Calculation of Rayleigh and Raman polarizabilities within the electric dipole approximation has been done using exact electronic wavefunctions. The results provide the most accurate data available for future comparison with experiment.
Although Raman scattering is one of the most popular fields in studying molecules, liquids, solids, etc., the exact treatment of Raman scattering is also well known for the difficulties encountered in performing the actual calculation. To be more specific, the polarizability tensor component (a,,,),, for a molecular normal vibrational Raman process based on the Kramers-Heisenberg dispersion expression [ 1 ] contains a summation over all intermediate vibronic states as given in eq. ( 2) below. Since the number of such intermediate states is, in principle, infinite the actual summation can be done exactly only in cases where some suitable sum rules are available such as for the electronic Raman scattering from a hydrogen atom [ 2 1. For a general vibronic Raman process it seems very difficult to perform the summation except using various approximations. In persuing exact solutions, however, there is one method known as the ground-state approach of Tang and Albrecht [ 3,4]. This ground-state method depends quite sensitively on how good the wavefunction approaches the exact one. As suggested by these authors on using exact wavefunctions [ 31, we consider here the system of hydrogen molecule ion, Hz, since it has the advantage over other molecular systems by having exact analytic wavefunctions. Very recently, Bishop and Lam [ 51 reported various vibrational polarizabilities including those of H: _ Our results, being smaller than theirs, would be the most accurate data available up to now.