  The symmetrical quasi-classical dynamics method based on the Meyer-Miller
mapping Hamiltonian (MM-SQC) shows the great potential in the treatment of the
nonadiabatic dynamics of complex systems. We performed the comprehensive
benchmark calculations to evaluate the performance of the MM-SQC method in
various site-exciton models with respect to the accurate results of quantum
dynamics method multilayer multiconfigurational time-dependent Hartree
(ML-MCTDH). The parameters of the site-exciton models are chosen to represent a
few of prototypes used in the description of photoinduced excitonic dynamics
processes in photoharvesting systems and organic solar cells, which include the
rather board situations with the fast or slow bath and different system-bath
couplings. When the characteristic frequency of the bath is low, the MM-SQC
method performs extremely well, and it gives almost the identical results to
those of ML-MCTDH. When the fast bath is considered, the deviations exist
between the MM-SQC and ML-MCTDH results if the high-frequency bath modes are
improperly treated by the classical manner. When the so-called adiabatic
renormalization was employed to construct the reduced Hamiltonian by freezing
high-frequency modes, the MM-SQC dynamics can give the results comparable to
the ML-MCTDH ones. Thus, the MM-SQC method itself provide reasonable results in
all test site-exciton models, while the proper treatments of the bath modes
must be employed. The possible dependence of the MM-SQC dynamics on the
different initial sampling methods for the nuclear degrees of freedom is also
discussed.
