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 lo 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 D-3d 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 approximation is adequate. The tetrahedral cobalt anion undergoes a much larger geometrical distortion, which results in a larger Duschinsky effect, upon formation of the nearly C-3 nu, neutral species. The analysis of the cobalt system, with a C-1 symmetry for the neutral, demonstrates the methods required when there is no simplification from symmetry. These two examples show the validity of the zero-order axis-switching approximation. The cobalt complex has much larger reorganization energy and a much greater dependence of reorganization energy on the choice of reference state, as expected when the Duschinsky effect is larger. We briefly outline the method of applying these computations to electron-transfer rate calculations.