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 legacy of Gilbert Newton Lewis (1875-1946) pervades the lexicon of chemical bonding and reactivity. The power of his concept of donor-acceptor bonding is evident in the eponymous foundations of electron-pair acceptors (Lewis acids) and donors (Lewis bases). Lewis recognized that acids are not restricted to those substances that contain hydrogen (Bronsted acids), and helped overthrow the "modern cult of the proton". His discovery ushered in the use of Lewis acids as reagents and catalysts for organic reactions. However, in recent years, the recognition that Lewis bases can also serve in this capacity has grown enormously. Most importantly, it has become increasingly apparent that the behavior of Lewis bases as agents for promoting chemical reactions is not merely as an electronic complement of the cognate Lewis acids: in fact Lewis bases are capable of enhancing both the electrophilic and nucleophilic character of molecules to which they are bound. This diversity of behavior leads to a remarkable versatility for the catalysis of reactions by Lewis bases.

Lewis Base Catalysis in Organic Synthesis

Which electrophiles react with which nucleophiles? The correlation log k20 °C = s(E + N), in which electrophiles (carbocations, metal-π-complexes, diazonium ions) are characterized by one (E) and nucleophiles are characterized by two parameters (N, s), proved to be applicable for a wide variety of electrophile−nucleophile combinations. Since the introduction of this correlation in 1994 (Angew. Chem., Int. Ed. Engl. 1994, 33, 938−957), numerous new reagents have been characterized, and in 2001 (J. Am. Chem. Soc. 2001, 123, 9500−9512), a new method of parametrization was proposed that facilitates a continuous extension of the data sets without the need for reparametrization of existing data. This Account adjusts the N and s parameters of all presently characterized π-nucleophiles (arenes, alkenes, organometallics) to the new parametrization and illustrates how to employ the resulting reactivity scales for analyzing synthetic and mechanistic problems in organic and macromolecular chemistry. Predictions of ab...

π-Nucleophilicity in Carbon−Carbon Bond-Forming Reactions

The electrophilic/nucleophilic character of a series of captodative (CD) ethylenes involved in polar cycloaddition reactions has been studied using DFT methods at the B3LYP/6-31G(d) level of theory. The transition state structures for the electrophilic/nucleophilic interactions of two CD ethylenes toward a nucleophilically activated ethylene, 2-methylene-1,3-dioxolane, and an electrophilically activated ethylene, 1,1-dicyanoethyelene, have been studied, and their electronic structures have been characterized using both NBO and ELF methods. Analysis of the reactivity indexes of the CD ethylenes explains the reactivity of these species. While the electrophilicity of the molecules accounts for the reactivity toward nucleophiles, it is shown that a simple index chosen for the nucleophilicity, Ν, based on the HOMO energy is useful explaining the reactivity of these CD ethylenes toward electrophiles.

Understanding the reactivity of captodative ethylenes in polar cycloaddition reactions. A theoretical study.

The nucleophilicity N index (J. Org. Chem.2008, 73, 4615), the inverse of the electrophilicity, , and the recently proposed inverse of the electrodonating power, , (J. Org. Chem.2010, 75, 4957) have been checked toward (i) a series of single 5-substituted indoles for which rate constants are available, (ii) a series of para-substituted phenols, and for (iii) a series of 2,5-disubstituted bicyclic[2.2.1]hepta-2,5-dienes which display concurrently electrophilic and nucleophilic behaviors. While all considered indices account well for the nucleophilic behavior of organic molecules having a single substitution, the nucleophilicity N index works better for more complex molecules. Unlike, the inverse of the electrophilicity, , (R2 = 0.71), and the inverse of the electrodonating power, (R2 = 0.83), a very good correlation of the nucleophilicity N index of twelve 2-substituted-6-methoxy-bicyclic[2.2.1]hepta-2,5-dienes versus the activation energy associated with the nucleophilic attack on 1,1-dicyanoethylene is found (R2 = 0.99). This comparative study allows to assert that the nucleophilicity N index is a measure of the nucleophilicity of complex organic molecules displaying concurrently electrophilic and nucleophilic behaviors.

