Study On Decoherence In High-dimensional Multilevel Nonadiabatic Scattering Dynamics

In various fields of chemistry,physics,biology,and materials,a large number of important processes need to be studied under the framework of nonadiabatic dynamics.As a typical mixed quantum-classical dynamics method,the trajectory surface hopping method achieves a good balance between efficiency and accuracy,thus presenting extensive prospects for applications.However,due to the classical treatment of nuclei,the traditional surface hopping method lacks essential quantum decoherence,which limits its precision in describing complex systems.In addition,several typical onedimensional two-level scattering models are widely used in theoretical chemistry to evaluate the accuracy of surface hopping methods,resulting in insufficient research on the universality of existing methods in high-dimensional multilevel systems.In this thesis,we focus on the systematic study of decoherence in high-dimensional multilevel nonadiabatic scattering dynamics,and propose the improved trajectory branching surface hopping method and machine learning approach for decoherence time formulas.Both of these decoherence strategies can achieve higher accuracy for nonadiabatic dynamics simulations based on independent trajectories.In the first part of this thesis,we develop a trajectory branching surface hopping method for multilevel systems.This method calculates the momentum of each wave packet on the adiabatic potential energy surface at each moment of the surface hopping trajectory with the parallel momentum approximation.All adiabatic states are categorized into reflection and non-reflection groups,based on whether the wave packet on each potential energy surface undergoes reflection within a time step.By using the wave packet on the active potential energy surface as a reference,we collapse the system wave function to the group containing the active state and renormalize the wave function.Surface hopping methods consider internal consistency to define hopping probabilities,and there are multiple alternative definitions available for trajectory branching surface hopping simulations in the adiabatic representation.To systematically evaluate various surface hopping methods,we construct a series of onedimensional three-level and four-level scattering models.Our new method successfully obtains results that are close to those of fully quantum dynamics,remaining insensitive to changes in system levels and independent of the transition probability definitions.In the second part of this thesis,we present a general machine learning assisted approach to identify decoherence time formulas.This method iteratively generates a large number of high-order descriptors based on the initial descriptor and constructs corresponding decoherence time formulas through Taylor expansion.By incorporating these decoherence time formulas into surface hopping simulations and taking fully quantum dynamics results as references,we perform discrete optimization of relevant parameters and conduct multilayer screening of decoherence time formulas to identify the optimal ones.Considering that the decoherence time is calculated at each step along each trajectory in surface hopping simulations,the decoherence time formulas obtained through the machine learning method are less prone to overfitting.This method demonstrates significant universality and in principle,can be applied to machine learning on arbitrary datasets to obtain the corresponding optimal decoherence time formula,which is expected to comprehensively improve the accuracy of surface hopping methods in dealing with complex systems.In the third part of this thesis,we apply the developed machine learning method for decoherence time formulas to study one-dimensional scattering systems.Based on the kinetic energy and the energy difference between two potential energy surfaces as initial descriptors,we iteratively generate high-order descriptors and conduct multilayer screening to identify the optimal second-order descriptor.In six standard onedimensional two-level scattering models and four different scattering model libraries,the decoherence time formula constructed by this descriptor reproduces highly accurate results as the trajectory branching surface hopping method,which is the first time that the surface hopping method with the decoherence time formula achieves unprecedented accuracy.Furthermore,unlike the trajectory branching surface hopping method,this formula does not involve force calculations and has equal efficiency as the traditional energy difference formula.In the last part of this thesis,we perform preliminary research on high-dimensional scattering systems by combining the trajectory branching surface hopping method with machine learning method of decoherence time formulas.By constructing and testing a series of two-dimensional scattering models,we observe significant errors in the trajectory branching surface hopping method for certain models.Building datasets with these two-dimensional models and typical one-dimensional scattering models,we obtain two novel energy-based decoherence time formulas through machine learning.Compared with the trajectory branching surface hopping method,surface hopping methods based on the new formulas exhibit enhanced stability in two-dimensional systems.In specific models,the new formulas systematically reduce the errors of surface hopping simulations to approximately half of those obtained by the trajectory branching surface hopping method,while demonstrating basically consistent results with the trajectory branching surface hopping method in other systems.These studies further illustrate the generality of our machine learning approach for decoherence time formulas,which can be widely applied to investigate decoherence in complex highdimensional multilevel systems.