Herzberg–Teller Vibronic Coupling and the Duschinsky Effect

Abstract

The assumption that the difference in composition, in terms of symmetry coordinates, between the normal vibrational motions of the ground and first excited state (Duschinsky effect) can be neglected in the Herzberg–Teller theory of absorption and fluorescence vibronic intensities is critically examined. A theory of the Duschinsky effect is described which involves expansion of the potential energy of the fluorescent state in terms of the ground state normal coordinate displacements. Off-diagonal quadratic contributions arise in the expansion whenever there is a coupling between the crude Born–Oppenheimer electronic wavefunctions of the fluorescent and other excited states through two or more ground state normal motions of the same symmetry. The importance of the Duschinsky effect depends on the magnitudes of the Herzberg–Teller vibronic matrix elements and the frequency differences between the fundamentals which effect vibronic perturbations. Inclusion of the Duschinsky effect in the Herzberg–Teller theory for two or more nontotally symmetric perturbing vibrations introduces a constructive–destructive interference problem, involving the “forbidden” transition moments similar to the one that arises in the theory of Craig and Small on totally symmetric vibrational perturbations. The interferences can lead to a breakdown in mirror symmetry between the absorption and fluorescence spectra. The theory presented for a two vibrational model enables the relative signs of the two forbidden moments to be determined by comparison of the relative intensities of the two vibronic bands in absorption and fluorescence. In the case of naphthalene the forbidden moments associated with the 509 and 938 cm−1 b3g modes are shown to be antiparallel. Calculations for phenanthrene suggest that, although the Duschinsky effect should be included in any attempt at accurate vibronic intensity calculations, the constructive–destructive interference effects described by Craig and Small are primarily responsible for the gross deviations from mirror symmetry experimentally observed. Illustrative calculations show that the Duschinsky effect should not be neglected in the Herzberg–Teller theory of both fluorescence and absorption vibronic intensities.