# Investigations in quantum Monte Carlo

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.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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