Surface Hopping Methods For Large-Scale Nonadiabatic Dynamics

Nonadiabatic dynamics is ubiquitous in chemistry,physics,biology,and material sciences.As a typical mixed quantum-classical dynamics method,the trajectory surface hopping method achieves a good balance between efficiency and accuracy,and is one of the most widely-utilized nonadiabatic dynamics methods.For large-scale nonadiabatic dynamics with a large number of electronic states,the direct application of traditional surface hopping method severely suffers from two fundamental problems:(1)When adiabatic states are close to degenerate,the corresponding nonadiabatic couplings change rapidly with time,resulting in the low numerical computational efficiency of surface hopping simulations;(2)In order to carry out surface hopping simulations in large-scale systems,electronic structure calculations are required at each time step of each trajectory,resulting in high computational costs for constructing the potential energy surfaces as well.On the basis of these problems,this thesis develops a series of surface hopping methods for large-scale nonadiabatic dynamics simulations,and systematically evaluate the performance in a variety of one and two-dimensional Holstein models.These methods significantly improve the computational efficiency while maintaining the accuracy in the meantime,showing broad application prospects.In the first part of this thesis,we focus on the basic characteristics of complex surface crossing problems,and classify the surface crossings into four general types.Through the proper assignment of adiabatic states based on the corresponding overlap integrals and the self-consistent correction of the hopping probabilities,each type of surface crossings is accurately treated.It is combined with Tully’s fewest switches surface hopping(FSSH)method,and the corresponding crossing corrected FSSH(CCFSSH)approach shows faster time-step size convergence than the widely-utilized locally diabatic formalism of FSSH(LD-FSSH)and self-consistent FSSH(SC-FSSH)methods.CC-FSSH successfully enlarges the time-step size from 0.002 fs to 1 fs and improves the efficiency by around 500-fold,achieving nonadiabatic dynamics simulations in systems with hundreds of molecular sites.In the second part of this thesis,we find that due to the quantum decoherence effect,the surface hopping simulations usually involve a limited number of important adiabatic states,and propose the subspace surface hopping method.With a proper treatment of surface crossings in the subspace by CC,the corresponding subspace crossing corrected(SCC)method greatly simplifies the surface crossings,and maintains the accuracy of nonadiabatic dynamics in the meantime.Besides FSSH,we also adopt the global flux surface hopping(GFSH)method.Both SCC-FSSH and SCC-GFSH methods achieve excellent system-size independence with a large time-step size of dt = 1 fs in systems with thousands of molecular sites,verifying the universality of SCC method.Especially,SCC-GFSH method does not rely on the nonadiabatic couplings at all,promising for nonadiabatic dynamics simulations in realistic systems.Based on the two parts of work,the complex surface crossing problems are no long the bottleneck limiting the efficiency of large-scale surface hopping simulations.In the third part of this thesis,we further reduce the computational costs of largescale nonadiabatic dynamics simulations by reducing the size of effective Hamiltonian matrices.As the contribution of each localized electronic state to the important adiabatic states varies greatly,an effective Hamiltonian matrix can be constructed with a limited number of diabatic states to reproduce important adiabatic potential energy surfaces for nonadiabatic dynamics simulations.We propose a multilayer subsystem surface hopping(MSSH)method,where only molecular sites with significant influence on the important adiabatic states are carried out with surface hopping simulations,while the rest of the system are treated by molecular dynamics or statistical descriptions to describe the memory effect of the dynamics.Compared with surface hopping simulations in the full system,the MSSH method reduces the computational costs by2～6 orders of magnitude and maintains the accuracy in the meantime in a series of one and two-dimensional Holstein models,achieving the nonadiabatic dynamics simulations in systems with hundreds of thousands of states.In the last part of this thesis,based on the fact that the corresponding adiabatic states at adjacent time steps in trajectory surface hopping are quite similar,we combine the MSSH with subspace surface hopping,and propose the surface hopping method with adaptive energy window.Different from the subspace surface hopping method in the second part,only eigenstates in a certain energy window are obtained to further reduce the computational costs.The condition of wave function normalization is achieved through the adaptive adjustment of the energy window.For two-dimensional Holstein models with strong electronic couplings,the method further improves the computational efficiency by 2～3 orders of magnitude on the basis of MSSH method,while maintaining the computational accuracy.So far,we successfully achieve such large-scale nonadiabatic dynamics simulations with millions of electronic states,which is of great promise for systematic studies in a variety of complex electron and exciton dynamics problems.