Monte Carlo Methods for Atoms and Molecules

这项蒙特卡罗方法和应用的理论研究是由美国国家科学基金会理论和计算化学计划支持的。变分蒙特卡罗理论和格林函数蒙特卡罗理论都被应用于分子电子结构的计算和软性范德华团簇的结构和动力学研究。蒙特卡罗理论在方法上的新发展包括：研究电子相关效应的显式相关变分函数，使用格林加德快速多极法对静电电位进行数值评估，内芯电子的伪势，修正的固定节点方法，以及蒙特卡罗和密度泛函方法的结合。讨论了基态和激发态。特别地，该理论被应用于计算稀有气团中双原子或小芳香分子的光谱位移。蒙特卡罗方法是一类利用在多维物理空间中随机游走的概念来近似求解微分方程的数值方法。本课题将蒙特卡罗方法应用于原子和分子中电子的薛定谔方程，研究电子能谱和分子结构。这些数学方法也适用于松散键合分子簇中原子大振幅运动的薛定谔方程。

9407309 Schmidt Arizona State Univ. This theoretical study of Monte Carlo methods and applications is supported by the NSF Theoretical and Computational Chemistry Program. Both variational and Greens Function Monte Carlo theory is applied to the calculation of molecular electronic structure and to the study of structure and dynamics of floppy van der Waals clusters. New methodological developments in Monte Carlo theory include: study of explicitly-correlated variational functions for electron correlation effects, use of Greengard's fast multipole method for numerical evaluation of electrostatic potentials, pseudopotentials for inner core electrons, modified fixed node methods, and the combination of Monte Carlo and density functional methods. Both ground and excited states are treated. In particular, the theory is applied to the calculation of spectral shifts for a diatomic or small aromatic molecule in a rare gas cluster. Monte Carlo methods constitute a class of numerical methods for the approximate solution of differential equations using the concept of random walks through the many-dimensional physical space. In this project, Monte Carlo methods are applied to the Schroedinger equation of electrons in atoms and molecules to study electronic spectra and molecular structure. These mathematical methods are also applied to the Schroedinger equation for the large amplitude motions of atoms in loosely bonded molecular clusters.