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.

In recent years, much efforts have been invested to apply information theory for different physical and chemical problems. In this regard, one can make use of one or many of the information theoretic quantities together within an approach so‐called information functional theory to describe the energetic components and electronic properties of various systems. In the present contribution, several information theoretic quantities such as Fisher information, Shannon entropy, Onicescu information energy, and Ghosh–Berkowitz–Parr entropy based on the two representations of electron density and shape function are utilized for the prediction of kinetic component of the correlation energy density functional as an important quantity in density functional theory. Taking the atoms and isoelectronic series as benchmark sets we find that with more or less different accountabilities of the considered quantities they can be introduced as reliable measures for the kinetic energy functional. Concerning different natures of the information theoretic quantities with variety of scaling properties and physiochemical propensities, it is shown that instead of describing all data using one of such quantities individually, considering all of them concurrently provides a better view on the prediction of the kinetic component of correlation energy density functional. Hopefully, the information theoretic approach can provide an alternative pathway toward the theoretical prediction and rationalization of important quantities in density functional calculations from the perspective of information theory.