Masters Theses
Date of Award
12-2016
Degree Type
Thesis
Degree Name
Master of Science
Major
Chemistry
Major Professor
Robert J. Hinde
Committee Members
Charles Collins, Tessa Calhoun, Sharani Roy, Michael D. Best
Abstract
Three body interactions can become important in solids at higher pressures and densities as the molecules can come into close contact. At low temperatures, accurate studies of three body interactions in solids require averaging the three-body terms over the molecules' zero point motions. An efficient, but approximate, averaging approach is based on a polynomial approximation of the three-body term. The polynomial approximation can be developed as a function of the symmetry coordinates of a triangle displaced from its average geometry and also as a function of the Cartesian zero point displacements from each atom’s average position. The polynomial approximation approach can be checked through two more accurate, but more time-consuming methods: Gaussian quadrature or Monte Carlo integration of the exact three-body function. Results are presented for solid helium, solid neon and solid argon, treated as Einstein solids. An evaluation of the quality of the Einstein model approximation will also be presented. Results for helium will be compared with quantum Monte Carlo simulations.
Recommended Citation
D'Andrea, Dan, "Three Body Interactions of Rare Gas Solids Calculated Within the Einstein Model. " Master's Thesis, University of Tennessee, 2016.
https://trace.tennessee.edu/utk_gradthes/4284
Included in
Numerical Analysis and Scientific Computing Commons, Organic Chemistry Commons, Other Chemistry Commons, Physical Chemistry Commons, Programming Languages and Compilers Commons