Quantum Chemistry by Random Walk

随机游走的量子化学

• 批准号: 9411181
• 负责人: James Anderson
• 金额: $ 24万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9411181&HistoricalAwards=false
• 关键词: Quantum; Chemistry; Random; Walk

This project, supported by the NSF Theoretical and Computational Chemistry Program, further develops the direct simulation Monte Carlo method for the solution of the electronic Schroedinger equation. The goal is to compute definitive theoretical energy surfaces for various molecular systems with two to six electrons including small Helium clusters, Lithium hydride, and the proton transfer reaction between the Helium atom and the Hydrogen molecule ion. Approximate Monte Carlo methods for larger systems will be developed based on cancellation of Monte Carlo walkers with opposite signs. The goal is to achieve significant improvement in accuracy over that of fixed-node Monte Carlo methods. These methods will be applied to the water molecule and to some small hydrocarbons. Direct simulation Monte Carlo methods employ a rigorous mathematical relationship between the solutions of certain differential equations and the statistical average of a large sample of weighted random walks in many-dimensional space. The accuracy of the method applied to the approximate solution of the electronic Schroedinger equation is limited only by the size of the statistical sample. Monte Carlo calculations have yielded the most accurate quantum mechanical potential energy surfaces for the hydrogen atom hydrogen molecule exchange reaction, and for various other small molecular systems, and so provide reliable standards against which to test all other computational methods in molecular electronic structure theory. The present research project is of fundamental importance because it will provide additional benchmarks needed to better establish the foundations of theoretical methods to be applied to a wide range of chemical problems. A second goal of this research is the development of less precise but more efficient Monte Carlo methods applicable to somewhat larger molecular systems.

该项目得到了美国国家科学基金会理论与计算化学项目的支持，进一步发展了求解电子薛定谔方程的直接模拟蒙特卡罗方法。 目标是计算具有两到六个电子的各种分子系统的明确理论能量表面，包括小氦簇、氢化锂以及氦原子和氢分子离子之间的质子转移反应。 针对较大系统的近似蒙特卡罗方法将基于具有相反符号的蒙特卡罗步行者的取消而开发。 目标是显着提高固定节点蒙特卡罗方法的精度。 这些方法将应用于水分子和一些小碳氢化合物。 直接模拟蒙特卡罗方法在某些微分方程的解与多维空间中加权随机游走的大样本的统计平均值之间采用严格的数学关系。 应用于电子薛定谔方程近似解的方法的精度仅受统计样本大小的限制。 蒙特卡罗计算为氢原子氢分子交换反应以及各种其他小分子系统提供了最准确的量子力学势能表面，因此为测试分子电子结构理论中的所有其他计算方法提供了可靠的标准。 本研究项目具有根本重要性，因为它将提供更好地建立应用于广泛化学问题的理论方法基础所需的额外基准。 这项研究的第二个目标是开发不太精确但更有效的蒙特卡罗方法，适用于更大的分子系统。