论文标题
SU（N）谎言组相位空间中的非绝热环聚合物分子动力学
Non-adiabatic Ring Polymer Molecular Dynamics in the Phase Space of the SU(N) Lie Group
论文作者
论文摘要
我们在SU（N）Lie组的相空间中得出非绝热环聚合物分子动力学（RPMD）方法。我们称之为旋转映射非绝热rpmd（SM-NRPMD）的方法基于电子自由度（DOFS）和核DOF的环形聚合物路径综合描述的旋转映射形式。使用Stratonovich-Weyl转换电子DOF，并为核DOFS的Wigner变换，我们得出了Kubo转换的时间相关函数（TCF）的精确表达。我们使用Matsubara近似值来得出旋转映射非绝热Matsubara动力学，从而消除了非绝热Matsubara动力学，从而删除了Liouvillian的假想部分，从而消除了TCF中的高频核法线模式，并从非耐绝热的Matsubara动力学中得出了SM-NRPMD方法。与原始的NRPMD方法相比，SM-NRPMD方法具有基于MMST映射形式主义的原始NRPMD方法的数值优势，这是由于使用SU（n）Lie Group的更自然的映射，该图（n）谎言组可保留原始系统的对称性。我们从数值计算三态模型系统的Kubo转换位置自动相关函数和电子总体相关函数。数值结果证明了SM-NRPMD方法的准确性，该方法的表现优于原始的基于MMST的NRPMD。我们设想SM-NRPMD方法将是一种有力的方法，可以准确模拟电子非绝热动力学和核量子效应。
We derive the non-adiabatic ring polymer molecular dynamics (RPMD) approach in the phase space of the SU(N) Lie Group. This method, which we refer to as the spin mapping non-adiabatic RPMD (SM-NRPMD), is based on the spin-mapping formalism for the electronic degrees of freedom (DOFs) and ring polymer path-integral description for the nuclear DOFs. Using the Stratonovich-Weyl transform for the electronic DOFs, and the Wigner transform for the nuclear DOFs, we derived an exact expression of the Kubo-transformed time-correlation function (TCF). We further derive the spin mapping non-adiabatic Matsubara dynamics using the Matsubara approximation that removes the high frequency nuclear normal modes in the TCF and derive the SM-NRPMD approach from the non-adiabatic Matsubara dynamics by discarding the imaginary part of the Liouvillian. The SM-NRPMD method has numerical advantages compared to the original NRPMD method based on the MMST mapping formalism, due to a more natural mapping using the SU(N) Lie Group that preserves the symmetry of the original system. We numerically compute the Kubo-transformed position auto-correlation function and electronic population correlation function for three-state model systems. The numerical results demonstrate the accuracy of the SM-NRPMD method, which outperforms the original MMST-based NRPMD. We envision that the SM-NRPMD method will be a powerful approach to simulate electronic non-adiabatic dynamics and nuclear quantum effects accurately.
