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Investigations in quantum Monte Carlo

by Wilson, Matthew Clifford.

Abstract (Summary)
A scheme to calculate a correction to the energy obtained by the variational quantum Monte Carlo (VQMC) method by using the diffusion quantum Monte Carlo (DQMC) method is applied to three systems, neon, H2, and cyclical C10. This scheme has the advantage that the time step error incurred in the use of the DQMC method is minimized since it only applies to the correction to the energy, rather than the entire energy. The simulation for neon validated the use of the scheme in correctly calculating the ground state energy of an atom. In this case, the scheme obtained 97% of the difference in energy between the VQMC and DQMC energies. The simulation for H2 was done to reproduce results of a simple, well-known system for various bond lengths. Again, in this case, the correction scheme succeeded in correcting the VQMC energy to close to the DQMC values. Finally, for cyclical C10, the scheme was run for a number of geometries in which either the bond angles or bond lengths were varied at different ring sizes. It was found that for smaller rings, a more symmetrical geometry is preferred, while for larger ring sizes there tend to be at least a local minimum energy for rings distorted by either their bond angles or bond lengths. Also included are DQMC calculations of the potential energies of interaction of helium atoms in helium dimers and trimers. Statistical errors are lower by a factor of two to ten than for earlier diffusion calculations. The calculations for the trimers reveal interaction energies very nearly pairwise-additive for internuclear distances near the dimer equilibrium distance of 5.6 bohr and longer. iii
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School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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