HERZBERG-TELLER THEORY AND THE DUSCHINSKY EFFECT

Author Institution: Institute for Atomic Research and Department of Chemistry, Iowa State UniversityThe 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 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 wave-functions 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 non-totally 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. Constructive-destructive interference can lead to a break-down in mirror symmetry between the absorption and fluorescence spectra. The theory is applied to napthalene and phenantherene