Information theoretical statistical discrimination measures for electronic densities

• Published in: Journal of mathematical chemistry 2022-08, Vol.60 (7), p.1422-1444
• Main Authors: Laguna, Humberto G., Salazar, Saúl J. C., Sagar, Robin P.
• Format: Article
• Language: English
• Subjects: Chemistry; Chemistry and Materials Science; Density; Hydrogen atoms; Least squares; Math. Applications in Chemistry; Optimization; Original Paper; Physical Chemistry; Theoretical and Computational Chemistry; Wave functions
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-022-01363-6

Information theoretical measures are examined as methodologies for optimizing linear and non-linear parameters to obtain the best densities for particular classes of functions. We focus on the use of Gaussian type functions to represent the hydrogen atom, and examine combinations of these functions which have been used in the STO- n G basis sets. The densities obtained from these procedures are compared and contrasted to those obtained from energy optimization, and from least-squares fitting to the wave function and to the density, by evaluation of density expectation values and comparisons to their exact values. We show how densities obtained from the optimization of Kullback–Leibler (KL) measures yield better results in general, as compared to the ones obtained from energy optimization or least-squares fitting procedures. Furthermore, these types of densities are observed to provide exact results in the case of two expectation values, for all the studied classes of functions. The densities obtained from optimization of the cumulative residual KL measures, based on survival densities, provide the most accurate tail behaviour of the densities and hence the most accurate higher-order moments.