Organic Chemistry and Synthesis Rely More and More upon Catalysts

: A few months before the COVID-19 pandemic, Pierre Vogel and Kendall N. Houk published with a new textbook Wiley-VCH, “ Organic Chemistry: Theory, Reactivity, and Mechanisms in Modern Synthesis ”, with a foreword from the late Roberts H. Grubbs. The book demonstrates how catalytic processes dominate all ﬁelds of modern organic chemistry and synthesis, and how invention combines thermodynamics, kinetics, spectroscopy, quantum mechanics, and thermochemical data libraries. Here, the authors present a few case studies that should be of interest to teachers, practitioners of organic and organometallic chemistry, and the engineers of molecules. The Vogel–Houk book is both textbook and reference manual; it provides a modern way to think about chemical reactivity and a powerful toolbox to inventors of new reactions and new procedures. models that help to show the analogies that exist between reactions of organic compounds and transition organometallic compounds. They help to understand a large number of catalyzed processes.


Introduction
Our planet and its people face new problems that require new solutions. Many of us are concerned by climate change, by the loss of biodiversity, by human population growth, by the ageing of people, by neurodegenerative diseases and cancer that are expanding, by the threat of new infectious diseases recently demonstrated so vividly, by the continuously increasing cost of medical care in general, by drinking water availability and its contamination, by air and ocean pollution, and by the degradation of the soil that nourishes us. These problems should not make us fall into a depressed funk. Most scientists are stimulated by these problems and can propose solutions that represent new opportunities for engineers, investors, and business. In the search for these solutions, new molecules and new devices are invented. The first industrial commodity produced by organic chemistry was Perkin's purple (mauveine) in 1856 [1][2][3]. The first synthetic drug was chloral hydrate (Cl 3 CCH(OH) 2 introduced on the market in 1869, a compound prepared first by Liebig in 1832 (chlorination of ethanol) [4][5][6]. At that time, all dyestuffs and drugs were extracted from minerals, plants, and animals [7][8][9]. Only 300 organic compounds were known in 1800; the first edition of the Beilstein Handbook of Organic Chemistry described 20,000 organic compounds in 1882. Now, more than 80 million organic compounds are known. Nowadays, most dyestuffs are synthetic; most drugs are chemicals obtained through synthesis or are biologics derived from cell cultures [10,11]. At the end of the 19th century, most materials and commodities were made from minerals, plants, wood, animals, and metals. Today many of them are made out of polymers derived from fossil carbon. Sooner or later, engineers will find economical ways to obtain these commodities, and better ones, from left-overs of agriculture and forestry, and from urban waste [12]. The molecules and devices we need now are more and more sophisticated and must be invented at a faster and faster

Invention Is Quicker if Physical Organic Chemistry Principles Are Integrated in Preparative Chemistry
The study of physical organic chemistry is a prerequisite for becoming a modern molecular scientist [18,19]. The main feature of physical organic chemistry is to associate chemical reactions that define chemical functions with quantitative measurements (equilibrium constants, heat of reaction, rate constants, isotopic effects). Chemical informatics estimate that 166.4 billion possible molecules can be made with up to 17 atoms of C, N, O, S, and halogens based on known or estimated stability of compounds and their possible reactions (known feasibility) [20]. When criteria of medicinal chemistry and pharmacokinetics are used to filter the above database, Reymond and co-workers estimate that about 10 million small molecules are potential drugs [21]. With the assistance of robots, these molecules can be obtained quickly and one can generate large libraries of new compounds, most of which are made by applying robust reactions (typically amide formation, Suzuki-Miyaura C-C-coupling, Buchwald-Hartwig nucleophilic aromatic substitutions, azide + alkyne cycloadditions) [22][23][24][25]. We think this is not optimal today; the chemical space exploration must add many less-common reactions, especially recently developed catalytic processes [26]. Moreover, reactions permitting access to enantio-pure compounds (asymmetric synthesis) must be developed and applied. This requires not only imitation of literature procedures, but the invention of new and better ones. Nature remains a source of inspiration; complicated bioactive compounds such as alkaloids, polyphenols, polyketides, peptides, nucleic acids, oligosaccharides, and glycoproteins, as well as their mimics, should be available through synthetic chemistry. Synthesis can produce analogs and eventually better drugs than those offered by nature. For that, knowledge of physical chemistry, physics, mechanics (when designing micro-reactors and automatic systems, for instance), quantum chemistry, and the application of artificial intelligence can be quite beneficial. Molecular scientists must have a profound understanding of chemical reactivity and must be able to predict whether a planned reaction is possible or not, and at what rate it will occur under the conditions chosen. For more than 100 years, successes of synthetic chemistry have been the result of trial and error and serendipity [27]. This has turned many talented students away from synthesis and from chemistry. Today, synthetic chemistry, and especially organic and organometallic chemistry in homogeneous systems, is a reliable science with reproducible procedures based on thermodynamics, kinetics, and availability of highly performing analytical tools. Scientists using all this knowledge and techniques have more productive and inventive intuition [28]. The relationships between molecule dynamics and energy (heat, light) are established on a quantitative basis. With the help of quantum mechanical calculations, one can invent models that can be applied to almost any reaction. Literature and data banks (e.g., NIST WebBook of Chemistry [29]) provide us with quantitative and accurate thermodynamic data. The latter must be used to predict chemical reactivity (equilibrium constant and reaction rates) and the properties of the new compounds targeted. This is one of the messages that the Vogel-Houk book tries to pass to students, chemists, biochemists, and engineers. The domestication of fire one million years ago has permitted humans to continuously improve their quality of life. The treatment of matter with heat has created new objects and new knowledge (metallurgy, pottery, ceramics). The understanding of how matter and heat are interrelated is the basis of the sciences of matter. This should be kept in mind when teaching or/and applying chemistry, for instance.
Because the transformation of matter should not produce waste, atom economical reactions should be preferred to reactions producing co-products [30][31][32]. Catalytic processes should be chosen, as they save significant energy; furthermore, they should be run in inexpensive, non-toxic, and recoverable solvents, if any.
Amide formation is one of the most important reaction in cells and in the laboratory. The direct amidification of carboxylic acids by amines requires the elimination of water [33]. New catalysts have been invented that achieve direct amidification of carboxylic acids with amines in an aqueous solvent (DMSO, 70 • C) [34].
Thermochemical data for Equilibrium (1) in the gas phase tells us that this direct amidification is exothermic, with ∆ r H • (1) = −8 ± 1.5 kcal mol −1 . Gas phase experimental entropies are not available for Me 2 NH and CH 3 CONMe 2 . The entropy variation ∆ r S • (1) of Equilibrium (1) under 1 atmosphere and at 25 • C can be estimated from the variation of translation entropies [35], which depend on the molecular weights of reactants and products, according to Equation (2) for equilibrium A + B P + Q: For Equilibrium (1) in the gas phase, ∆ r S • (1) ∼ = −1 eu (entropy unit = cal mol −1 K −1 ). This gives an entropy cost of -T∆S r • ∼ = 300 cal mol −1 = 0.3 kcal mol −1 at 25 • C. This indicates that the reaction must be exergonic (K 298K (1) > 1): ∆ r G • = ∆ r H • -T∆S r • ∼ = −7.7 ± 1.5 kcal mol −1 at room temperature. In solution, this value will be affected by differential solvation effects, and, when using larger carboxylic acids than acetic acid and different amines than methyl amine, the entropy variation will be more negative (e.g., for a carboxylic acid and an amine having both a molecular weight of 200, one obtains with relationship (2) ∆ r S • ∼ = −5 eu, and an entropy cost -T∆S r • ∼ = 1.5 kcal mol −1 ). Thermochemical data for model Equilibrium (1) in the gas phase should encourage chemists to look for more catalysts that can induce the direct formation of amides at room temperature without a co-solvent such as DMSO, or with a co-solvent that can be recovered more readily, as well as for carboxylic acids and amines that contains other functions (e.g., ketone, aldehyde, ester, etc.). We hope that this example will convince chemists, biochemists, and engineers to use thermochemical data available for compounds in the gas phase, even though the planned reaction must be run in solution and at a temperature different than 25 • C.

