Vibrational coherence in excited state decay: the role of the type of electron-vibrational interactions

Abstract

The vibrational coherence in excited electronic state decay is studied theoretically. The model coherent system is assumed to consist of two electronic levels coupled to a single vibrational mode and dissipating its energy to a thermal bath. Time dependence of the excited electronic state population is investigated and characteristics of the coherent structure are determined for three cases of the off-diagonal excited–ground electronic states coupling: (a) constant (Franck–Condon) term; (b) linear in vibrational coordinate; (c) quadratic in vibrational coordinate. Interesting dependences of the amplitude, frequencies, and life-time of the coherent oscillations are found with respect to several parameters like, e.g., Herzberg–Teller correction, Stokes shift, vertical energy and rate of vibrational relaxation. It was shown that coherent part of excited state population is different for various types of interactions and it is sensitive to a proper definition of diabatic states. For the linear and quadratic cases, the vibrational coherence in electronic population is significantly increased compared to the constant coupling. A simple relation of these parameters to the life-time of the excited electronic state decay is briefly mentioned.