非绝热动力学的部分线性自旋映射方法。II。与相关方法的分析和比较
A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related approaches
摘要：
在以前的论文[J. R。Mannouch和J.O. Richardson，J.~化学~物理学~ xxx，xxxxx（xxxx）]，我们得出了一个新的部分线性映射为基础的经典轨迹技术，称为自旋PLDM。该方法描述了与前向和后向电子路径积分相关的动力学，在自旋映射空间内使用Stratonovich-Weyl方法。虽然这是部分线性化自旋映射方法的第一个例子，但完全线性化自旋映射已经被认为能够相当准确地再现一系列非绝热模型系统的动态可观测量。在这里，我们提出了一个彻底的比较的条款的基本表达式的实时量子关联函数自旋PLDM和完全线性化的自旋映射，以确定这两种方法的相对精度。特别是，我们表明，自旋PLDM包含一个额外的长期内的定义，其实时关联函数，这减少了许多已知的错误，是无处不在的完全线性化的方法。与完全线性化方法相比，部分线性化方法的一个优点是可以通过在中间时间重新采样映射变量来系统地改进结果。我们推导出这样一个计划自旋PLDM和表明，对于经典核的近似是有效的系统，数值精确的结果可以得到使用只有几个“跳跃”。此外，我们实现了集中的初始条件的自旋PLDM方法，这减少了经典的轨迹，以达到收敛的动力学量的数量，似乎没有什么区别的结果的准确性。
英文摘要：
In the previous paper [J. R. Mannouch and J. O. Richardson, J.~Chem.~Phys.~xxx, xxxxx (xxxx)] we derived a new partially linearized mapping-based classical-trajectory technique, called spin-PLDM. 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.
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