发展用于研究实际复杂分子体系的非绝热动力学过程中量子效应的理论和实用计算方法有着极其重要的意义。准确描述复杂体系非绝热动力学的理论方法应当同时保证热平衡体系任何包括原子核和电子自由度的热力学物理量随时间的不变性，而且在绝热极限下原子核自由度的量子波尔兹曼分布函数随时间的不变性。已有的适用于和真实分子体系第一性原理电子结构方法直接结合的理论模型不能同时满足这两个基于非绝热动力学方程和量子统计力学的重要要求。申请人近期提出和完成基于量子相空间表象复杂分子体系的动力学理论和实用算法满足各种时间关联函数的量子谐振子极限和平衡体系的量子波尔兹曼分布不随时间变化，可以对真实分子体系原子核自由度的动力学和统计力学的量子效应进行合理定量描述。本项目拟将该相空间量子动力学理论进一步推广到两个或多个电子态的非绝热动力学，进而发展新的相空间理论模型和高效算法，为解释和预测实验现象和结果提供新的实用理论计算工具。

It is crucial to develop practical theoretical methods/models for studying quantum effects of both nuclear and electronics degrees of freedom in nonadiabatic dynamics of real (complex) molecular systems. A theoretical method/model for faithfully describing nonadiabatic dynamics in complex systems in thermal equilibrium should preserve thermodynamic properties of both nuclear and electronic degrees of freedom during evolution, and in the adiabatic limit should conserve the quantum Boltzmann distribution of the nuclear degrees of freedom. Most practical theoretical methods/models that can be combined with first principle electronic structure methods are not able to meet both requirements from quantum dynamics and statistics. We have recently presented a new theoretical framework in phase space formulations of quantum mechanics which leads to exact correlation functions in the classical, high-temperature, and harmonic limits and time-invariance of the quantum Boltzmann distribution of the nuclear degrees of freedom. The present proposal aims to extend our theoretical framework to nonadiabatic dynamics where two- or multi-electronic states are involved, which will initiate novel models and methodologies based on quantum phase space formulations and then provide efficient computational tools for experiment on nonadiabatic dynamics behaviors of real (complex) molecular systems.