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 [PtBr6]2– 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.