Molecular softness, hypersoftness, infrared absorption, and vibrational Raman scattering: New relations derived from nonlocal polarizability densities

Abstract

This work rigorously relates electromagnetic properties and characteristics of molecular potential energy surfaces to the empirical concept of ‘‘softness,’’ used to categorize Lewis acids and bases, and to summarize observed patterns of reactivity. New equations are derived that connect infrared absorption intensities, vibrational force constants, intermolecular forces at first order, and linear electric-field shielding tensors to softness kernels as defined in density functional theory. A generalization to nonlinear response—by introduction of the hypersoftness—leads to new equations in density-functional terms for vibrational Raman band intensities, the cubic anharmonicities in molecular potential energy surfaces, intermolecular forces at second order, and nonlinear electric-field shielding tensors. The analysis employs relations of the softness and hypersoftness to nonlocal polarizability and hyperpolarizability densities that represent the intramolecular distribution of response to inhomogeneous electric fields.