ANALYSIS OF RAMAN TRACE SCATTERING INTENSITIES IN ALKANES WITH THE THEORY OF ATOMS IN MOLECULES

In this paper, we report the detailed ab initio analysis of charge flo w that occurs within a molecule during a molecular vibration, under co nditions corresponding to a Raman experiment. Theoretical values for t he molecular polarizability and polarizability derivatives are obtaine d in two ways for methane, ethane, and propane. Initially they are obt ained 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 determin ed 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 fr om the change in the molecular polarizability as the atoms are displac ed from their equilibrium positions. It is apparent that a molecule be haves like a dielectric material, developing a depolarizing surface ch arge while atomic dipoles of interior atoms oppose the charge transfer . For nonspherical molecules, the polarizability derivatives for the s ymmetric CH stretching modes show considerable dependence on the orien tation of the bonds with respect to the principal axes of the molecula r polarizability, and hence, the carbon chain. The polarizability deri vatives are characterized as arising from the atom-to-atom charge tran sfer or changes in the induced atomic dipoles. Previously observed dep endence 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 regular ly with chain length. The question of transferability of intensity par ameters from one molecule to another, as is assumed in the bond polari zability model, is addressed in the light of this new information.