Development and Applications of Quantum Monte Carlo

Citation

Fisher, Daniel Ross (2010) Development and Applications of Quantum Monte Carlo. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4YCS-9T88. https://resolver.caltech.edu/CaltechTHESIS:12152009-120706357

Abstract

Quantum Monte Carlo is a relatively new class of electronic structure methods that has the potential to calculate expectation values for atomic, molecular, and materials systems to within chemical accuracy. QMC scales as (ON³ or better with the size of the system, which is much more favorable than traditional electronic structure methods capable of comparable accuracy. In addition, the stochastic nature of QMC makes it relatively easy to parallelize over multiple processors.

QMC calculations use the Metropolis algorithm to sample the electron density of the system. This method has an inherent equilibration phase, during which the configurations do not represent the desired density and must be discarded. Because the time spent on equilibration increases linearly with the number of processors, this phase limits the efficiency of parallel calculations, making it impossible to use large numbers of processors to speed convergence.

This thesis presents an algorithm that generates statistically independent walker configurations in regions of high probability density, shortening the length of the equilibration phase and ensuring the accuracy of calculations. Shortening the length of the equilibration phase greatly improves the efficiency of large parallel calculations, which will allow QMC calculations to use the next generation of homogeneous, heterogeneous, and distributed computing resources to conduct highly accurate simulations on large systems.

The most common formulation of diffusion Monte Carlo has two sources of error: the time step used to propagate the walkers and the nodes of the trial function. In order to explore these sources of error, DMC calculations were carried out on three pericyclic hydrocarbon reactions using Hartree-Fock, generalized valence bond, and multiconfiguration self-consistent field trial functions and time steps ranging from 10^-4 to 10^-2 au. The results are compared to values from experiment and high quality ab initio calculations, as well as the recently developed X3LYP, M06, and XYG3 density functionals. The appropriate time step and trial functions for the reactants, transition states, and products are identified to begin to develop guidelines for researchers carrying out calculations on larger systems.

Thesis Files