Mixed Quantum-Classical Dynamics Based On Branching Correction

In the field of chemistry,physics,biology,and materials,a large number of important processes belong to the category of non-adiabatic dynamics.In these processes,the electronic and nuclear motion is strongly coupled,leading to the breakdown of the traditional Born-Oppenheimer approximation.When quantum particles interact with a classical bath,the quantum coherence will naturally decay with time,leading to the quantum decoherence effects,which are of key significance in nonadiabatic dynamics.As the representative methods of mixed quantum-classical dynamics,the trajectory surface hopping and mean-field dynamics use classical trajectories to describe the nuclear motion,which largely improves the simulation efficiency while considering important quantum degrees of freedom.For these reasons,both methods have become the mainstream strategies for non-adiabatic dynamics.Nonetheless,because of the classical treatment of nuclei,the reasonable description of quantum decoherence effects is intrinsically missing in these two methods,which severely limits their accuracy and universality.In this thesis,relevant theoretical studies are carried out to solve the decoherence problem,and a unified trajectory branching correction method within the mixed quantum-classical dynamics is proposed,by which the accurate trajectory-based dynamics are achieved in scattering problems.In the first part of the thesis,we convert the classical trajectory description of mixed quantum-classical dynamics to quantum wave packets description and analyze the conditions of using the time-dependent Schr(?)dinger equation.We point out that the trajectory branching of wave packets will significantly destroy the self-consistency of the equation.A branching correction method is proposed on the basis of wave packet reflection,which can be combined with the fewest switches surface hopping and introduce the key decoherence correction effectively.In a series of diverse scattering model systems,the new method successfully obtained the scattering probabilities which is close to those of fully quantum dynamics,performing significantly better than other decoherence methods in the field.The results show that the wave packet reflection is the important mechanism of trajectory branching,and the new method can effectively describe the strong decoherence effects caused by the rapid separation of wave packets.In the second part of the thesis,we propose a novel method for surface hopping trajectory analysis,which satisfies the intrinsic relation between coherence and population automatically.In our method,the density matrix of the system can be constructed straightforwardly with the information of independent trajectories.The method is further combined with branching corrected surface hopping and highly accurate spatial-temporal evolution results are reproduced,which are consistent with the exact quantum references in all investigated systems.The results shows that both trajectory analysis and surface hopping methods are important to non-adiabatic dynamics simulations.Moreover,in addition to electronic population,the quantum coherence can also be properly described with surface hopping.In the third part of the thesis,we further introduce the branching correction into mean-field dynamics,through which the decoherence effects can be effectively described when the mean-field approximation fails.Two different fundamental branching algorithms are proposed,which are based on stochastic wavefunction collapse and weights of child trajectories,respectively.Both algorithms have their different advantages in simulation efficiency and can characterize the complicated dynamics in various systems.According to our systematic studies based on onedimensional scattering models,the branching correction improves accuracy of the mean-field dynamics by a factor of 10,and accurate results that are almost identical to branching corrected surface hopping are obtained.The accurate full channel dynamics that cannot be described in the traditional mean-field method are successfully reproduced with our new method.The results strongly empathize that branching correction is universal in quantum scattering problems and provides a new unified framework for mixed-quantum-classical dynamics.