From Surface Hopping to Quantum Dynamics and Back. Finding Essential Electronic and Nuclear Degrees of Freedom and Optimal Surface Hopping Parameters.

We report an efficient iterative procedure that exploits surface-hopping trajectory methods and quantum dynamics to achieve two complementary purposes: to identify the minimum dimensionality of a molecular Hamiltonian in terms of electronic and nuclear degrees of freedom to study radiationless relaxation mechanisms as well as to provide a reference quantum dynamical calculation that allows assessing of the validity of surface-hopping parameters. This double goal is achieved by a feedback loop between surface hopping and MCTDH calculations based on potential energy surfaces parametrized with a linear vibronic coupling method. Initially, a surface hopping calculation in full dimensionality with a chosen set of parameters is performed, and it is repeated, gradually reducing its dimensionality until divergence with the initial calculation is observed or the system is small enough to be treated quantum dynamically. A comparison between the quantum dynamics and surface hopping simulations dictates the validity of the surface hopping parameters. Using these new parameters, the reduction loop is started again, until convergence. As an example, this strategy is applied to simulate the ultrafast intersystem crossing dynamics of [PtBr] in solution. The 15-dimensional space initially including 200 electronic states is reduced to a 9-dimensional problem with 76 electronic states, without a considerable loss of accuracy.