Enhancing the quantum Monte Carlo method for electronic properties of large molecules and excited states

This thesis describes advances to the quantum Monte Carlo (QMC) method of computing electronic energies of atoms and molecules. The contributions include reductions to the computational expense of QMC calculations, a new method for computing excited state properties and an application of QMC to compute the excitation energies of the retinal molecule.;The vast majority of the computer time used by QMC calculations is spent evaluating molecular orbitals and the correlation function. The cost of evaluating these functions scales with the third power of the molecular size, M. A new algorithm reduces cost of evaluating the MOs to O (M) and is 50--75% faster than an earlier linear scaling algorithm. Nonorthogonal localized molecular orbitals (NOLMOs) are explored as a route to faster MO evaluation. The NOLMOs constructed in this thesis provide a tiny speedup over the Boys localized orbitals when the O (M) algorithm named above is used. The efficiency of evaluating the three body terms in the Schmidt-Moskowitz-Boys-Handy correlation function was improved by rewriting the function as a trace over a matrix product. The introduction of sparse matrix multiplication techniques reduced the scaling of the algorithm to O (M).;QMC methods are inherently parallel, but some consideration must be paid in order to use massively parallel computers most efficiently. An earlier load balancing algorithm required O (N2) memory per processor for redistributing walkers among N processors. A new algorithm requires only one global communication step and O (N) memory per processor and has been validated using up to 32,000 processors on the Cray XT4 platform.;A new method for computing the energy of Fermi excited states is derived by combining the fixed-node (FN) approximation with the correlation function QMC method. The suggested approach should be more rigorous than the FN approximation because it ensures that the excited state solutions are orthogonal to lower energy states. An initial application to the beryllium atom shows that the correlation function QMC does correct for nonvariational errors in excited state fixed-node diffusion Monte Carlo (FN-DMC) calculations, but the value of this benefit is somewhat reduced by its sensitivity to statistical errors.;The FN-DMC is used to compute the energies of the S0 and S 1 states of a protonated Schiff base of retinal. The S0 -- S1 gap of retinal is a significant biophysical quantity relevant to mechanisms of vision and photosynthesis. Quantitative results cannot of the DMC calculations cannot be given because the calculations have not completed at the time of this writing. The progress that has been made and the impediments encountered during the calculation are discussed.;The QMC methods described in this thesis are implemented in the Zori program. Zori has been substantially reorganized and enhanced since its last release. The revised structure of the code and its new features are outlined. A detailed description of the program options is given in an appendix.