Date of Award

Spring 6-21-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Michael R. Shirts

Second Advisor

Adam Holewinski

Third Advisor

Aaron Holder

Fourth Advisor

Matthew Glaser

Fifth Advisor

Christine Hrenya

Abstract

Many properties of small organic molecules are dependent on the crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Computational prediction of the most stable crystalline form is done by determining the crystalline form with the lowest Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of organic solids, especially those molecules which have not been synthesized yet.

In this study, we use multistate reweighting methods to determine the most stable polymorph for two test systems, crystalline benzene and Lennard-Jones spheres, across a variety of temperatures and pressures. In order to achieve this, sampling is performed at a selection of temperature and pressure states in the region of interest. Multistate reweighting methods are then employed to determine the reduced free energy differences between T and P states within a polymorph. By combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs, the relative stability of the polymorphs at the sampled states can be determined and interpolated to create the phase diagram.

We have determined the efficiency of using multistate reweighting for this process by determining the relationship between the size of the system and the number of samples required to obtain a constant uncertainty in the results. We have also explored increasing the efficiency of this method by adding coordinate mapping between systems at very different pressures and temperatures in order to increase the phase space overlap between adjacent states and therefore decrease the amount of sampling that must be performed. We have thus far shown this to be a feasible method for significantly increasing the spacing between sampled pressures in a system of Lennard-Jones spheres.

We have also studied the effect of moving to the quantum level of approximation to the Hamiltonian on calculations of Gibbs free energy, enthalpy, and entropy using lattice dynamics. This method includes entropic effects and the harmonic vibrations of a crystal, allowing stability at nonzero temperatures to be estimated. We have shown that different energy functions, both in classical and quantum potentials, have a large effect on the predicted enthalpy and Gibbs free energy. This magnitude of this effect has been correlated to the difference in equilibrium box vectors between potentials.

Available for download on Thursday, January 27, 2022

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