Quantum Chemistry by Random Walk

该项目得到了NSF理论和计算科学中心的支持。 化学程序，进一步发展了直接模拟蒙特卡罗 方法的解决方案的电子薛定谔方程。 的 目标是计算各种不同的确定的理论能量表面。 分子系统有2到6个电子，包括小氦 团簇，氢化锂，和质子转移反应之间的 氦原子和氢分子离子。 近似蒙特卡罗 将在取消 蒙特卡洛步行者与相反的标志。 目标是实现 与固定节点蒙特卡罗方法相比， 方法. 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采用严格的数学 某些微分方程的解与 大样本加权随机游动的统计平均值， 多维空间 该方法应用于 电子薛定谔方程的近似解是有限的 只取决于统计样本的大小。 Monte Carlo计算 得到了最精确的量子力学势能 用于氢原子氢分子交换反应的表面，和 对于各种其他小分子系统，因此提供可靠的 测试所有其他计算方法的标准 分子电子结构理论 目前的研究项目是 因为它将提供额外的基准 需要更好地建立理论方法的基础， 适用于广泛的化学问题。 第二个目标是 研究是开发不太精确但更有效的Monte 适用于较大分子系统的卡洛方法。

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.