Pr-F + HBr
Pr-Br+ H-F vinyl-F + HBr vinyl-Br + H-F (4) In contrast, Equilibria (5) that exchange the fluoride of acetyl fluoride (Ac-F = CH3CO-F) with chloride, bromide, or iodide with the corresponding hydrogen halide H-X disfavor the formation of H-F, meaning that fluorine prefers to be bonded to an acyl carbon atom rather than to a hydrogen atom. In contrast, equilibria of acetyl chloride (Ac-Cl) with the corresponding bromide and iodide are nearly thermoneutral in the gas phase.
Ac-F + H-X ⇄ Ac-X + H-F (5) ΔrH o (5) = 4.6 (X = Cl), 4.0 (X = Br), 4.0 (X = I) kcal mol −1 Why does fluorine prefer the left side (C center instead of the H atom) of Equilibria (5)? Donation of the non-bonding electrons of the oxygen atom of the carbonyl group stabilizes the ionic form of the acetyl-halide bond. This negative hyperconjugation effect (n(C=O:)/σ* interaction) involves the interaction of the non-bonding or lone pair, orbitals n(CO:) of the carbonyl group, and the anti-bonding, empty orbital σ*(C-F) of the C-F bond. This interaction is not possible in alkyl, alkenyl, and hydrogen halides, which do not possess lone pair electrons. Of all acyl halides, this hyperconjugative interaction is strongest in acyl fluorides, where the difference in electronegativity between carbon and fluorine is larger than in the other acyl halides. Because of the large electronegativity difference between F and C, σ*(C-F) is the best σ-acceptor of all C-X bonds. Furthermore, the conjugation n(X:)/π*(C=O) (donation from the non-bonded electron pairs of X: to the carbonyl double bond), which stabilizes the carbonyl compound, is the weakest for X=F, and strongest for amino groups ( Figure 1). The infrared carbonyl stretching frequencies of acyl derivatives (νC=O) increase with the C=O bond strength, as shown below. Hyperconjugation in acyl halides (donation from the carbonyl group n(CO:) non-bonded electron-pairs to the σ(C-X) bond) competes with the n(X:)/π(C=O) conjugation. This competition exists also in carboxylic esters and carboxamides. Reprinted with permission from Ref. [17]. Copyright 2019 Wiley.

Scheme 1.
Homoconjugated carbonyl group can be electron-releasing. Norborn-5-en-2-one (1) adds to electrophiles E-X giving the corresponding adducts 3 with high stereo-and regioselectivity arising from the quenching of cationic intermediates 2 by the nucleophiles X -. 2-Cyanonorborn-5en-2-yl acetate (4) adds to electrophiles E-X with opposite regioselectivity giving the corresponding adducts 6 arising from the quenching of cationic intermediate 5 by the nucleophiles X -. In cationic intermediates 2 the positively charged center C(6) is homoconjugated with the carbonyl group whereas in cationic intermediates 5 the positive charge prefers to reside on C(5), away from the two electron-withdrawing substituents CN and AcO.
Carbon monoxide (C=O) has a dipole moment that places a partial negative charge on its carbon atom [46,47]. In contrast, carbon dioxide (O=C=O) has partial negative charges on its two oxygen atoms and a partial positive charge on its carbon atom. Carbon monoxide is in fact an electron-rich carbene because of the electron donation by the nonbonding electron of its oxygen atom. In carbonylmetal complexes, CO is a σ-donor and a π-attractor.

Mnemonic Devices Are Very Useful to Learn Chemistry, but They Must Be Applied Critically
We now discuss Markovnikov's rule about the orientation of the additions of H-X to alkenes. The rule states that when water, a carboxylic acid, or a hydrogen halide adds to an unsymmetrical alkene, the hydrogen atom joins the carbon atom bearing the largest number of hydrogen atoms and the nucleophile (X) bonds to the vicinal center that is more substituted. The classic explanation invokes a two-step mechanism in which the proton adds first to the alkene forming a carbenium ion intermediate in the rate determining step, which is then quenched by the nucleophile irreversibly. This hypothesis implies kinetic control (the rate of the two competing regioselective additions are different and the major regioisomer results from the fastest reaction). The stability sequence for alkyl cations is tertiary > secondary > primary [48][49][50]. However, in addition, in the cases where R-X are alcohols, amines, thiols, and alkyl halides, secondary derivatives are more stable than their primary isomers (see Equilibria (8)). Similarly, tertiary systems are more stable than their secondary isomers [51]. The formulation of Markovnikov's rule as a kinetic control is not always valid [52][53][54][55]. Additions to alkenes are exothermic but have negative entropies (condensations) that can cause the reactions to be reversible (with standard Gibbs energy variation ΔrG T = ±1 kcal/mol). For example, additions of water to unstrained alkenes in the gas phase are exothermic by ca. −12 kcal/mol, a value very similar to the entropy cost of the addition at 25 °C. For instance, in the gas phase, the standard heat of reaction ΔrH°(2-methylpropene + H2O ⇄ t-butanol) ≅ −12.6 kcal/mol, and the standard Scheme 1. Homoconjugated carbonyl group can be electron-releasing. Norborn-5-en-2-one (1) adds to electrophiles E-X giving the corresponding adducts 3 with high stereo-and regioselectivity arising from the quenching of cationic intermediates 2 by the nucleophiles X -. 2-Cyanonorborn-5-en-2-yl acetate (4) adds to electrophiles E-X with opposite regioselectivity giving the corresponding adducts 6 arising from the quenching of cationic intermediate 5 by the nucleophiles X -. In cationic intermediates 2 the positively charged center C(6) is homoconjugated with the carbonyl group whereas in cationic intermediates 5 the positive charge prefers to reside on C(5), away from the two electron-withdrawing substituents CN and AcO.
Carbon monoxide (C=O) has a dipole moment that places a partial negative charge on its carbon atom [46,47]. In contrast, carbon dioxide (O=C=O) has partial negative charges on its two oxygen atoms and a partial positive charge on its carbon atom. Carbon monoxide is in fact an electron-rich carbene because of the electron donation by the non-bonding electron of its oxygen atom. In carbonylmetal complexes, CO is a σ-donor and a π-attractor.

