{"title":"Efficient high-order operator-splitting schemes for solving the time-dependent Schrödinger equation","authors":"Yajian Shu , Zhigang Sun","doi":"10.1016/j.chemphys.2024.112458","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":272,"journal":{"name":"Chemical Physics","volume":"588 ","pages":"Article 112458"},"PeriodicalIF":2.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chemical Physics","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0301010424002878","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
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.
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.