A Mixed Quantum-Classical View to the Kinetics of Chemical Reactions Involving Multiple Electronic States
The time evolution of molecular systems, including multiple electronic states, is in principle described by complicated sets of equations that include the dynamical coupling between the electrons and nuclear motions. A valuable route of simplification is to use classical mechanics to describe the nuclear motion. But although they are of critical importance for understanding the kinetics of multiple electronic state reactions, non-Born–Oppenheimer effects are manifest only for brief periods while most of the time the semi-classical description remains perfectly acceptable. Decoherence theory provides a means to operate the quantum-to-classical transition. We focus in this chapter on the development of chemical kinetics theories that are, in our view, very important for the diffusion of the notion of decoherence to non-specialists. In the first part of the chapter we show under which conditions the transition to the classical description can be operated. A rate constant expression sharing formal similarities the Marcus theory or the non-adiabatic transition state theory is obtained. Importantly, the mixed quantum–classical rate constant includes a characteristic decoherence time which captures the idea that molecular systems, although intrinsically obeying quantum mechanical laws, behave semi-classically after a finite but non-zero amount of time. In the second part of the chapter we employ density functional theory molecular dynamics simulations to investigate the molecular mechanisms governing decoherence in various molecular systems of biological interest (electron transfers or spin-crossing reactions). The respective roles of the local structure and dynamics of the cofactors, as well as the role of their environment, are investigated.