Microscopic modelling of photoisomerization and internal-conversion dynamics

Ultrafast internal conversion triggered by the twisting of a double bond is believed to be a fundamental process of organic photochemistry. A class of model Hamiltonians is constructed, which are suitable to describe basic features of photoisomerization and internal conversion at the quantum mechanical level. Apart from the torsional mode, which is assumed to lead to an intersection of the S₁ and the S₀ potential-energy functions, a vibronically active coupling mode and a set of totally symmetric Condon active modes are considered. The adiabatic potential-energy surfaces of these models exhibit a multidimensional conical intersection (or photochemical funnel). Using an expansion of the time-dependent state vector in a direct-product basis of diabatic electronic states, free-rotor states and harmonic-oscillator basis states, the time-dependent Schrödinger equation is solved (numerically) exactly. The time evolution of electronic populations, cis/trans populations and the energy content of individual modes are investigated for a model example involving up to four nuclear degrees of freedom. The calculations reveal the transition from reversible torsional dynamics in the one-dimensional case to irreversible photoisomerization in the multi-dimensional case.