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

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

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

Available for download on Thursday, April 09, 2026

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