Ha Jong-Kwon, Min Seung Kyu
Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, South Korea.
J Chem Phys. 2022 May 7;156(17):174109. doi: 10.1063/5.0084493.
Mixed quantum-classical dynamics based on the exact factorization exploits the "derived" electron-nuclear correlation (ENC) term, aiming for the description of quantum coherences. The ENC contains interactions between the phase of electronic states and nuclear quantum momenta, which depend on the spatial shape of the nuclear density. The original surface hopping based on the exact factorization (SHXF) [Ha et al., J. Phys. Chem. Lett. 9, 1097 (2018)] exploits frozen Gaussian functions to construct the nuclear density in the ENC term, while the phase of electronic states is approximated as a fictitious nuclear momentum change. However, in reality, the width of nuclear wave packets varies in time depending on the shape of potential energy surfaces. In this work, we present a modified SHXF approach and a newly developed Ehrenfest dynamics based on the exact factorization (EhXF) with time-dependent Gaussian functions and phases by enforcing total energy conservation. We perform numerical tests for various one-dimensional two-state model Hamiltonians. Overall, the time-dependent width of Gaussian functions and the energy conserving phase show a reliable decoherence compared to the original frozen Gaussian-based SHXF and the exact quantum mechanical calculation. In particular, the energy conserving phase is crucial for EhXF to reproduce the correct quantum dynamics.
基于精确因式分解的混合量子-经典动力学利用了“导出的”电子-核关联（ENC）项，旨在描述量子相干性。ENC包含电子态相位与核量子动量之间的相互作用，这取决于核密度的空间形状。基于精确因式分解的原始表面跳跃（SHXF）[Ha等人，《物理化学快报》9，1097（2018）]利用冻结的高斯函数来构建ENC项中的核密度，而电子态的相位则近似为虚拟的核动量变化。然而，在实际中，核波包的宽度会根据势能面的形状随时间变化。在这项工作中，我们提出了一种改进的SHXF方法以及一种新开发的基于精确因式分解的含时高斯函数和相位的埃伦费斯特动力学（EhXF），通过强制总能量守恒来实现。我们对各种一维两态模型哈密顿量进行了数值测试。总体而言，与原始的基于冻结高斯的SHXF和精确的量子力学计算相比，高斯函数的含时宽度和能量守恒相位显示出可靠的退相干。特别是，能量守恒相位对于EhXF重现正确的量子动力学至关重要。
