Calculating dipole and quadrupole polarizabilities relevant to surface enhanced Raman spectroscopy

Abstract

We have used ab initio electronic structure calculations to calculate the frequency dependent dipole–dipole polarizability ( α ), quadrupole–dipole polarizability ( A), quadrupole–quadrupole polarizability ( C), (electric) dipole–magnetic dipole polarizability ( G), and their normal coordinate derivatives for CO. The polarizability derivatives are of relevance to the interpretation of surface enhanced Raman (SER) spectra. Basis set convergence of these spectroscopic properties is studied, along with the effect of including electron correlation at the second-order polarization propagator (SOPPA) level, and the variation of the results with excitation frequency. The largest basis set SOPPA results that we have generated appear to be converged to within 20% or better for most of the properties we have studied, however in a few cases the convergence is much poorer. The most difficult property to converge involves the off-diagonal component of the derivatives of the quadrupole–dipole polarizability tensor. Our results show that the ratio of the largest components of A to the largest components of α are on the order of one atomic unit in size, and a similar statement can be made concerning the corresponding ratios of the normal coordinate derivatives. This means that the ratio of field derivatives to field strengths will also have to be on the order of one atomic unit in order for A and C to contribute comparably to α in determining SERS intensities.