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.

3.1. C-M and X-H as Nucleophiles 1806 3.2. C-H and X-M as Nucleophiles 1809 3.2.1. C-Halogen Bond Formations 1809 3.2.2. C-O Bond Formations 1812 3.3. C-H and X-H as Nucleophiles 1812 3.3.1. C-O Bond Formations 1812 3.3.2. C-N Bond Formations 1815 4. Oxidative X-X Bond Formations between Two Nucleophiles 1819 5. Conclusions 1819 Author Information 1819 Biographies 1819 Acknowledgment 1820 References 1820

Bond Formations between Two Nucleophiles: Transition Metal Catalyzed Oxidative Cross-Coupling Reactions

A review of the various possible definitions of diradicals leads the authors to describe these systems as having two odd electrons in degenerate or nearly-degenerate molecular orbitals. A study of the wave-function for the two odd electrons shows that its form depends entirely on whether the diradical is homo- or heterosymmetric. Energy schemes are given in these two cases, as well as in the intermediate “non-symmetric” case. The extent of zwitterionic character in diradical states is also investigated. This is followed by a discussion of intersystem crossing between singlet and triplet diradical states via spin-orbit coupling and other mechanisms. The electronic matrix elements for spin-orbit coupling are calculated and evaluated numerically for various model cases. It is then possible to establish general rules for favorable (electronic) intersystem crossing. In 1,3 or 1,4 diradicals its efficiency is estimated to be comparable with that in aromatics. The role of the electron-nuclear hyperfine interaction in mixing singlet and triplet states, particularly in CIDNP, is explained.

Finally the question of whether diradicals actually occur as secondary minima on potential energy surfaces is examined. Recent quantum-mechanical calculations, in contradiction to some thermochemical and kinetic evidence, lead to flat singlet surfaces without significant minima.

The Electronic Properties of Diradicals

A reduced HOMO−LUMO gap, which is defined as the HOMO−LUMO energy separation of a molecule divided by that of the hypothetical polyene reference, can be used as an index of kinetic stability for a variety of polycyclic aromatic hydrocarbons (PAHs). The reduced HOMO−LUMO gap < 1.00 indicates that the HOMO contributes to the decrease in the topological resonance energy. In general, PAHs with reduced HOMO−LUMO gaps < 1.30 are chemically very reactive. Fully benzenoid hydrocarbons are kinetically very stable with very large reduced HOMO−LUMO gaps. Many of the PAH molecules with large reduced HOMO−LUMO gaps are closed-shell substructures of nonmetallic one-dimensional benzenoid polymers.

John F. Garst

Papers

Absolute hardness as a measure of aromaticity

Grignard reagent formation

Wittig rearrangements of aralkyl alkyl ethers

Reactions of alkali benzophenone ketyls with alkyl iodides

Radical mechanism of alkylation of sodium naphthalenide