In this work, we present an approach that is designed to unite non-empirical (constraint-satisfying) and semi-empirical (data-driven) strategies for developing improved density functional approximations (DFAs). This is achieved with the use of piece-wise cubic uniform basis splines (B-splines) to construct the exchange and correlation inhomogeneity correction factors (ICFs). The resulting Constrained and Smoothed semi-Empirical (CASE) approach offers several distinct advantages over commonly employed polynomial expansions by enabling explicit enforcement of linear and non-linear constraints (including inequality constraints) using a generalized form of Tikhonov regularization, as well as ICF smoothness by penalizing non-physical ICF "bumps" or "wiggles" using penalized B-splines (P-splines). In doing so, this framework combines the physical rigor and transferability of non-empirical DFAs while leveraging high-quality quantum-mechanical data to improve the overall accuracy. As a proof-of-concept, we use this approach to construct CASE21, a global hybrid generalized gradient approximation that satisfies all but one (and partially satisfies the remaining one) of the constraints satisfied by the non-empirical PBE0 functional. On a diverse series of chemical properties, we find that CASE21 outperforms PBE0 as well as other popular DFAs in the chemical sciences.

CASE21: Using B-splines to construct constraint-satisfying and data-driven density functional approximations

ACS Spring 2022

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.