Changes in electronic polarizability densities due to shifts in nuclear positions, and a new interpretation for integrated intensities of vibrational Raman bands

Abstract

The nonlocal polarizability density α(r;r′,ω) is a linear-response tensor that determines the electronic polarization induced at point r in a molecule, by an external electric field of frequency ω, acting at r′. This work focuses on the change in α(r;r′,ω) when a nuclear position shifts infinitesimally. We prove directly that the electronic charge distribution responds to the change in Coulomb field due to the nucleus via the same hyperpolarizability density that describes its response to external fields. This generalizes a result found previously for the static (ω=0) polarizability density. The work also provides a new interpretation for the integrated intensities of vibrational Raman bands: it proves that the intensities depend on the hyperpolarizability densities and the dipole propagator.