Study Of Nonadiabatic Dynamics At Low Temperatures By Quantum Wave Packet Method

The Born-Oppenheimer（BO）approximation is the foundation of theoretical studies of molecular reaction dynamics.It assumes that the motion of the nucleus can be described by a single BO adiabatic potential energy surface,thus ignoring the nonadiabatic coupling between the electronic states.However,in many cases,nonadiabatic coupling plays an important role in molecular collision dynamics,especially at low temperatures,the effect of nonadiabatic coupling is generally enhanced.So far,studies of low temperature reaction dynamics,including the studies of low temperature nonadiabatic dynamics,have been performed with the time-independent close-coupling（TICC）method.However,due to the limitation of the TICC method,it is difficult to extend to complex reaction system.Compared with TICC method,quantum wave packet（QWP）method has better scalability and can be used to characterize the reaction dynamics of more complex systems.However,the general QWP method is difficult to be applied to the study of reaction dynamics at low temperatures.In this paper,the QWP method is developed for the study of nonadiabatic dynamics at low temperatures by improving the grid method.In this paper,the nonadiabatic dynamics of the Na（3p）+HD→Na H+D/Na D+H reaction at higher temperatures is studied by general QWP method.Because the reactants and products in the reaction are in different electronic states,the transition of electronic states must occur through nonadiabatic coupling.The minimum energy reaction path indicates that the Na（3p）+HD reaction prefers the insertion reaction path.However,the results of QWP calculation show that the reaction mechanism is different from the typical adiabatic insertion reactions.By comparing the results of adiabatic and nonadiabatic calculations,it is found that the nonadiabatic coupling in the reaction reduces the lifetime of the intermediate complex.Although the reaction occurs via insertion reaction path,it does not form long-lived complex like typical adiabatic insertion reaction,but instead the incident Na（3p）atom directly abstract H or D atom to form products.Finally,the insertion-abstraction reaction mechanism is proposed for this nonadiabatic reaction.In the study of reaction dynamics at low temperatures,the QWP method encounters several serious problems.First,the long de Broglie wavelengths associated with low and ultralow collision energies force the use of extremely large grids in the scattering coordinate.Then,the slow movement of the wave packet also necessitates a very long propagation time.In order to apply the QWP method to the calculations of reaction dynamics at low temperatures,the L-shaped grid method is improved in this paper.In the improved L-shaped grid method,the total grid space is divided into the interaction and asymptotic regions,and different numbers of vibrational and rotational basis functions are used for the two regions.The improved L-shaped grid method could save a considerable amount of grid points and in the meantime accelerate the propagation,thus making it possible to describe reaction dynamics at low temperatures with the QWP method.The dynamics of the nonadiabatic H+Na D→Na（3s,3p）+HD reaction in the collision energy range of 1～80 cm^-1（almost 1～100 K）is studied by using the QWP method with improved L-shaped grids.The dynamic results show that the Na（3s）channel is mainly formed by collinear collision and the Na（3p）channel is mainly formed by side-on collision in the collision energy range of 20～80 cm^-1.Therefore,the relative collision angle of H and Na D plays an important role in the product branching of this nonadiabatic reaction.When the collision energy is lower than 20 cm^-1,both Na（3s）and Na（3p）reaction channels are dominated by resonance-mediated reaction mechanism.In addition,nonadiabatic couplings can reduce the total reactivity of this reaction.At low temperatures,the QWP calculation based on the improved L-shaped grids becomes very difficult when the colliding molecules are in the electronically excited state.In this paper,the total grid space is further divided into the interaction,asymptotic and long-range regions（IALR）,and an IALR-QWP method is proposed to study the nonadiabatic dynamics of electronic excited state reactions at low temperatures.For the IALR-QWP method,different numbers of vibrational and rotational basis functions are used for the three regions,especially for the long-range region,only one basis function corresponding to the initial reactant ro-vibrational state is used.Thus,the number of grids along scattering coordinate has little influence for total computational costs.The nonadiabatic dynamics of the Li（2s,2p）+HF reaction at low temperatures are studied by using the IALR-QWP method.The calculated results show that the electronic energy in the Li（2p）+HF reaction can effectively increase the reactivity at low temperatures.For the Li（2s）+HF reaction,the nonadiabatic coupling has little effect on the reaction,mainly causing a small energy shift in reaction probability curves,and the effect of nonadiabatic coupling is not enhanced at low temperatures.In addition,the IALR-QWP method is extended to study inelastic scatterings,and the accuracy of the method in characterizing adiabatic and non-adiabatic dynamics of molecular inelastic scatterings at low temperatures is demonstrated by applying it to three typical collision systems.This paper focuses on the efficiency and accuracy of IALR-QWP method in low temperature dynamics calculation.Due to its better scalability,the IALR-QWP method can be applied to study the nonadiabatic dynamics of more complex collision systems at low temperatures.