The nucleophilicity N index in organic chemistry

Twenty-three diarylcarbenium ions and 38 π-systems (arenes, alkenes, allyl silanes and stannanes, silyl enol ethers, silyl ketene acetals, and enamines) have been defined as basis sets for establishing general reactivity scales for electrophiles and nucleophiles. The rate constants of 209 combinations of these benzhydrylium ions and π-nucleophiles, 85 of which are first presented in this article, have been subjected to a correlation analysis to determine the electrophilicity parameters E and the nucleophilicity parameters N and s as defined by the equation log k(20 °C) = s(N + E) (Mayr, H.; Patz, M. Angew. Chem., Int. Ed. Engl. 1994, 33, 938−957). Though the reactivity scales thus obtained cover more than 16 orders of magnitude, the individual rate constants are reproduced with a standard deviation of a factor of 1.19 (Table 1). It is shown that the reactivity parameters thus derived from the reactions of diarylcarbenium ions with π-nucleophiles (Figure 3) are also suitable for characterizing the nucleoph...

Reference Scales for the Characterization of Cationic Electrophiles and Neutral Nucleophiles

The electrophilicity parameter (E = 9.6) of the 1-phenylethyl cation, 1+, has been determined and combined with the nucleophilicity parameter (N = 0.78, s = 0.95) of styrene (St) to predict diffusion-limited propagation in the cationic polymerization of St by the linear free energy relationship log k = s(N + E). This prediction has been experimentally verified using two different diffusion clock methods, which provided a value of kp± ≈ 2 × 109 L mol-1 s-1, 6 orders of magnitude higher than previously accepted, for the absolute rate constant of propagation of the TiCl4-induced polymerization of St in methylcyclohexane/methyl chloride 60/40 (v/v) at −80 °C. The kp± value remained unchanged in the temperature range −50 to −80 °C, indicating that propagation does not have an enthalpic barrier; however, it increased moderately with increasing solvent polarity. The nature of the Lewis acid has little effect on kp± as similar values have been obtained with TiCl4 or SnCl4. The apparent rate constant of ionization...

Determination of Rate Constants in the Carbocationic Polymerization of Styrene: Effect of Temperature, Solvent Polarity, and Lewis Acid1

Kinetics of the reactions of benzhydryl cations with 2,4,6-trimethylstyrene have been performed to determine its nucleophilicity parameters N = 0.68 and s = 1.09, which are comparable to styrene and considerably less nucleophilic than 4-methylstyrene, indicating the retarding effect of the ortho methyl groups. Kinetic investigations of the reactions of the 2,4,6-trimethylstyryl cation 6+ and the corresponding dimer 7+ with the reference nucleophile 2-chloropropene allow us to calculate the closely similar electrophilicity parameters E(6+) = 6.04 and E(7+) = 6.16 which are considerably lower than that of the styryl cation (E = 9.6). As a consequence, the propagation rate constant of the cationic polymerization of 2,4,6-trimethylstyrene is considerably lower than that of styrene. Substituting these values into the correlation log k20 °C = s(N + E) yields a propagation rate constant of 3 × 107 M-1 s-1, which has to be considered an upper limit because extra steric strain generated in the reaction of 7+ with ...

Propagation rate of the cationic polymerization of 2,4,6-trimethylstyrene: A linear free energy approach

The electrophilic reactivities of the bis(p-methylphenyl)carbenium ion 1b+ and its macromolecular analogue 1a+ have been compared in slow reactions with allylsilanes and in fast reactions with sily...

Influence of Chain Length on the Electrophilic Reactivity of Carbocations

The kinetics of the reactions of benzhydryl cations with N-vinylcarbazole (1) and of the reactions of the N-ethylidenecarbazolium ion (6) with π-nucleophiles have been investigated to determine the nucleophilicity parameters N and s for 1 and the electrophilicity parameter E for 6. These values were employed to predict potential initiators for the cationic polymerization of N-vinylcarbazole (1) and to calculate the propagation rate constant for this process.

Holger Schimmel

Papers

Reference Scales for the Characterization of Cationic Electrophiles and Neutral Nucleophiles

Determination of Rate Constants in the Carbocationic Polymerization of Styrene: Effect of Temperature, Solvent Polarity, and Lewis Acid1

Propagation rate of the cationic polymerization of 2,4,6-trimethylstyrene: A linear free energy approach

Influence of Chain Length on the Electrophilic Reactivity of Carbocations

Initiation and Propagation Rate Constants for the Cationic Polymerization of N-Vinylcarbazole