Semester

Spring

Date of Graduation

2022

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Aldo H. Romero

Committee Co-Chair

Matthew B. Johnson

Committee Member

Tudor D. Stanescu

Committee Member

Charter Stinespring

Abstract

Density-functional theory (DFT) has gained popularity because of its ability to predict the properties of a large group of materials a priori. Even though DFT is exact, there are inaccuracies introduced into the theory due to the approximations in the exchange-correlation (XC) functionals. Over the 50 years of its existence, scientists have tried to improve the design of the XC functionals. The errors introduced by these functionals are not consistent across all types of solid-state materials. In this project, a high throughput framework was utilized to compare the theoretical DFT predictions with the experimental results available in the Inorganic Crystal Structure Database (ICSD). We analyzed the accuracy of over 1500 structures with different XC functionals, ranging from the most basic (local density approximation) to the recently designed meta-GGA functionals. Afterward, we focus on strongly correlated systems, where the triumphant ability of DFT stops short and the non-universality of the XC functionals becomes substantial. One solution to this problem is to introduce a Hubbard correction (+U) for the treatment of the strongly correlated electronic states, used in the so-called DFT+U approaches. Unfortunately, this correction turns the theory into a semi-empirical method as the exact values of the correction parameters are unknown and their parameterization can vary considerably from one material to another composed of the same strongly correlated atoms. In this work, we select a group of iron-based compounds to explore the space of the correction parameters that simultaneously improve the prediction for all the studied materials. We perform this exploration using a Bayesian calibration assisted by Markov chain Monte Carlo sampling to determine the distribution of the correction parameters for three widely used XC functionals. Finally, we use the insight gained from the previous studies to design a machine learning approach to the problematic XC functional approximations. We propose a streamlined route to generating data needed for a learner to produce personalized XC functionals (material specific) for any DFT calculation. This approach capitalizes on the unwanted non-universality of XC functionals. Further, we demonstrate a machine-driven unbiased approach to finding the global reaction coordinate. As an example, we use the azobenzene molecule to thoroughly describe a reaction mechanism for its photoisomerization. Our global reaction coordinate includes all of the internal coordinates of azobenzene contributing to the photoisomerization reaction coordinate. This method quantifies the contribution of each internal coordinate of the system to the overall reaction mechanism. Finally, we provide a detailed mapping on how each significantly contributing internal coordinate changes throughout the energy profile (in our example from trans to transition state and subsequently to cis).

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