Nonadiabatic Dynamics of Intersystem Crossings with the Symmetrical Quasi-Classical Dynamics Method Based on the Meyer--Miller Mapping Hamiltonian

We extended the symmetric quasi-classical (SQC) method based on the Meyer--Miller mapping Hamiltonian (MM) to treat the non-adiabatic dynamics simulation including spin-orbit couplings (SOCs). We studied the photoinduced ultrafast excited state dynamic involving intersystem crossing (ISC) process of the ReBr(CO)_3bpy molecule by performing the dynamics based on a pre-constructed model Hamiltonian as well as with the on-the-fly ab initio calculations. For the model system, the dynamics results obtained with the SQC/MM method consist very well with those obtained with the ML-MCTDH method. The SQC/MM method also outperforms the widely used trajectory surface hopping (TSH) method for the system studied here. For the realistic system, we employed the quasi-diabatic propagation scheme to enable the on-the-fly ab initio dynamics with the SQC/MM method. In this case, the dynamics results obtained with the SQC/MM method are very similar to those obtained with the TSH method, and both of them show great discrepancy with the model system ones, which implies it is necessary to perform the full atom on-the-fly dynamics for some molecular systems. Due to the great performance of the SQC/MM method in this work, we strongly recommend using it in the study of ISC processes in the future, both for model and realistic systems. The implementation of the SQC/MM method in the on-the-fly dynamics including the SOCs also paves the way to employing the SQC/MM or other more advanced semi-classical dynamics methods based on the mapping Hamiltonian to study the ISC processes for complex realistic molecular systems.