Toward Electron Correlation and Electronic Properties from the Perspective of Information Functional Theory

Abstract

Over the last years, immense efforts have been made to apply the quantities of information theory to the electronic structure and properties of various systems. In this context, one can make use of one or many of the information theoretic quantities together to describe the total energy, its components, and other electronic properties. Such an idea is feasible through an approach so-called information functional theory, which in turn constitutes the cornerstone of the present investigation. More specifically, in this work several information theoretic quantities like Fisher information, Shannon entropy, Onicescu information energy, and Ghosh-Berkowitz-Parr entropy with the two representations of electron density and shape function are considered for reliable prediction of atomic and molecular correlation energies as well as several electronic properties such as atomization energies, electron affinities, and ionization potentials. It is shown that with more or less different accountabilities of the information theoretic quantities they can be introduced as useful descriptors for estimation of electron correlation energies for a large variety of systems including neutral atoms, cations, isoelectronic series, and molecules. This is also indeed the case for the electronic properties under study. Considering different notions of the information theoretic quantities with various scaling properties and varied physiochemical meanings about the electron density distribution, we find that instead of simulating all data using one of these quantities individually taking all of them together provides a better view for the description of correlation effects and electronic properties of systems.

Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

“…Here, Onicescu informational energy in Equation 9 contains a factor 1/(α − 1), closer to Pardo's definition in Equation 4. Furthermore, conversions between information-theoretic quantities in terms of these two densities are [72,73,86,100,102,[124][125][126]142]…”

“…of He are calculated at the level of Hatree-Fock [35] or DFT [72,74,86] or by trial wave function up to three terms, [79,80] to the best of our knowledge. Therefore, we endeavor to take electron correlation into further account for these information-theoretic quantities.…”

Information‐theoretic approach in density functional theory and its recent applications to chemical problems

“…Originated from Claude Shannon's 1948 paper entitled “The mathematical theory of communication,” and still entertaining widespread applications in mathematics, statistics, computer science, physics, neurobiology and many other disciplines, information theory studies the quantification and communication of information, for which a probability function is often associated. Because the electron density can in principle be regarded as such a continuous local distribution function, ever since its early days of density functional theory (DFT), there have been tremendous interests in the literature to apply information theory to the electronic structure theory of atoms and molecules . This effort is usually categorized as the information‐theoretic approach (ITA) in DFT.…”

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

“…Furthermore, Tsallis statistics is relevant to certain systems of ultracold atoms [124][125][126][127]. Moreover, these IT quantities are applied to investigate electron correlation [30,31,33,39,72,[128][129][130][131][132][133][134][135][136] and various molecular properties as well [28,36,45,48,49,[59][60][61]72,73]. Calculated with the highly correlated Hylleraas wave functions, the results in this work then serve as a useful and reliable reference for the various applications mentioned above.…”

“…Formulas for conversion between IT quantities using the two different densities are [27,29,32,[55][56][57]59,72]…”