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 site-selective formation of carbon-carbon bonds through direct functionalizations of otherwise unreactive carbon-hydrogen bonds constitutes an economically attractive strategy for an overall streamlining of sustainable syntheses. In recent decades, intensive research efforts have led to the development of various reaction conditions for challenging C-H bond functionalizations, among which transition-metal-catalyzed transformations arguably constitute thus far the most valuable tool. For instance, the use of inter alia palladium, ruthenium, rhodium, copper, or iron complexes set the stage for chemo-, site-, diastereo-, and/or enantioselective C-H bond functionalizations. Key to success was generally a detailed mechanistic understanding of the elementary C-H bond metalation step, which depending on the nature of the metal fragment can proceed via several distinct reaction pathways. Traditionally, three different modes of action were primarily considered for CH bond metalations, namely, (i) oxidative addition with electronrich late transition metals, (ii) σ-bond metathesis with early transition metals, and (iii) electrophilic activation with electrondeficient late transition metals (Scheme 1). However, more recent mechanistic studies indicated the existence of a continuum of electrophilic, ambiphilic, and nucleophilic interactions. Within this continuum, detailed experimental and computational analysis provided strong evidence for novel C-H bond metalationmechanisms relying on the assistance of a bifunctional ligand bearing an additional Lewis-basic heteroatom, such as that found in (heteroatom-substituted) secondary phosphine oxides or most prominently carboxylates (Scheme 1, iv). This novel insight into the nature of stoichiometric metalations has served as stimulus for the development of novel transformations based on cocatalytic amounts of carboxylates, which significantly broadened the scope of C-H bond functionalizations in recent years, with most remarkable progress being made in palladiumor ruthenium-catalyzed direct arylations and direct alkylations. These carboxylate-assisted C-H bond transformations were mostly proposed to proceed via a mechanism in which metalation takes place via a concerted base-assisted deprotonation. To mechanistically differentiate these intramolecular metalations new acronyms have recently been introduced into the literature, such as CMD (concerted metalationdeprotonation), IES (internal electrophilic substitution), or AMLA (ambiphilic metal ligand activation), which describe related mechanisms and will be used below where appropriate. This review summarizes the development and scope of carboxylates as cocatalysts in transition-metal-catalyzed C-H functionalizations until autumn 2010. Moreover, experimental and computational studies on stoichiometric metalation reactions being of relevance to the mechanism of these catalytic processes are discussed as well. Mechanistically related C-H bond cleavage reactions with ruthenium or iridium complexes bearing monodentate ligands are, however, only covered with respect to their working mode, and transformations with stoichiometric amounts of simple acetate bases are solely included when their mechanism was suggested to proceed by acetate-assisted metalation.

Carboxylate-assisted transition-metal-catalyzed C-H bond functionalizations: mechanism and scope.

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.

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 acetylation of tert-butanol with acetic anhydride catalyzed by 4-(dimethylamino)pyridine (DMAP) has been studied at the Becke3 LYP/6-311 + G(d,p)//Becke3 LYP/6-31G(d) level of theory. Solvent effects have been estimated through single-point calculations with the PCM/UAHF solvation model. The energetically most favorable pathway proceeds through nucleophilic attack of DMAP at the anhydride carbonyl group and subsequent formation of the corresponding acetylpyridinium/acetate ion pair. Reaction of this ion pair with the alcohol substrate yields the final product, tert-butylacetate. The competing base-catalyzed reaction pathway can either proceed in a concerted or in a stepwise manner. In both cases the reaction barrier far exceeds that of the nucleophilic catalysis mechanism. The reaction mechanism has also been studied experimentally in dichloromethane through analysis of the reaction kinetics for the acetylation of cyclohexanol with acetic anhydride, in the presence of DMAP as catalyst and triethylamine as the auxiliary base. The reaction is found to be first-order with respect to acetic anhydride, cyclohexanol, and DMAP, and zero-order with respect to triethyl amine. Both the theoretical as well as the experimental studies strongly support the nucleophilic catalysis pathway.

The DMAP-catalyzed acetylation of alcohols- : A mechanistic study (DMAP = 4-(dimethylamino)pyridine)

The kinetics of the reactions of benzhydryl cations with 22 enamines, three pyrroles, and three indoles were investigated photometrically in dichloromethane. The nucleophilicity parameters N and slope parameters s of these electron-rich pi-systems were derived from equation log k (20 degrees C)=s(E+N) and compared with the nucleophilicities of other pi-systems (silyl enol ethers, silyl ketene acetals) and carbanions. It is shown that the nucleophilic reactivities of enamines cover more than ten orders of magnitude, comparable to enol ethers on the low reactivity end and to carbanions on the high reactivity end. Since the products of N-attack are thermodynamically less stable than the reactants, the observed rate constants refer to the formation of the carbon bond;carbon bonds. In some cases, equilibrium constants for the formation of iminium ions were measured, which allow one to determine the intrinsic rate constants of these reactions.

Structure-nucleophilicity relationships for enamines.

Rate and equilibrium constants for the reactions of pyridines with donor-substituted benzhydrylium ions have been determined spectrophotometrically. The correlation equation log k(20 degrees C)=s(N+E), in which s and N are nucleophile-specific parameters and E is an electrophile-specific parameter, has been used to determine the nucleophilicity parameters of various pyridines in CH(2)Cl(2) and aqueous solution and to compare them with N of other nucleophiles. It is found that the nucleophilic organocatalyst 4-(dimethylamino)pyridine (DMAP) and tertiary phosphanes have comparable nucleophilicities and carbon basicities despite widely differing Bronsted basicities. For that reason, these reactivity parameters are suggested as guidelines for the development of novel organocatalysts. The Marcus equation is employed for the determination of the intrinsic barriers of these reactions.

Bernhard Kempf

Papers

π-Nucleophilicity in Carbon−Carbon Bond-Forming Reactions

Reference Scales for the Characterization of Cationic Electrophiles and Neutral Nucleophiles

The DMAP-catalyzed acetylation of alcohols- : A mechanistic study (DMAP = 4-(dimethylamino)pyridine)

Structure-nucleophilicity relationships for enamines.

Nucleophilicities and carbon basicities of pyridines.