Theory of vibronic intensity borrowing. Comparison of Herzberg-Teller and Born-Oppenheimer coupling

The Herzberg-Teller theory of vibronic intensity borrowing is reinvestigated. A potentially serious deficiency is found in the conventional approximation scheme based on neglecting vibronic perturbation of the ground state relative to that of the excited state. Simple theoretical models are studied and show systematic cancellation of the lowest-order induced transition dipole moment if both vibronic perturbations are included. As a result the vibronic coupling between Born-Oppenheimer states via nuclear momenta, for which such a cancellation does not occur, tends to contribute measurably to the induced transition moment, contrary to what usually is assumed. Two methods to distinguish between Herzberg-Teller-type (HT) and Born-Oppenheimer-type (BO) contributions are discussed, namely the absorption-emission asymmetry and the isotope effect. The former results from interference between HT and BO terms, which is usually constructive in absorption and destructive in emission; the latter is due to the fact that BO coupling is much more sensitive to isotopic substitution than HT coupling. The induced components of S0−S1 transitions in benzene, pyrazine, and pyrene are shown to exhibit anomalous isotope effects and/or absorption-emission asymmetries which indicate substantial BO contributions, even when normal-coordinate rotation upon deuteration or excitation is taken into account. It is concluded that a quantitative calculation scheme for vibronically induced intensities must include vibronic perturbation of the ground state and both HT and BO couplings.