Efficient high-order operator-splitting schemes for solving the time-dependent Schrödinger equation

IF 2 3区 化学 Q4 CHEMISTRY, PHYSICAL Chemical Physics Pub Date : 2024-09-12 DOI:10.1016/j.chemphys.2024.112458
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Abstract

Several fourth-order symmetric operator-splitting schemes with four and five stages for solving the time-dependent Schrödinger equation have been proposed. These schemes have been studied and compared with some optimal fourth- and sixth-order operator split schemes reported in the literature using a one-dimensional model and several realistic three-dimensional triatomic reactive scattering problems in Jacobi coordinates. Two new fourth-order operator-splitting schemes with four and five stages, which are more efficient than previously reported schemes, are recommended for the realistic numerical solution of the time-dependent Schrödinger equation in the field of molecular dynamics. It was found that the order-preserving method proposed by McLachlan works well for three-dimensional triatomic reactive scattering problems in Jacobi coordinates, despite the complicated form of the Hamiltonian.

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求解时变薛定谔方程的高效高阶算子分裂方案
为求解时变薛定谔方程,提出了几种四阶和五阶对称算子分割方案。利用雅可比坐标中的一维模型和几个现实的三维三原子反应散射问题,对这些方案进行了研究,并与文献中报道的一些最优四阶和六阶算子分割方案进行了比较。与之前报道的方案相比,两种新的四阶和五阶算子拆分方案效率更高,被推荐用于分子动力学领域时变薛定谔方程的现实数值求解。研究发现,尽管哈密顿形式复杂,但麦克拉克兰提出的保阶方法在雅可比坐标的三维三原子反应散射问题中效果良好。
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来源期刊
Chemical Physics
Chemical Physics 化学-物理:原子、分子和化学物理
CiteScore
4.60
自引率
4.30%
发文量
278
审稿时长
39 days
期刊介绍: Chemical Physics publishes experimental and theoretical papers on all aspects of chemical physics. In this journal, experiments are related to theory, and in turn theoretical papers are related to present or future experiments. Subjects covered include: spectroscopy and molecular structure, interacting systems, relaxation phenomena, biological systems, materials, fundamental problems in molecular reactivity, molecular quantum theory and statistical mechanics. Computational chemistry studies of routine character are not appropriate for this journal.
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