Uniting Nonempirical and Empirical Density Functional Approximation Strategies Using Constraint-Based Regularization.

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) 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 traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Optimized micro-sampling and computational analysis for SERS identification of red organic dyes on prints.

The goals of this study were to develop a robust methodology and data analysis procedure to identify red dyes in artwork where dye collection is inaccessible by traditional methods. With Surface-Enhanced Raman Spectroscopy (SERS) it is possible to obtain identifying molecular information from dilute and degraded dyes. A minimally invasive, soft-mechanical sampling method to gently contact printed paper is described; using a customized polymeric hydrogel surface with an exposure area of about 1 mm2, micrometer-diameter colorant particles were collected. To validate that the sample collection methodology is minimally invasive, test papers were photographed before and after sampling under UV and white light; and DART-MS analysis of the sampled area was conducted. A reference library of SERS spectra from binder (hide glue), dyes (safflower, sappan, and madder), and binder-dye mixtures was built and used by a spectral-matching genetic algorithm (GA). Fifty individual GA runs returned results that precisely matched at least one dye component in 48-50 of the 50 runs, and matched both dyes in a mixture between 29 and 50 of the 50 runs. Finally, in an artwork application, the methodologies were demonstrated on micro-samples from three areas of an 18th century Japanese woodblock print by Suzuki Harunobu in the collection of the Portland Art Museum, on which, madder dyes were positively identified. Conclusions and extensions from this work are expected to contribute to the body of knowledge about 18th c. Japanese woodblock prints.