Path integrals for nonadiabatically coupled electrons and nuclei in molecules: Force analysis for branching nuclear paths and conservation laws

摘要: Real-time dynamics in electron-nucleus coupled systems molecules is studied using the path-integral formalism, with a special emphasis on nonadiabatic interactions. We first establish formal description of entire system. Applying stationary phase approximation, we then derive equations for mixed quantum-classical treatment system: motion electron wave-packet and those nuclear driven by what call force form. Thus present theory also serves as general quantum classical systems. On this theoretical foundation, analyze two theories from viewpoint path branching: semiclassical Ehrenfest recently developed method phase-space averaging natural branching [T. Yonehara, S. Takahashi, K. Takatsuka, J. Chem. Phys. 130, 214113 (2009)]. give unified account essential feature their physical implications limitations. Path-integral formalism leads to further refinement idea caused coupling, thus giving deeper insight into dynamics. Further, study conservation laws energy, linear momentum, angular momentum representation. extend formulation so handle laser fields.