Mnemonic Devices Are Very Useful to Learn Chemistry, but They Must Be Applied Critically
We now discuss Markovnikov's rule about the orientation of the additions of H-X to alkenes. The rule states that when water, a carboxylic acid, or a hydrogen halide adds to an unsymmetrical alkene, the hydrogen atom joins the carbon atom bearing the largest number of hydrogen atoms and the nucleophile (X) bonds to the vicinal center that is more substituted. The classic explanation invokes a two-step mechanism in which the proton adds first to the alkene forming a carbenium ion intermediate in the rate determining step, which is then quenched by the nucleophile irreversibly. This hypothesis implies kinetic control (the rate of the two competing regioselective additions are different and the major regioisomer results from the fastest reaction). The stability sequence for alkyl cations is tertiary > secondary > primary [48][49][50]. However, in addition, in the cases where R-X are alcohols, amines, thiols, and alkyl halides, secondary derivatives are more stable than their primary isomers (see Equilibria (8)). Similarly, tertiary systems are more stable than their secondary isomers [51]. The formulation of Markovnikov's rule as a kinetic control is not always valid [52][53][54][55]. Additions to alkenes are exothermic but have negative entropies (condensations) that can cause the reactions to be reversible (with standard Gibbs energy variation ∆ r G T = ±1 kcal/mol). For example, additions of water to unstrained alkenes in the gas phase are exothermic by ca. −12 kcal/mol, a value very similar to the entropy cost of the addition at 25 • C. For instance, in the gas phase, the standard heat of reaction ∆ r H • (2-methylpropene + H 2 O t-butanol) ∼ = −12.6 kcal/mol, and the standard entropy variation of the equilibrium ∆ r S • (2-methylpropene + H 2 O t-butanol) ∼ = −37 eu; at 25 • C, the entropy cost −T∆ r S • amounts to −298·(−37 cal mol −1 K −1 ) ∼ = 11.0 kcal mol −1 [29,56]. Thus, one predicts that the regioselectivity of the additions of water, alcohols, and carboxylic acids to acyclic alkenes might be thermodynamically rather than kinetically controlled above 25 • C. As shown with Equilibria (8) in the gas phase, the linear adducts are less stable than their "branched" isomers. Additions of HX to terminal alkenes or 1,2-dialkylethylenes avoid the generation of secondary carbenium intermediates and follow other mechanisms that do not involve carbenium ion intermediates. The reverse reactions, that is, eliminations, also may follow concerted mechanisms avoiding carbenium ion intermediates. Even for such reactions, Markovnikov's rule is generally followed. This is because of the Dimroth principle, which was enunciated in 1933 [57]. If one or a set of reactants can undergo two competitive one-step reactions that follow the same mechanism and produce two different isomers, the favored product under conditions of kinetic control is the most stable one. The energy barrier is the lowest for the most exothermic reaction (Bell-Evans-Polanyi theory established in 1936-1938 for radical exchange reactions such as R-X + Y • → R • + X-Y, and proton transfers: ∆ ‡ H = α∆ r H + β) [58,59]. Deviations to this principle are observed when differential steric factors and solvation effects affect the reactions.
Mnemonic tools such as the Markovnikov's rule and the ever-popular arrow-pushing are very useful when one learns chemistry [60]. At some point, we need to remember how they have been constructed and on what measurements they are based upon. Scientists should not be afraid to be critical of the models proposed to them and should ask for more experimental proofs.

