First Advisor
Prof. Gwen Shusterman
Date of Award
Fall 12-10-2021
Document Type
Thesis
Degree Name
Bachelor of Science (B.S.) in Chemistry and University Honors
Department
Chemistry
Language
English
Subjects
DFT, semi-empirical, non-empirical, DFA, B-spline, constraints
Abstract
In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): non-empirical (NE) constraint satisfaction and semi-empirical (SE) data-driven optimization. The proposed method employs B-splines—bell-shaped spline functions with compact support—to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over a polynomial basis by enabling explicit enforcement of linear and non-linear constraints as well as ICF smoothness using Tikhonov regularization and penalized B-splines (P-splines). As proof of concept, we use this approach to construct CASE21—a Constrained And Smoothed semi-Empirical global hybrid generalized gradient approximation that completely satisfies all but one constraint (and partially satisfies the remaining one) met by the PBE0 NE-DFA and exhibits enhanced performance across a diverse set of chemical properties. As such, we argue that the paradigm presented herein maintains the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to improve performance.
Rights
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Recommended Citation
Quady, Trine K.; Sparrow, Zachary M.; Ernst, Brian G.; and DiStasio, Robert A. Jr., "Uniting Non-Empirical and Semi-Empirical Density Functional Approximation Strategies using Constraint-Based Regularization" (2021). University Honors Theses. Paper 1444.