Mannouch Jonathan R, Richardson Jeremy O
Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
J Chem Phys. 2020 Nov 21;153(19):194110. doi: 10.1063/5.0031173.
In a previous paper [J. R. Mannouch and J. O. Richardson, J. Chem. Phys. 153, 194109 (2020)], we derived a new partially linearized mapping-based classical-trajectory technique called the spin partially linearized density matrix (spin-PLDM) approach. This method describes the dynamics associated with the forward and backward electronic path integrals using a Stratonovich-Weyl approach within the spin-mapping space. While this is the first example of a partially linearized spin-mapping method, fully linearized spin-mapping is already known to be capable of reproducing dynamical observables for a range of nonadiabatic model systems reasonably accurately. Here, we present a thorough comparison of the terms in the underlying expressions for the real-time quantum correlation functions for spin-PLDM and fully linearized spin mapping in order to ascertain the relative accuracy of the two methods. In particular, we show that spin-PLDM contains an additional term within the definition of its real-time correlation function, which diminishes many of the known errors that are ubiquitous for fully linearized approaches. One advantage of partially linearized methods over their fully linearized counterparts is that the results can be systematically improved by re-sampling the mapping variables at intermediate times. We derive such a scheme for spin-PLDM and show that for systems for which the approximation of classical nuclei is valid, numerically exact results can be obtained using only a few "jumps." Additionally, we implement focused initial conditions for the spin-PLDM method, which reduces the number of classical trajectories that are needed in order to reach convergence of dynamical quantities, with seemingly little difference to the accuracy of the result.
在之前的一篇论文[J. R. 马努奇和J. O. 理查森，《化学物理杂志》153, 194109 (2020)]中，我们推导了一种新的基于部分线性化映射的经典轨迹技术，称为自旋部分线性化密度矩阵（spin-PLDM）方法。该方法使用自旋映射空间内的斯特拉托诺维奇-外尔方法来描述与正向和反向电子路径积分相关的动力学。虽然这是部分线性化自旋映射方法的首个示例，但人们已经知道完全线性化自旋映射能够相当准确地再现一系列非绝热模型系统的动力学可观测量。在此，我们对spin-PLDM和完全线性化自旋映射的实时量子关联函数的基础表达式中的各项进行了全面比较，以确定这两种方法的相对准确性。特别是，我们表明spin-PLDM在其实时关联函数的定义中包含一个额外项，这减少了许多完全线性化方法中普遍存在的已知误差。部分线性化方法相对于完全线性化方法的一个优点是，可以通过在中间时刻重新采样映射变量来系统地改进结果。我们推导了spin-PLDM的这样一种方案，并表明对于经典原子核近似有效的系统，仅使用几次“跳跃”就可以获得数值精确结果。此外，我们为spin-PLDM方法实现了聚焦初始条件，这减少了达到动力学量收敛所需的经典轨迹数量，而结果的准确性似乎几乎没有差异。