Models Must Be Based on Measurements and Thermochemical Data
We next discuss the mechanisms of some pericyclic reactions. Among them, cycloadditions, cheletropic additions, and ene-reactions all permit the construction of C-C and C-hetero bonds in an atom economical fashion, sometimes with high chemo-, regio-, stereo-, and enantioselectivity. Isomerizations such as electrocyclic ring opening or closing reactions and sigmatropic rearrangements are also very interesting synthetic tools and will continue to play an important role in synthesis. Most pericyclic reactions tolerate a large variety of substituents and permit access to a large molecular diversity. Furthermore, these reactions can be catalyzed and run under very smooth conditions, saving energy. Before 1965, concerted pericyclic processes were called "no-mechanism reactions" to imply that there are no detectable intermediates and everything happens in one step. Since then, the study of their mechanisms has revealed many subtleties and has contributed enormously to our understanding of chemical reactivity. Depending upon the nature of the reactants (type of substituents, number of substituents, etc.) and reaction conditions (temperature, solvent, presence of additives and of catalysts), the pericyclic reactions may not follow concerted, one-step mechanisms, but can be multi-step processes.
The Woodward-Hoffmann rules explain the stereoselectivity of concerted pericyclic reactions [61]. The rules and other related theories such as the Longuet-Higgins correlation of electronic configurations between reactants and products rely upon symmetry in the transition structures [62]. Perfectly symmetrical transition structures are very rare, especially when non-symmetrical reactants are engaged (as demonstrated by kinetic isotopic effects). The activation enthalpy (∆ ‡ H) of a concerted reaction is the sum of repulsive steric effects and skeletal distortion energies, minus stabilization energies resulting from stabilizing orbitals interactions in the transition state [63]. The FMO theory applied to transition structures of pericyclic reactions also predicts their stereochemistry, as well as their aromatic character [64,65] (Evans' rule) [66]. FMO theory provides estimates of substituent and additive effects on the rate and the chemo-, regio-, and stereoselectivity of the reactions without requiring symmetrical transition structures [67]. Another approach takes advantage of the fact that non-symmetrical transition structures of pericyclic reactions are , the substituent effect on the relative stability of radicals, cations and anions, ionization energies (IE(R • ) [68], and electron affinities of radicals (-EA(R • )) [69] can be used to predict relative rates and chemo-, regio-, and stereoselectivities of concerted, one-step pericyclic reactions. The diradicaloid model, advocated by Dewar for Diels-Alder reactions [70,71], is simple because it is based on thermochemical data (measurements) and it can be applied to catalyzed pericyclic reactions.
For the cyclodimerization of ethylene into cyclobutane (reaction (9), gas phase, 25 • C, 1 atm.), one estimates the temperature at which cyclobutane equilibrates with ethylene. The equilibrium constant K T (9) = 1 (∆ r G • = ∆ r H • − T∆ r S • = 0) is realized at a relatively low temperature, as given by ∆ r H • /∆ r S • ≈ 18,400/41.6 ≈ 442 K = 169 • C. Above this temperature, the cyclodimerization is endergonic (K T < 1). The cycloreversion of cyclobutane into ethylene occurs between 350 and 450 • C with a measured barrier ∆ ‡ H = 61.1 kcal mol −1 . One  (9), which has been demonstrated through femtochemistry by Zewail and co-workers [72]. The reaction is not concerted or pericyclic; there is no assistance between the σ-bond breaking and π-bond forming processes (Scheme 2). The thermally "allowed" concerted [π 2 s + π 2 a] cycloreversion is not followed, since it involves too severe distortions of cyclobutane to reach the twisted transition structures predicted by the Longuet-Higgins theory and the Woodward-Hoffmann rules. The entropy of activation ∆ ‡ S of this condensation is that of the reaction ∆ r S • corrected for the three free rotations about the three single C-C bonds of the 1,4-diradical ( applied to transition structures of pericyclic reactions also predicts their stereochemistry, as well as their aromatic character [64,65] (Evans' rule) [66]. FMO theory provides estimates of substituent and additive effects on the rate and the chemo-, regio-, and stereoselectivity of the reactions without requiring symmetrical transition structures [67]. Another approach takes advantage of the fact that non-symmetrical transition structures of pericyclic reactions are diradicaloids, i.e., species with very narrow HOMO-LUMO gaps, or in valence bond terminology, diradical ↔ zwitterion species. Thus, without having to calculate molecular orbitals, by using just thermochemical data (homolytical bond dissociation enthalpies: DH°(R • /H • ) or DH°(R • /X • )), the substituent effect on the relative stability of radicals, cations and anions, ionization energies (IE(R • ) [68], and electron affinities of radicals (-EA(R • )) [69] can be used to predict relative rates and chemo-, regio-, and stereoselectivities of concerted, one-step pericyclic reactions. The diradicaloid model, advocated by Dewar for Diels-Alder reactions [70,71], is simple because it is based on thermochemical data (measurements) and it can be applied to catalyzed pericyclic reactions.
For the cyclodimerization of ethylene into cyclobutane (reaction (9), gas phase, 25 °C, 1 atm.), one estimates the temperature at which cyclobutane equilibrates with ethylene. The equilibrium constant K T (9) = 1 (ΔrG° = ΔrH° − TΔrS° = 0) is realized at a relatively low temperature, as given by ΔrH°/ΔrS° ≈ 18,400/41.6 ≈ 442 K = 169 °C. Above this temperature, the cyclodimerization is endergonic (K T < 1). The cycloreversion of cyclobutane into ethylene occurs between 350 and 450 °C with a measured barrier Δ ‡ H = 61.1 kcal mol −1 . One calculates ΔfH° (tetramethylene diradical) = ΔfH° (cyclobutane) + DH° (Et • /Et • ) -ring strain of cyclobutane = 6.6 + 86.0 − 26.5 = 66.1 kcal mol −1 . This gives an enthalpy difference ΔrH°(cyclobutane ⇄ tetramethylene diradical) = 66.1 − 6.6 = 59.5 kcal mol −1 . With a measured barrier Δ ‡ H(cyclobutane → 2 ethylene) = 61.1 kcal mol −1 , the thermochemical data support the hypothesis of a diradical mechanism for the cycloreversion (9), which has been demonstrated through femtochemistry by Zewail and co-workers [72]. The reaction is not concerted or pericyclic; there is no assistance between the σ-bond breaking and π-bond forming processes (Scheme 2). The thermally "allowed" concerted [π 2 s + π 2 a] cycloreversion is not followed, since it involves too severe distortions of cyclobutane to reach the twisted transition structures predicted by the Longuet-Higgins theory and the Woodward-Hoffmann rules. The entropy of activation Δ ‡ S of this condensation is that of the reaction ΔrS° corrected for the three free rotations about the three single C-C bonds of the 1,4-diradical (  If one considers the substituent effects on the relative stability of radicals, one can predict the relative rate and the regioselectivity of all (2 + 2)-cycloadditions of alkenes. Thermochemical analysis analogous to that given for the cyclodimerization (9) of ethylene into cyclobutane suggests that the octa-1,7-diene-3,6-diyl diradical is also an intermediate of the (2 + 2)-cyclodimerization of butadiene. When the alkenes are substituted with polar If one considers the substituent effects on the relative stability of radicals, one can predict the relative rate and the regioselectivity of all (2 + 2)-cycloadditions of alkenes. Thermochemical analysis analogous to that given for the cyclodimerization (9) of ethylene into cyclobutane suggests that the octa-1,7-diene-3,6-diyl diradical is also an intermediate of the (2 + 2)-cyclodimerization of butadiene. When the alkenes are substituted with polar groups, their cycloadditions are solvent dependent because zwitterions can be formed in place of diradicals. Figure 2 represents the possible paths of a Diels Alder reaction. For the same orientation (regioselectivity), there are three limiting mechanisms; two of them involve the formation of (Z)-hex-5-en-1,4-diyl diradicals, and the third one corresponds to the synchronous one-step reaction, as implied by the Woodward-Hoffmann rules. Between these Catalysts 2022, 12, 758 8 of 31 extremes are the concerted but two-stage mechanism proposed in 1959 by Woodward and Katz [73]. For the retro-Diels-Alder reaction of norbornene into cyclopentadiene and ethylene, Zewail and co-workers proposed from their femtosecond real-time studies that both concerted and non-concerted trajectories are possible; however, they decomposed norbornene by an intense laser pulse and generated the diradical by a photochemical process [74]. Were (E)-hex-5-en-1,4-diyl diradicals to be formed, they could not cyclize, but would induce polymerization of the cycloaddends, as already discussed by Littmann in 1936 [75]. Polymerization often accompanies cycloadditions of relatively unreactive dienes unless a radical scavenging agent is added to the reaction mixture. In between the three limiting mechanisms defined above, a spectrum of non-synchronous one-step mechanisms are generally thought to occur, as supported on the basis of kinetic isotope effects [76]. orientation (regioselectivity), there are three limiting mechanisms; two of them the formation of (Z)-hex-5-en-1,4-diyl diradicals, and the third one correspond synchronous one-step reaction, as implied by the Woodward-Hoffmann rules. B these extremes are the concerted but two-stage mechanism proposed in Woodward and Katz [73]. For the retro-Diels-Alder reaction of norborne cyclopentadiene and ethylene, Zewail and co-workers proposed from their femt real-time studies that both concerted and non-concerted trajectories are p however, they decomposed norbornene by an intense laser pulse and genera diradical by a photochemical process [74]. Were (E)-hex-5-en-1,4-diyl diradica formed, they could not cyclize, but would induce polymerization of the cycloadd already discussed by Littmann in 1936 [75]. Polymerization often accom cycloadditions of relatively unreactive dienes unless a radical scavenging agent i to the reaction mixture. In between the three limiting mechanisms defined a spectrum of non-synchronous one-step mechanisms are generally thought to o supported on the basis of kinetic isotope effects [76]. Thermochemical data tell us that the preferred diradical intermediate is the which the substituents stabilize the radicals the best, and this implies, as a rule, diradical results from combining the least substituted centers of the diene and die In other words, the most stable isomeric diradical intermediate is the one generated the strongest bond between the two reactants (for instance D1 or D1 3). Since many Diels−Alder reactions have measured activation enthalpies Δ ‡ H lower than the enthalpy difference ΔrH° between the diradical and the cycloadde difference ΔrH° − Δ ‡ H can be taken as Doering's energy of concert ( Figure 3). The tr state of such reactions can be readily described in terms of frontier molecula interaction theory [77,78]. An alternative valence-bond representation is that tr structures can be represented by diradicaloids, i.e., diradicals that exchange between the two radical entities. Within the valence bond theory, this electron e Thermochemical data tell us that the preferred diradical intermediate is the one for which the substituents stabilize the radicals the best, and this implies, as a rule, that this diradical results from combining the least substituted centers of the diene and dienophile. In other words, the most stable isomeric diradical intermediate is the one that has generated the strongest bond between the two reactants (for instance D1 or D1', Figure 3). Since many Diels−Alder reactions have measured activation enthalpies ∆ ‡ H that are lower than the enthalpy difference ∆ r H • between the diradical and the cycloaddends, the difference ∆ r H • − ∆ ‡ H can be taken as Doering's energy of concert ( Figure 3). The transition state of such reactions can be readily described in terms of frontier molecular orbital interaction theory [77,78]. An alternative valence-bond representation is that transition structures can be represented by diradicaloids, i.e., diradicals that exchange electron between the two radical entities. Within the valence bond theory, this electron exchange can be represented by a (Z)-diradical and one or two zwitterions, as shown in Figure 3 with D1 Z1 Z2. can be represented by a (Z)-diradical and one or two zwitterions, as shown in Figure 3 with D1 ↔ Z1 ↔ Z2. Figure 3. The valence-bond diradicaloid model for transition states of concerted Diels-Alder reactions. The lower is the sum EI(diene) + (−EA(dienophile)), or EI(dienophile) + (−EA(diene)); the faster is the cycloaddition; the higher is the degree of concert.

