Fourth-Order Perturbative Model for Photoinduced Internal Conversion Processes

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Essential to the functionality of numerous biological and synthetic molecular systems is the ability to rapidly convert electronic excitation energy into heat. Such internal conversion (IC) transitions often cannot be described by traditional second-order kinetic theories because of time-coincident electronic and nuclear relaxation processes. Here, we present a perturbative fourth-order phenomenological model for photoinduced IC that incorporates effects associated with finite laser bandwidths and nonequilibrium nuclear motions. Specialized knowledge of first-principles computational methods is not required, and many parameters can be obtained with standard spectroscopic measurements. The model is applied to the IC processes that precede electrocyclic ring-opening in α-terpinene. It is shown that the primary factor governing the shape of the population decay profile (Gaussian versus exponential) is the rate at which the wavepacket approaches the geometry corresponding to degeneracy between the excited states. Other parameters such as the displacement in the promoting mode and the thermal fluctuation amplitudes affect the sensitivity of the IC dynamics to motion of the wavepacket but do not alter the basic physical picture. Finally, we suggest a wavepacket representation of the IC process to visualize correlations between population-transfer dynamics and the amount of energy transferred from the system to the bath.