electronic energy E with respect to the electric field F. For example, the first order polarizability tensor is defined as