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.
