Lang Haifeng, Hauke Philipp
Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Via Sommarive 14, Trento I-38123, Italy.
Theoretical Chemistry, Institute of Physical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany.
J Chem Phys. 2024 Dec 21;161(23). doi: 10.1063/5.0242276.
Nonadiabatic quantum-classical mapping approaches have significantly gained in popularity over the past several decades because they have acceptable accuracy while remaining numerically tractable even for large system sizes. In the recent few years, several novel mapping approaches have been developed that display higher accuracy than the traditional Ehrenfest method, linearized semiclassical initial value representation (LSC-IVR), and Poisson bracket mapping equation (PBME) approaches. While various benchmarks have already demonstrated the advantages and limitations of those methods, unified theoretical justifications of their short-time accuracy are still demanded. In this article, we systematically examine the intra-electron correlation, as a statistical measure of electronic phase space, which has been first formally proposed for mapping approaches in the context of the generalized discrete truncated Wigner approximation and which is a key ingredient for the improvement in short-time accuracy of such mapping approaches. We rigorously establish the connection between short-time accuracy and intra-electron correlation for various widely used models. We find that LSC-IVR, PBME, and Ehrenfest methods fail to correctly reproduce the intra-electron correlation. While some of the traceless Meyer-Miller-Stock-Thoss (MMST) approaches, partially linearized density matrix (PLDM) approach, and spin partially linearized density matrix (spin-PLDM) approach are able to sample the intra-electron correlation correctly, the spin linearized semiclassical (spin-LSC) approach, which is a specific example of the classical mapping model, and the other traceless MMST approaches sample the intra-correlation faithfully only for two-level systems. Our theoretical analysis provides insights into the short-time accuracy of semiclassical methods and presents mathematical justifications for previous numerical benchmarks.
在过去几十年中，非绝热量子 - 经典映射方法的受欢迎程度显著提高，因为它们具有可接受的精度，并且即使对于大型系统规模，在数值计算上仍然易于处理。近年来，已经开发了几种新颖的映射方法，这些方法显示出比传统的埃伦费斯特方法、线性化半经典初值表示（LSC-IVR）和泊松括号映射方程（PBME）方法更高的精度。虽然各种基准测试已经证明了这些方法的优点和局限性，但仍然需要对它们的短时精度进行统一的理论论证。在本文中，我们系统地研究了电子内相关性，作为电子相空间的一种统计度量，它最初是在广义离散截断维格纳近似的背景下为映射方法正式提出的，并且是提高此类映射方法短时精度的关键因素。我们严格地建立了各种广泛使用的模型的短时精度与电子内相关性之间的联系。我们发现LSC-IVR、PBME和埃伦费斯特方法未能正确再现电子内相关性。虽然一些无迹迈耶 - 米勒 - 斯托克 - 托斯（MMST）方法、部分线性化密度矩阵（PLDM）方法和自旋部分线性化密度矩阵（spin-PLDM）方法能够正确地采样电子内相关性，但作为经典映射模型的一个具体例子的自旋线性化半经典（spin-LSC）方法以及其他无迹MMST方法仅对两能级系统忠实地采样内相关性。我们的理论分析为半经典方法的短时精度提供了见解，并为先前的数值基准测试提供了数学依据。