Diradicaloids Are Transition Structures of Concerted Cycloadditions
The diradicaloid model explains the chemo-, regio-, and stereoselectivity (e.g., endo rule of the Diels-Alder reactions) of all cycloadditions and cheletropic additions. If one of the substituents A or D can be coordinated selectively to an additive, a catalytical effect can be observed, which is explained also by the diradicaloid model.

Diradicaloid Transition Structures of Concerted Sigmatropic Rearrangements
Sigmatropic rearrangements and especially the (3,3)-sigmatropic rearrangements such the 3,4-diaza-Cope rearrangement in the Fischer's indole synthesis, the Claisen rearrangements and its various variants, the aza-Claisen, the Overman, and the Cope rearrangements have played an important role in synthesis, and will continue to do so. Here, also one considers a spectrum of mechanisms ( Figure 4) in which there are two limiting paths involving diradical intermediates, and in between these two limits, concerted one-step mechanisms. One limiting mechanism is dissociation with the formation of two allyl radicals 7 + 8; the other is the associative formation of cyclohexa-1,4-diyl diradical intermediate of type D3 (Grob's hypothesis). The lower is the sum EI(diene) + (−EA(dienophile)), or EI(dienophile) + (−EA(diene)); the faster is the cycloaddition; the higher is the degree of concert.
The diradicaloid model explains the chemo-, regio-, and stereoselectivity (e.g., endo rule of the Diels-Alder reactions) of all cycloadditions and cheletropic additions. If one of the substituents A or D can be coordinated selectively to an additive, a catalytical effect can be observed, which is explained also by the diradicaloid model.

Diradicaloid Transition Structures of Concerted Sigmatropic Rearrangements
Sigmatropic rearrangements and especially the (3,3)-sigmatropic rearrangements such the 3,4-diaza-Cope rearrangement in the Fischer's indole synthesis, the Claisen rearrangements and its various variants, the aza-Claisen, the Overman, and the Cope rearrangements have played an important role in synthesis, and will continue to do so. Here, also one considers a spectrum of mechanisms ( Figure 4) in which there are two limiting paths involving diradical intermediates, and in between these two limits, concerted one-step mechanisms. One limiting mechanism is dissociation with the formation of two allyl radicals 7 + 8; the other is the associative formation of cyclohexa-1,4-diyl diradical intermediate of type D3 (Grob's hypothesis).
Gajewski and Conrad mapped out the positions of transition states on such diagrams through their measurements of secondary deuterium kinetic isotope effects and comparisons to equilibrium isotope effects [79]. In the concerted one-step mechanisms, the bond forming process assists the bond breaking process. Their transition states can be represented by transition structures belonging to two types of diradicaloids ( Figure 5). The two allyl radicals 7 + 8 exchange an electron, forming ion-pairs IP1 or/and IP2. On its side, diradical D3 is stabilized by electron-exchange leading to zwitterions Z3 or/and Z4. Substituent effects on the relative stability of radicals, cations, and anions allow one to predict the reactivity of these concerted reactions. This model explains substituent effects on rates and the accelerating effects of catalysts. For instance, any additive that can stabilize one or the other of the charge-transferred limiting structures will catalyze the (3,3)-sigmatropic rearrangement. Gajewski and Conrad mapped out the positions of transition states on such diagrams through their measurements of secondary deuterium kinetic isotope effects and comparisons to equilibrium isotope effects [79]. In the concerted one-step mechanisms, the bond forming process assists the bond breaking process. Their transition states can be represented by transition structures belonging to two types of diradicaloids ( Figure 5). The two allyl radicals 7 + 8 exchange an electron, forming ion-pairs IP1 or/and IP2. On its side, diradical D3 is stabilized by electron-exchange leading to zwitterions Z3 or/and Z4. Substituent effects on the relative stability of radicals, cations, and anions allow one to predict the reactivity of these concerted reactions. This model explains substituent effects on rates and the accelerating effects of catalysts. For instance, any additive that can stabilize one or the other of the charge-transferred limiting structures will catalyze the (3,3)-sigmatropic rearrangement.

Diradicaloid Transition Structures in Concerted Ene-Reactions and Related Processes
The Alder−ene reaction is the thermal reaction of two alkenes that are condensed into another alkene with the formation of a new σ(C-C) bond and the transfer of a hydrogen atom between them. A large number of analogous reactions are known for heteroatoms containing unsaturated reactants, such as the aldol reaction (10) and the carbonyl-ene reaction (11) (Figure 6). In the absence of Lewis or Brønsted acid, the transition structure of the enol aldol condensation can be represented by a diradicaloid (1,4-diradical ↔1,4zwitterion) of type D4 ↔ Z5 if it follows a concerted one-step mechanism ( Figure 6, reaction (10)). The role of the acid catalyst A is to stabilize the zwitterionic limiting structure Z5 by equilibrating with zwitterion Z5'. As a consequence, the reaction may

Diradicaloid Transition Structures in Concerted Ene-Reactions and Related Processes
The Alder−ene reaction is the thermal reaction of two alkenes that are condensed into another alkene with the formation of a new σ(C-C) bond and the transfer of a hydrogen atom between them. A large number of analogous reactions are known for heteroatoms containing unsaturated reactants, such as the aldol reaction (10) and the carbonyl-ene reaction (11) (Figure 6). In the absence of Lewis or Brønsted acid, the transition structure of the enol aldol condensation can be represented by a diradicaloid (1,4-diradical 1,4zwitterion) of type D4 Z5 if it follows a concerted one-step mechanism ( Figure 6, reaction (10)). The role of the acid catalyst A is to stabilize the zwitterionic limiting structure Z5 by equilibrating with zwitterion Z5'. As a consequence, the reaction may follow a multi-step mechanism in which Z5' is one reaction intermediate that can adopt quasi-cyclic or acyclic conformations. Similar diradicaloid models (D5 Catalysts 2022, 12, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/catalysts Z6) can be considered for metallacarbonyl-ene reactions promoted by a Lewis acid ( Figure 6, reaction (11)). Very electrophilic ketones such as hexafluoroacetone react with allylsilanes without catalyst [80]. The Hosomi-Sakurai reaction promoted by TiCl 4 (Figure 6, reaction (11)) is not only regiospecific, but also stereospecifically anti with respect to the silyl group, which leads to the formation of a (E)homoallylic alcohol [80][81][82]. ((E)-crotyl)trimethylsilane and ((E)-cinnamyl)trimethylsilane react with aldehydes in the presence of TiCl 4 to give homoallyl alcohols with over 93% syn-selectivity ( Figure 6, reactions (12) and (13)). Lower syn-selectivity is observed for the reactions of (Z)-crotylsilanes [83,84]. The stereoselectivity is generally accepted to be determined by chair-like six-membered ("closed") transition states [85][86][87][88][89][90].   (10) and (11) permits to explain the catalytic effect of added protic or Lewis acids (A) to enolate aldol condensations, to metallacarbonyl-ene reactions, and the carbonyl-ene-reaction.

