Information Functional Theory: Electronic Properties as Functionals of Information for Atoms and Molecules

Abstract

How to accurately predict electronic properties of a Columbic system with the electron density obtained from experiments such as X-ray crystallography is still an unresolved problem. The information-theoretic approach recently developed in the framework of density functional reactivity theory is one of the efforts to address the issue. In this work, using 27 atoms and 41 molecules as illustrative examples, we present a study to demonstrate that one is able to satisfactorily describe such electronic properties as the total energy and its components with information-theoretic quantities like Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, and Onicescu information energy. Closely related to the earlier attempt of expanding density functionals using simple homogeneous functionals, this work not only confirms Nagy's proof that Shannon entropy alone should contain all the information needed to adequately describe an electronic system but also provides a feasible pathway to map the relationship between the experimentally available electron density and various electronic properties for Columbic systems such as atoms and molecules. Extensions to other electronic properties are straightforward.

Information theoretic approach provides a reliable description for kinetic component of correlation energy density functional

“…However, although the analytical justifications in this context are robust and valid, their practical implementations and numerical verifications deserve to be more analyzed. To address this issue, the IFT is of concern herein where we rely on a strategy in which the electronic property P can be expressed in terms of information theoretic quantities Q as follows …”

“…However, there are many options to express the relations defined in Equations and explicitly. Following earlier suggestions in the field the linear combination form of information theoretic quantities has been considered, though other cases are also possible which their applicability may be examined elsewhere. Therefore, the working expressions employed in our calculations take the below forms, where the summations run over information theoretic quantities Q j and c j and c ne are the expansion coefficients to be determined by the least squares fitting procedure.…”

Multivariate Dependence beyond Shannon Information

“…Due to its focus on probability distributions, it allows one to compare dissimilar systems (e.g., species abundance to ground state configurations of a spin system) and has found many successes in the physical, biological and social sciences [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] far outside its original domain of communication. Often, the issue on which it is brought to bear is discovering and quantifying dependencies [20][21][22][23][24][25].…”

Molecular acidity: An accurate description with information‐theoretic approach in density functional reactivity theory

“…At first, in principle, as one of the most important intrinsic properties of a molecule, molecular acidity should be adequately accounted for and thus satisfactorily described by quantities from DFRT. This is because, according to DFT theorems as well as our recent numerical results for various other properties, the electron density in the ground state should have included all the information necessary to describe and quantify each and every molecular property including molecular acidity. Second, even though acidity is expressed via p K a values as a global property of a molecule, it is indeed a localized property near the acidic atom and dissociating proton.…”