Matrix elements of doubly degenerate vibrations and the Herzberg-Teller series

摘要

The non-zero terms in doubly degenerate vibrations in the Herzberg-Teller series are discussed and simplified formulae for the matrix elements for transitions between the degenerate l-components of such vibrational levels in upper and lower electronic states are given, with the emphasis on the change of vibrational frequency accompanying the transition. The results are applied to the analysis of degenerate components in the ν_6 and ν_(16) vibrational transitions in the benzene A~1B2 _u-X~1A1_g system, and it is shown that in cases where the second order Herzberg-Teller terms are important, cancelation effects in the matrix elements can lead to the disappearance of certain transitions which are otherwise allowed.