Analysis of Raman trace scattering intensities in alkanes with the theory of atoms in molecules

Abstract

In this paper, we report the detailed ab initio analysis of charge flow that occurs within a molecule during a molecular vibration, under conditions corresponding to a Raman experiment. Theoretical values for the molecular polarizability and polarizability derivatives are obtained in two ways for methane, ethane, and propane. Initially they are obtained from ab initio molecular orbital calculations employing coupled perturbed Hartree–Fock theory. Second, wave functions corresponding to the molecule in the presence and in the absence of an electric field, generated by the calculation, are analyzed according to the theory of atoms in molecules (AIM). The molecular polarizabilities are determined from the amount of charge transferred from one atom to another plus a contribution from reorganization of atomic charge within each atom, due to the presence of an electric field. Derivatives are obtained from the change in the molecular polarizability as the atoms are displaced from their equilibrium positions. It is apparent that a molecule behaves like a dielectric material, developing a depolarizing surface charge while atomic dipoles of interior atoms oppose the charge transfer. For nonspherical molecules, the polarizability derivatives for the symmetric CH stretching modes show considerable dependence on the orientation of the bonds with respect to the principal axes of the molecular polarizability, and hence, the carbon chain. The polarizability derivatives are characterized as arising from the atom-to-atom charge transfer or changes in the induced atomic dipoles. Previously observed dependence of the intensity on bond orientation is due, in large part, to charge transfer along a carbon chain. It is greatest for the terminal CH bonds lying in the plane of the carbon chain and increases regularly with chain length. The question of transferability of intensity parameters from one molecule to another, as is assumed in the bond polarizability model, is addressed in the light of this new information.