I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

The halogen bond occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity. In this fairly extensive review, after a brief history of the interaction, we will provide the reader with a snapshot of where the research on the halogen bond is now, and, perhaps, where it is going. The specific advantages brought up by a design based on the use of the halogen bond will be demonstrated in quite different fields spanning from material sciences to biomolecular recognition and drug design.

The Halogen Bond

Halogen bonding refers to the non-covalent interactions of halogen atoms X in some molecules, RX, with negative sites on others. It can be explained by the presence of a region of positive electrostatic potential, the sigma-hole, on the outermost portion of the halogen's surface, centered on the R-X axis. We have carried out a natural bond order B3LYP analysis of the molecules CF(3)X, with X = F, Cl, Br and I. It shows that the Cl, Br and I atoms in these molecules closely approximate the [Formula: see text] configuration, where the z-axis is along the R-X bond. The three unshared pairs of electrons produce a belt of negative electrostatic potential around the central part of X, leaving the outermost region positive, the sigma-hole. This is not found in the case of fluorine, for which the combination of its high electronegativity plus significant sp-hybridization causes an influx of electronic charge that neutralizes the sigma-hole. These factors become progressively less important in proceeding to Cl, Br and I, and their effects are also counteracted by the presence of electron-withdrawing substituents in the remainder of the molecule. Thus a sigma-hole is observed for the Cl in CF(3)Cl, but not in CH(3)Cl.

Halogen bonding: the σ-hole

Halogen bonding (XB) is a type of noncovalent interaction between a halogen atom X in one molecule and a negative site in another. X can be chlorine, bromine or iodine. The strength of the interaction increases in the order Cl<Br<I. After a brief review of experimental evidence relating to halogen bonding, we present an explanation for its occurrence in terms of a region of positive electrostatic potential that is present on the outermost portions of some covalently-bonded halogen atoms. The existence and magnitude of this positive region, which we call the σ-hole, depends upon the relative electron-attracting powers of X and the remainder of its molecule, as well as the degree of sp hybridization of the s unshared electrons of X. The high electronegativity of fluorine and its tendency to undergo significant sp hybridization account for its failure to halogen bond. Some computed XB interaction energies are presented and discussed. Mention is also made of the importance of halogen bonding in biological systems and processes, and in crystal engineering.

An overview of halogen bonding

Halogen Bonding in Supramolecular Chemistry.

It is shown that the electronic charge density of a ground-state atom decreases monotonically as a function of radial distance from the nucleus, contrary to the widespread belief that the shell structure is reflected by relative maxima in the density. Any proposed relationship between chemical bonding and the maxima in the radial density functions of atoms should therefore be regarded with caution. It is proven that the electrostatic potential of an atom must be monotonically decreasing. The changes in charge distribution upon molecule formation are also discussed.

Peter Politzer

Papers

A misconception concerning the electronic density distribution of an atom