Consistent treatment of quantum-mechanical and classical degrees of freedom in mixed quantum-classical simulations

A mixed quantum-classical formulation of nonadiabatic molecular processes is outlined. Based on a recently introduced mapping formalism [Stock and Thoss, Phys. Rev. Lett. 78, 578 (1997)], the formulation employs a quantum-mechanically exact mapping of discrete electronic states onto continuous variables, thus describing the dynamics of both electronic and nuclear degrees of freedom by continuous variables. It is shown that the classical evaluation of the mapping formalism results in a self-consistent description of electronic and nuclear degrees of freedom, which treats both types of dynamical variables in a completely equivalent way. The applicability of the approach is thus solely determined by the validity of the classical approximation and does not rest on additional assumptions such as the ad hoc combination of classical and quantum-mechanical theories. The observation of unrestricted flow of zero-point energy in the electronic degrees of freedom indicates the limits of the classical approximation. H...