Studies in Raman Intensity Theory

Abstract

Raman intensity theory is investigated with the Kramers–Heisenberg dispersion theory as a basis. The sum over excited states is transformed into an infinite series in ground-state matrix elements involving an average energy. Particular choice of this average energy and neglect of all terms N ≥ 2 amount to the same approximations as in a variation–perturbation approach used by others. This truncated series, after a transformation through a quantum mechanical identity, assumes a particularly simple form. Calculations using this simple expression are presented for both the H2+ ion and the H2 molecule for several approximate wavefunctions. In several additional calculations for the H2 molecule, a more drastic approximation is employed where it is assumed that the major contribution to the derived polarizability is from the normalization factor of the wavefunction rather than from the detail of the wavefunction itself. The results of these calculations are compared with other calculations and, in the case of H2, also with experimental data. The qualitative success is encouraging. Finally, tentative explanations, based on the present approximation, are offered for some common empirical rules in Raman spectroscopy. These concern (1) the additivity properties for various bond types, (2) the fact that highly ionic bonds tend to exhibit weak Raman intensity while covalent bonds exhibit strong intensity, and (3) that totally symmetric vibrations almost always exhibit significantly greater intensity than do nontotally symmetric vibrations.