Dynamics at Conical Intersections

The nonadiabatic coupling of electronic and vibrational degrees of freedom is the defining feature of electronically excited states of polyatomic molecules. Once considered a theoretical curiosity, conical intersections (CIs) are now generally accepted as being the dominant source of coupled charge and vibrational energy flow in molecular excited states. Passage through CIs leads to the conversion of electronic to vibrational energy, which drives the ensuing photochemistry, isomerization being a canonical example. It has often been remarked that the CI may be thought of as a transition state in the excited state. As such, we expect that both the direction and the velocity of approach to the CI will matter. We explore this suggestion by looking for dynamical aspects of passage through CIs and for analogies with well-known concepts from ground-state reaction dynamics. Great progress has been made in the development of both experimental techniques and ab initio dynamics simulations, to a degree that direct comparisons may now be made. Here we compare time-resolved photoelectron spectroscopy results with on-the-fly ab initio multiple spawning calculations of the experimental observables, thereby validating each. We adopt a phenomenological approach and specifically concentrate on the excited-state dynamics of the C=C bond in unsaturated hydrocarbons. In particular, we make use of selective chemical substitution (such as replacing an H atom by a methyl group) so as to alter the inertia of certain vibrations relative to others, thus systematically varying (mass-weighted) directions and velocities of approach to a CI. Chemical substituents, however, may affect both the nuclear and electronic components of the total wave function. The former, which we call an inertial effect, influences the direction and velocity of approach. The latter, which we call a potential effect, modifies the electronic structure and therefore the energetic location and topography of the potential energy surfaces involved. Using a series of examples, we discuss both types of effects. We argue that there is a need for dynamical pictures and simple models of nonadiabatic dynamics at CIs and hope that the phenomenology presented here will help inspire such developments.