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# Applications of the Information Theory to Problems of Molecular Electronic Structure and Chemical Reactivity

Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland

Received: 28 September 2001 / Accepted: 7 January 2002 / Published: 25 April 2002

(This article belongs to the Special Issue Application of Density Functional Theory)

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# 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.*Keywords:*Atoms-in-Molecules; Density Difference Function; Density Functional Theory; Donor-Acceptor Systems; Electron Densities and Probabilities; Electronic Structure Theory; Fukui Function; Hirshfeld Analysis; Information Theory; Reactivity Theory; Subsystems; Surprisal Analysis; Thermodynamical Approach

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**MDPI and ACS Style**

Nalewajski, R.F. Applications of the Information Theory to Problems of Molecular Electronic Structure and Chemical Reactivity. *Int. J. Mol. Sci.* **2002**, *3*, 237-259.

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