Ab Initio Computation of the Duschinsky Mixing of Vibrations and Nonlinear Effects

Abstract

We present an analysis of the Duschinsky effect and its application to real molecules. We discuss the many subtle aspects of applying the theory to calculations and give examples of a nonlinear normal coordinate transformation. We show how to judge if nonlinear effects are small enough to be neglected through use of the zero-order axis-switching approximation, which allows calculation of Franck−Condon factors (FCF). However, even with the zero-order axis-switching approximation, nonorthogonality can occur in the Duschinsky matrix, and this must be corrected to allow proper FCF calculations. We have calculated the Duschinsky effect for two systems that form the anion in an electron-transfer ion pair, V(CO)6- and Co(CO)4-. The formation of the D3d neutral vanadium species is accompanied by a small geometric distortion and small Duschinsky effect, despite the change in point group from Oh. We discuss how to perform the calculations to properly represent degenerate vibrations and how to test if the linear app...