Kullback–Leibler and relative Fisher information as descriptors of locality

• Published in: International journal of quantum chemistry 2018-06, Vol.118 (12), p.n/a
• Main Authors: Levämäki, Henrik, Nagy, Ágnes, Vilja, Iiro, Kokko, Kalevi, Vitos, Levente
• Format: Article
• Language: English
• Subjects: Approximation; Chemistry; Density; density functional theory; descriptors of locality; Electron gas; Fisher information; Functionals; Kinetic energy; Kullback-Leibler information; Mathematical analysis; Physical chemistry; Quantum physics; relative Fisher information
• ISSN: 0020-7608; 1097-461X; 1097-461X
• DOI: 10.1002/qua.25557

Kullback–Leibler and relative Fisher information functionals are applied in studying deviation from local density approximation. The reduced density gradient s and the local kinetic energy parameter α are key ingredients of these new locality descriptors. The relative Kullback–Leibler information density contains extra knowledge as it is negative where the given probability density is smaller than the reference density. The relative Fisher information incorporates the highest order deviations from the uniform electron gas approximation. Information theoretical concepts are making their way in mainstream density functional theory. Kullback–Leibler and relative Fisher information are here applied to study atomic densities and their deviation from the uniform electron gas. Compared to currently used measures of deviations, the relative Kullback–Leibler information density is shown to incorporate extra knowledge about the nature of deviations, while the relative Fisher information is able to detect deviations with a higher sensitivity.