Uniting Non-Empirical and Semi-Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization

Author

Trine K. Quady, Portland State UniversityFollow

First Advisor

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

DOI

10.15760/honors.1476

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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Comments

Other authors: Zachary M. Sparrow (Cornell University), Brian G. Ernst (Cornell University), and Robert A. DiStasio Jr. (Cornell University)

Persistent Identifier

https://archives.pdx.edu/ds/psu/41703

Recommended Citation

Quady, Trine K., "Uniting Non-Empirical and Semi-Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization" (2021). University Honors Theses. Paper 1444.
https://doi.org/10.15760/honors.1476