Valence Bond Theory Can Be Used to Explain Structural and Medium Effects on the Rates of Displacement Reactions
The diradicaloid model is not limited to the transition structures of concerted pericyclic reactions. Concerted displacement reactions (14) are quite important in synthesis.
− − Figure 6. The diradicaloid model illustrated with Equilibria (10) and (11) permits to explain the catalytic effect of added protic or Lewis acids (A) to enolate aldol condensations, to metalla-carbonylene reactions, and the carbonyl-ene-reaction.

Valence Bond Theory Can Be Used to Explain Structural and Medium Effects on the Rates of Displacement Reactions
The diradicaloid model is not limited to the transition structures of concerted pericyclic reactions. Concerted displacement reactions (14) are quite important in synthesis.
Shaik and Pross, as well as others, have described the S N 2 reaction transition states in terms of valence bond theory [91][92][93][94][95][96][97][98]. The transition structure of a S N 2 reaction (Figure 7) engaging a negatively charged nucleophile can be represented by the limiting structures: This representation allows one to predict that the weaker the R-X bond (DH°(R • /X • ) = ΔfH°(R • ) + ΔfH°(X • ) -ΔfH°(R-X), ΔfH° = standard heat of formation); the faster the nucleophilic displacement. Furthermore, the higher the stability of cation R + and of nucleofugal group X: − , or/and the higher the stability of the carbanion R: − the faster the reaction is. Nucleophilicity of Y: − depends on how much the anion is dissociated from its counter-ion M + , and this depends upon the medium polarity and/or catalyst that interact specifically with M + . The lower the ionization energy (EI(Y: − )) of the nucleophile Y: -, the faster the displacement reaction is. The higher the electron affinity (−EA(R-X)) of the electrophile R-X, the faster the reaction is. Thermochemical data such as ionization energies and electron affinities permit one to evaluate the power of the pushing effect of the arrow associated with the attack of the electrophile by the nucleophile, and of the power of the pulling effect of the arrow associated with the departure of the nucleofugal group X: − . Additives that can combine with the nucleofugal group X (and not with the nucleophile Y) are catalysts of the displacement reaction.

Hydrocarbation of Unsaturated Compounds by R-H Reagents Do Not Produce Waste
Classically, for the formation of single C-C bonds, chemists have relied upon displacement reactions by matching a nucleophile with an electrophile (e.g., Nu-H + R-X + base → Nu-R + base-H + /X − , or Nu-metal + R-X → Nu-R + metal + /X − ; R = alkyl, alkenyl, aryl, heteroaryl, alkynyl) [99] and on electrophilic substitutions (Ar-H + E-X ⇄ Ar-E + HX; e.g.,: Friedel-Crafts alkylation and acylation) [100]. Catalyzed or photo-catalyzed freeradical additions to C-C multiple bond are applied more and more in fine organic synthesis, not only to generate polymers (e.g., R-X (X= I, Br) + BCH=CHA → R-CH(B)-CH(X)-A) [101][102][103][104][105][106]. Aldehyde and ketone olefinations are also powerful methods to create double C=C bonds. All these reactions are not atom economical, as they produce co-products. The same can be said for the very much used additions of organometallic reagents to unsaturated systems (Nu-metal + A=E ⇄ Nu-A-E-metal, with A, E = carbon or heteroelement; = is a double or triple bond) [107]. Direct additions (15) of R-H to unsaturated compounds are more atom economical [108,109]. One-step concerted [π 2 s+σ 2 s]-cycloadditions are predicted to be difficult reactions (symmetry forbidden, small LUMO/HOMO overlap, and large energy gaps between these reactant MO's). Conformational strain required for the theoretically allowed concerted [π 2 a+σ 2 s]-or [π 2 s+σ 2 a]-cycloadditions renders these one-step reactions impossible.
Many of them are base-catalyzed and involve the conjugate bases R − of R-H as intermediate. Examples are the aldol (e.g., R 1 CHO + R 2 CH2COR 3 ⇄ R 1 CH(OH)-CH(R 2 ) -COR 3 ) and the Claisen condensation (e.g., R 1 CH2COOR 2 + R 3 CHO ⇄ R 1 CH(COOR 2 ) -CH(OH)R 3 ), the Henry reaction (e.g., R 1 CH2NO2 + R 2 CHO ⇄ R 1 CH(NO2)-CH(OH)R 2 ), and the Michael addition (e.g., R 1 CH2COR 2 + CH2=CHCOR 3 → R 1 CH(COR 2 )-CH2-CH2COR 3 ) [110]. Under acidic conditions, the most common reactions are the Mannich reaction (e.g., R 1 COCH3 + CH2O + R2NH → R 1 COCH2-CH2-NR2 + H2O), the Alder ene-reaction (A-CH=CH2 + R2C=CH-C(R'2)H ⇄ A-CH2-CH2-C(R2)-CH=C(R'2), the alkylation of arenes by alkenes (e.g., Ar-H + CH2=CHR ⇄ ArCH(Me)R), the alkylation of alkenes with alkanes This representation allows one to predict that the weaker the R-X bond ( ; the faster the nucleophilic displacement. Furthermore, the higher the stability of cation R + and of nucleofugal group X: − , or/and the higher the stability of the carbanion R: − the faster the reaction is. Nucleophilicity of Y: − depends on how much the anion is dissociated from its counter-ion M + , and this depends upon the medium polarity and/or catalyst that interact specifically with M + . The lower the ionization energy (EI(Y: − )) of the nucleophile Y: -, the faster the displacement reaction is. The higher the electron affinity (−EA(R-X)) of the electrophile R-X, the faster the reaction is. Thermochemical data such as ionization energies and electron affinities permit one to evaluate the power of the pushing effect of the arrow associated with the attack of the electrophile by the nucleophile, and of the power of the pulling effect of the arrow associated with the departure of the nucleofugal group X: − . Additives that can combine with the nucleofugal group X (and not with the nucleophile Y) are catalysts of the displacement reaction.

