Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA.
J Chem Phys. 2023 Jan 28;158(4):044123. doi: 10.1063/5.0133970.
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 Meyer-Miller-Stock-Thoss (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.
我们在 SU(N)李群的相空间中推导出非绝热环聚合物分子动力学（RPMD）方法。这种方法，我们称之为自旋映射非绝热 RPMD（SM-NRPMD），基于电子自由度（DOFs）的自旋映射形式和核 DOFs 的环聚合物路径积分描述。我们使用电子 DOFs 的 Stratonovich-Weyl 变换和核 DOFs 的 Wigner 变换，推导出了 Kubo 变换的时相关函数（TCF）的精确表达式。我们进一步通过在 TCF 中去除高频核正则模态，使用 Matsubara 近似推导出自旋映射非绝热 Matsubara 动力学，并通过舍弃 Liouvillian 的虚部，从非绝热 Matsubara 动力学推导出 SM-NRPMD 方法。与基于 Meyer-Miller-Stock-Thoss（MMST）映射形式的原始 NRPMD 方法相比，SM-NRPMD 方法具有数值优势，因为它使用 SU(N)李群进行更自然的映射，保留了原始系统的对称性。我们对三态模型系统进行了数值计算，得到了 Kubo 变换的位置自相关函数和电子布居相关函数。数值结果证明了 SM-NRPMD 方法的准确性，它优于原始的基于 MMST 的 NRPMD。我们设想 SM-NRPMD 方法将成为一种强大的方法，可以准确地模拟电子非绝热动力学和核量子效应。
