Abstract
Recent studies on applications of the information theoretic concepts to molecular systems are reviewed. This survey covers the information theory basis of the Hirshfeld partitioning of molecular electron densities, its generalization to many electron probabilities, the local information distance analysis of molecular charge distributions, the charge transfer descriptors of the donor-acceptor reactive systems, the elements of a “thermodynamic” description of molecular charge displacements, both “vertical” (between molecular fragments for the fixed overall density) and “horizontal” (involving different molecular densities), with the entropic representation description provided by the information theory. The average uncertainty measures of bond multiplicities in molecular “communication” systems are also briefly summarized. After an overview of alternative indicators of the information distance (entropy deficiency, missing information) between probability distributions the properties of the “stockholder” densities, which minimize the entropy deficiency relative to the promolecule reference, are summarized. In particular, the surprisal analysis of molecular densities is advocated as an attractive information-theoretic tool in the electronic structure theory, supplementary to the familiar density difference diagrams. The subsystem information density equalization rules satisfied by the Hirshfeld molecular fragments are emphasized: the local values of alternative information distance densities of subsystems are equal to the corresponding global value, characterizing the molecule as a whole. These local measures of the information content are semi-quantitatively related to the molecular density difference function. In the density functional theory the effective external potentials of molecular fragments are defined, for which the subsystem densities are the ground-state densities. The nature of the energetic and “entropic” equilibrium conditions is reexamined and the entropy representation forces driving the charge transfer in molecular systems are introduced. The latter combine the familiar Fukui functions of subsystems with the information densities, the entropy representation “intensive” conjugates of the subsystem electron densities, and are shown to exactly vanish for the “stockholder” charge distribution. The proportionality relations between charge response characteristics of reactants, e.g., the Fukui functions, are derived. They are shown to follow from the minimum entropy deficiency principles formulated in terms of both the subsystems electron densities and Fukui functions, respectively.
Highlights
In chemistry an understanding of the electronic structure of molecules and reactive systems comes from transforming the experimental or computational results into statements in terms of chemical concepts, such as atoms-in-molecules (AIM), the building blocks of molecules, their collections, e.g., the functional groups, and the chemical bonds representing the AIM “connectivities”
As we have demonstrated in this survey, there is a wide range of problems in the theory of electronic structure and chemical reactivity, which can already be tackled using concepts and techniques of the information theory
They include the entropic definition of AIM, criteria of molecular similarity, the polarization promotion and the charge transfer (CT) stage of the reorganization of atoms, when they form chemical bonds in a molecule, a thermodynamic-like description of molecular systems and the electron transfer phenomena in reactive systems, bond multiplicities, charge sensitivities, etc
Summary
In chemistry an understanding of the electronic structure of molecules and reactive systems comes from transforming the experimental or computational results into statements in terms of chemical concepts, such as atoms-in-molecules (AIM), the building blocks of molecules, their collections, e.g., the functional groups, and the chemical bonds representing the AIM “connectivities”. The information theory (IT) [1,2,3] provides both the entropic measures of the information distance (similarity) between the compared distributions of electrons in a given molecular system and the associated promolecule [2, 4,5,6,7,8,9,10,11], respectively, and a convenient device, the information entropy variational principle, for assimilating in the optimized electron density (or probability) distribution the physical information contained in the constraints and the appropriate references, in the most unbiased manner This theoretical framework can be used to extract the entropic (information) characteristics of the probability distributions of simultaneously finding several electrons in a molecule and the associated promolecule, respectively [7, 10, 11], both continuous and discrete, e.g., in the AIM or molecular fragment resolutions. We shall conclude with elements of a more general “thermodynamic” description within the information theory of molecular and reactive systems, including both the “vertical” displacements of the electronic structure (for the constant molecular density) and the “horizontal” transitions from one ground-state density to another [5]
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