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.

Structural Aspects of Aromaticity

An old quantitative measureof aromaticcharacter named HOMA (harmonic oscillator measureof aromaticity) is reformulated and related to the Jug and Koester concept of resonance coordinate. In its new version, the HOMA index can be used to estimate an aromatic character of r-electron systems (molecules, ions, or their fragments) built up of the following bonds: CC, CN, CO, CP, CS, NN, and NO. It is shown that even if aromatic stabilization is due to a-electron structure inclined to maintain equal bond lengths, the aromatic character is mainly a result of r-electron properties of the system. Application of the HOMA index to benzene rings in various molecular and ionic systems showed that the aromatic character depends rather weakly on deformation from planarity whereas it may be strongly dependent on the intermolecular H-bonding net as well as on cooperative substituent interactions of push-pull type and on the topology of a mutual link between benzene rings in condensed benzenoid hydrocarbons,

Crystallographic studies of inter- and intramolecular interactions reflected in aromatic character of .pi.-electron systems

G. Clar 6n Rule versus Hückel 4n + 2 Rule 3464 H. Hydrocarbons versus Heteroatomic Systems 3465 IV. Hidden Treasures of Kekulé Valence Structures 3466 A. Conjugated Circuits 3467 B. Innate Degree of Freedom 3470 C. Clar Structures 3472 V. Graph Theoretical Approach to Chemical Structure 3473 A. Metric 3473 B. Chemical Graphs 3473 C. Isospectral Graphs 3473 D. Embedded Graphs 3475 E. Partial Ordering 3476 VI. On Enumeration of Benzenoid Hydrocarbons 3477 VII. Kekulé Valence Structures Count 3479 A. Non-branched Cata-condensed Benzenoids 3481 B. Branched Cata-condensed Benzenoids 3482 C. Benzenoid Lattices 3482 D. Peri-condensed Benzenoids 3483 E. Miscellaneous Benzenoids 3484 F. The Approach of Platt 3485 G. Computer Programs for Calculating K 3485 H. Transfer-Matrix Method 3486 I. Use of Recursion Relations 3486 J. Use of Signed Matrices 3487 VIII. Enumeration of Conjugated Circuits 3488 IX. Approximate Approaches versus Ambitious Computations 3490

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Aromaticity of polycyclic conjugated hydrocarbons.

Benzene is the emblematic example of an aromatic molecule, and the problem of its structure has given rise to a chemical serial story running over several decades. The epistemological digest of this story written by Stephen G. Brush1,2 shows how this problem has been at the root of important concepts such as those of mesomery and resonance. Before the advent of quantum mechanics, chemists had thought of the benzene structures in terms of two center bonds attempting to preserve the valence of the carbon atom and to explain its chemical properties. Kekulé’s theory of the structure of the benzene molecule3 invokes the oscillatory hypothesis in which “the fourth valence of each carbon oscillates between its neighbors, synchronously with all the other fourth valences, so that the structure switches rapidly between the two structures”,1 whereas Claus proposed a diagonal hypothesis4 in which the fourth valence of each carbon is directed toward the carbon in the para position. The latter hypothesis has been rejected because it enables only two derivatives, and it has been revised to remove this inconsistency: instead of forming a bond, the fourth valence stops near the center of the ring in the Armstrong-Baeyer formula,5 or there is only one bridging bond as in the Dewar’s bridged benzene formula.6 In Thiele’s partial valence model,7 the adjacent carbon-carbon bonds are considered as intermediate between single and double bonds. These formulas were later considered by K. C. Ingold to set up his intra-annular tautomerism,8 which appears to be the generalization of Kekulé’s oscillatory hypothesis. Ingold’s tautomerism hypothesis was later called mesomerism.9 The mesomery is an important concept in chemistry, which implicitly introduces the electron delocalization in the context of the prequantum electronic theory. The first applications of quantum chemistry to the benzene problem led on the molecular orbital (MO) side Erich Hückel to propose his famous 4n + 2 rule10 and on the valence bond (VB) side Pauling and Wheland to identify resonance with Ingold’s mesomerism.11,12 An enlighting contribution of modern VB theory on the benzene structure has been brought by Shaik et al.,13 who have shown that the hexagonal symmetry of benzene is due to the σ-system because the π component is distortive along a Kekulean distortion. * Authors to whom correspondence should be addressed (telephone +34-972-418912; fax +34-972-418356; e-mail miquel.sola@ udg.es or silvi@lct.jussieu.fr). ‡ Universitat de Girona. § Université Pierre et Marie Curie. 3911 Chem. Rev. 2005, 105, 3911−3947

Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches.

T.M. Krygowski

Papers

Definition of aromaticity basing on the harmonic oscillator model