Hydrocarbation of Unsaturated Compounds by R-H Reagents Do Not Produce Waste
Classically, for the formation of single C-C bonds, chemists have relied upon displacement reactions by matching a nucleophile with an electrophile (e.g., Nu-H + R-X + base → Nu-R + base-H + /X − , or Nu-metal + R-X → Nu-R + metal + /X − ; R = alkyl, alkenyl, aryl, heteroaryl, alkynyl) [99] and on electrophilic substitutions (Ar-H + E-X Ar-E + HX; e.g.,: Friedel-Crafts alkylation and acylation) [100]. Catalyzed or photo-catalyzed free-radical additions to C-C multiple bond are applied more and more in fine organic synthesis, not only to generate polymers (e.g., R-X (X= I, Br) + BCH=CHA → R-CH(B)-CH(X)-A) [101][102][103][104][105][106]. Aldehyde and ketone olefinations are also powerful methods to create double C=C bonds. All these reactions are not atom economical, as they produce co-products. The same can be said for the very much used additions of organometallic reagents to unsaturated systems (Nu-metal + A=E Nu-A-E-metal, with A, E = carbon or heteroelement; = is a double or triple bond) [107]. Direct additions (15) of R-H to unsaturated compounds are more atom economical [108,109]. One-step concerted [π 2 s+σ 2 s]-cycloadditions are predicted to be difficult reactions (symmetry forbidden, small LUMO/HOMO overlap, and large energy gaps between these reactant MO's). Conformational strain required for the theo-retically allowed concerted [π 2 a+σ 2 s]-or [π 2 s+σ 2 a]-cycloadditions renders these one-step reactions impossible.
Krische defines the process as being a hydro(hydroxycarbation) via transfer hydrogenation. An example is given with Reaction (17) (Scheme 3). The alcohol equilibrates with its aldehyde and an iridium hydride that adds chemoselectively to the alkene generating a methyl(propargyl)iridium intermediates, which, in turn, adds to the intermediate aldehyde. When the transition metal catalyst is coordinated to an enantiomerically pure ligand, the hydro(hydroxycarbation) can be highly stereo-(dr = diastereoisomeric ratio) and enantioselective (ee = enantiomeric excess) [125,126]. There have been many more exploratory studies on transition metal-catalyzed reactions than mechanistic studies. Thermochemical and kinetic data for transition metal complexes and their reactions are not as numerous as for organic compounds, but are being recorded more and more frequently. Nevertheless, because the structures and the There have been many more exploratory studies on transition metal-catalyzed reactions than mechanistic studies. Thermochemical and kinetic data for transition metal complexes and their reactions are not as numerous as for organic compounds, but are being recorded more and more frequently. Nevertheless, because the structures and the reactions of transition metal complexes can be modeled by the structures and reactions of organic compounds, simple models are available to "classify" the reactions catalyzed by transition metal species.
In classical chemistry, direct hydrocarbations of unsaturated compounds X=Y are non-concerted processes. If R is an allyl moiety, a concerted ene-reaction can occur (e.g., CH 2 =CH-CH 2 R' + X=Y → H-X-Y-CH 2 -CH=CHR'). If the catalyst is a base B:, it deprotonates R-H forming the conjugate base Ras an intermediate, which then adds to the alkene (or alkyne), generating an anionic adduct. The latter is then quenched by the conjugate acid BH + of the basic catalyst (nucleophilic addition (18)) or by R-H, realizing a chain process. Concurrently, the anionic adduct intermediate can add to another alkene (alkyne) and start the polymerization of the latter (anionic polymerization).
A second mechanism involves a radical intermediate R • in which the catalyst is a radical or a species that can abstract a hydrogen atom from R-H. The addition of radical R • to the alkene (alkyne) produces another radical that abstracts a hydrogen atom from H-X (radical addition (19)) or from R-H (chain process). Concurrently, the intermediate radical resulting from the initial radical addition can, in its turn, add to another alkene (alkyne) and lead to the polymerization of the latter (radical polymerization).
A third mechanism involves a cationic intermediate R + resulting from a hydride abstraction by a catalyst capable of abstracting a hydride from R-H reversibly. Such a mechanism corresponds to an electrophilic addition (20). Alternatively, the alkene can be protonated given a carbenium ion intermediate that adds to another alkene generating carbocationic adduct. At this stage, the latter is reduced by a hydride transfer from the alkane (e.g., the alkylate technology for the production of high octane number gasoline from a mixture of butene and isobutane) [127][128][129][130][131]. Concurrently, the first cationic adduct can add to another alkene, leading to its polymerization (cationic polymerization). Formally, instead of initiating the reaction by forming a carbenium ion intermediate R + , one can imagine a catalyst M + that combines with R-H forming an organometallic species R-M and a proton. The protonation of the alkene (alkyne) follows, forming a carbenium ion that is quenched by R-M (Reaction (21), Figure 8), or that adds to another alkene (alkyne), starting its polymerization [132][133][134][135][136][137][138][139]. Mechanisms that involve a single electron transfer are also possible [140][141][142].
Catalysts 2022, 12, x FOR PEER REVIEW 15 of 33 the alkene (or alkyne), generating an anionic adduct. The latter is then quenched by the conjugate acid BH + of the basic catalyst (nucleophilic addition (18)) or by R-H, realizing a chain process. Concurrently, the anionic adduct intermediate can add to another alkene (alkyne) and start the polymerization of the latter (anionic polymerization). A second mechanism involves a radical intermediate R • in which the catalyst is a radical or a species that can abstract a hydrogen atom from R-H. The addition of radical R • to the alkene (alkyne) produces another radical that abstracts a hydrogen atom from H-X (radical addition (19)) or from R-H (chain process). Concurrently, the intermediate radical resulting from the initial radical addition can, in its turn, add to another alkene (alkyne) and lead to the polymerization of the latter (radical polymerization).
A third mechanism involves a cationic intermediate R + resulting from a hydride abstraction by a catalyst capable of abstracting a hydride from R-H reversibly. Such a mechanism corresponds to an electrophilic addition (20). Alternatively, the alkene can be protonated given a carbenium ion intermediate that adds to another alkene generating carbocationic adduct. At this stage, the latter is reduced by a hydride transfer from the alkane (e.g., the alkylate technology for the production of high octane number gasoline from a mixture of butene and isobutane) [127][128][129][130][131]. Concurrently, the first cationic adduct can add to another alkene, leading to its polymerization (cationic polymerization). Formally, instead of initiating the reaction by forming a carbenium ion intermediate R + , one can imagine a catalyst M + that combines with R-H forming an organometallic species R-M and a proton. The protonation of the alkene (alkyne) follows, forming a carbenium ion that is quenched by R-M (Reaction (21), Figure 8), or that adds to another alkene (alkyne), starting its polymerization [132][133][134][135][136][137][138][139]. Mechanisms that involve a single electron transfer are also possible [140][141][142].

Transition Metal-Catalyzed Hydrocarbations
Transition metal-catalyzed processes follow mechanisms in which several intermediates equilibrate with reactants and products. Thus, thermodynamics control the outcome of the process in many instances. Other transition-metal-catalytic reactions that are not reversible have rate-determining steps that determine the chemo-, regio-, stereo-,

Transition Metal-Catalyzed Hydrocarbations
Transition metal-catalyzed processes follow mechanisms in which several intermediates equilibrate with reactants and products. Thus, thermodynamics control the outcome of the process in many instances. Other transition-metal-catalytic reactions that are not reversible have rate-determining steps that determine the chemo-, regio-, stereo-, and enantioselectivity. The latter can be guessed, or quantum chemical calculations can help, at least in rationalizing the observations. A number of rules are available from thermochemical data; for instance, the M-C bonds are weaker than the M-H bonds, and the C-C bonds are weaker than the C-H bonds for comparable systems (same type of substitution). Scheme 4 with reaction (22) is generally retained for transition metal-catalyzed direct hydrocarbation of unsaturated compounds.  [143][144][145][146][147]. This is called an oxidative addition [148]. The oxidative addition (23) of a transition metal complex ML to a C-H bond is modeled in organic chemistry with the insertion of a carbene into a single C-H bond to give an alkane. For instance, methane adds to methylene carbene (reaction (24)), giving ethane (ΔfH° = standard heat of formation in the gas phase). The carbene has a carbon atom with a sextet of VE, meaning that it is unsaturated, whereas the carbon center in the product (alkane) has an octet of VE, meaning it is saturated. Another comparison is the reaction of a methyl cation with methane that equilibrates with an ethonium ion (C2H7 + = protonated ethane) in the gas phase [149]. Dihydrogen (H2) reacts with methyl cations (which has a sextet of VE on its carbon atom), giving a methonium ion (CH5 + = protonated methane, carbon atom with an octet of VE) as shown (Scheme 5) with Equilibrium (25) [150][151][152][153][154].   [143][144][145][146][147]. This is called an oxidative addition [148]. The oxidative addition (23) of a transition metal complex ML to a C-H bond is modeled in organic chemistry with the insertion of a carbene into a single C-H bond to give an alkane. For instance, methane adds to methylene carbene (reaction (24)), giving ethane (∆ f H • = standard heat of formation in the gas phase). The carbene has a carbon atom with a sextet of VE, meaning that it is unsaturated, whereas the carbon center in the product (alkane) has an octet of VE, meaning it is saturated. Another comparison is the reaction of a methyl cation with methane that equilibrates with an ethonium ion (C 2 H 7 + = protonated ethane) in the gas phase [149]. Dihydrogen (H 2 ) reacts with methyl cations (which has a sextet of VE on its carbon atom), giving a methonium ion (CH 5 + = protonated methane, carbon atom with an octet of VE) as shown (Scheme 5) with Equilibrium (25) [150][151][152][153][154].
Transition metal complexes are good catalysts because they can exchange their ligand at relatively low temperature and assemble two reactants that must combine around the metal atom (template effect). Because bonds around the metallic center have bond angles that can be changed with little deformation energy, reactions that combine two reactants have relatively low energy barriers. Furthermore, the metallic center is highly polarizable, which means that it can take or give electrons very readily and at each step of the process.
The first and last steps of a transition-metal-catalytic process are ligand exchanges, as illustrated with the hydrocarbation reaction (22). The exchange of a ligand L (carbon monoxide, amine, phosphine, arsine, ether, aldehyde, ketone, alkene, alkyne, arenes, H 2 , etc.) with an alkene (Reaction (26)) is modeled by the cyclopropanation of alkenes with methylene generated by photolysis of ketene (Reaction (27)), for instance, (Scheme 6). Another reaction to consider as a model is the formation of a H-cycloproponium ion by the addition of a methyl cation to an alkene (reaction (28)). H-cycloproponium ions are intermediates (species longer-lived than transition structures) in Wagner-Meerwein rearrangements (see Table 1) [155].
C-H bond to give an alkane. For instance, methane adds to methylene carbene (reaction (24)), giving ethane (ΔfH° = standard heat of formation in the gas phase). The carbene has a carbon atom with a sextet of VE, meaning that it is unsaturated, whereas the carbon center in the product (alkane) has an octet of VE, meaning it is saturated. Another comparison is the reaction of a methyl cation with methane that equilibrates with an ethonium ion (C2H7 + = protonated ethane) in the gas phase [149]. Dihydrogen (H2) reacts with methyl cations (which has a sextet of VE on its carbon atom), giving a methonium ion (CH5 + = protonated methane, carbon atom with an octet of VE) as shown (Scheme 5) with Equilibrium (25) [150][151][152][153][154]. Transition metal complexes are good catalysts because they can exchange their ligand at relatively low temperature and assemble two reactants that must combine around the metal atom (template effect). Because bonds around the metallic center have bond angles that can be changed with little deformation energy, reactions that combine two reactants have relatively low energy barriers. Furthermore, the metallic center is highly polarizable, which means that it can take or give electrons very readily and at each step of the process.
The first and last steps of a transition-metal-catalytic process are ligand exchanges, as illustrated with the hydrocarbation reaction (22). The exchange of a ligand L (carbon monoxide, amine, phosphine, arsine, ether, aldehyde, ketone, alkene, alkyne, arenes, H2, etc.) with an alkene (Reaction (26)) is modeled by the cyclopropanation of alkenes with methylene generated by photolysis of ketene (Reaction (27)), for instance, (Scheme 6). Another reaction to consider as a model is the formation of a H-cycloproponium ion by the addition of a methyl cation to an alkene (reaction (28)). H-cycloproponium ions are intermediates (species longer-lived than transition structures) in Wagner-Meerwein rearrangements (see Table 1) [155]. Scheme 6. 14, 16 VE transition complexes form π-complexes with unsaturated systems that can be seen as metallacyclopropanes, just as carbenes and carbenium ions (6 VE species) do with alkenes, generating cyclopropanes and protonated cyclopropanes, respectively.  [17]. Copyright 2019 Wiley. Scheme 6. 14, 16 VE transition complexes form π-complexes with unsaturated systems that can be seen as metallacyclopropanes, just as carbenes and carbenium ions (6 VE species) do with alkenes, generating cyclopropanes and protonated cyclopropanes, respectively. Oxidative addition requires an unsaturated metallic species (with 16, 14 VE). The metal oxidation number is increased by two and the metal of the adduct has two more VE than the metal in the starting complex. Note that unsaturated [M] can add to any kinds of X-Y bonds reversibly. The addition of carbenes R2C: (C with a sextet) to X-H bonds generates stable compounds R2C(X)-H with an octet carbon center. The opposite reaction is an α-elimination or 1,1elimination.

α-Insertion/α-elimination
The number of VE is reduced by two when going from the reactant to the product in an α-insertion; the oxidation number of the metal is not changed (Z=O, NR', C(X)Y; R=H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

No change of valence electron count and oxidation number between the metal center of reactant [M]=CO and product [M]
(π-alkene) by convention. Oxidative addition requires an unsaturated metallic species (with 16, 14 VE). The metal oxidation number is increased by two and the metal of the adduct has two more VE than the metal in the starting complex. Note that unsaturated [M] can add to any kinds of X-Y bonds reversibly. The addition of carbenes R2C: (C with a sextet) to X-H bonds generates stable compounds R2C(X)-H with an octet carbon center. The opposite reaction is an α-elimination or 1,1elimination.

α-Insertion/α-elimination
The number of VE is reduced by two when going from the reactant to the product in an α-insertion; the oxidation number of the metal is not changed (Z=O, NR', C(X)Y; R=H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

β-Insertion/β-elimination
Oxidative addition requires an unsaturated metallic species (with 16, 14 VE). The metal oxidation number is increased by two and the metal of the adduct has two more VE than the metal in the starting complex. Note that unsaturated [M] can add to any kinds of X-Y bonds reversibly. The addition of carbenes R 2 C: (C with a sextet) to X-H bonds generates stable compounds R 2 C(X)-H with an octet carbon center. The opposite reaction is an α-elimination or 1,1-elimination. Oxidative addition requires an unsaturated metallic species (with 16, 14 VE). The metal oxidation number is increased by two and the metal of the adduct has two more VE than the metal in the starting complex. Note that unsaturated [M] can add to any kinds of X-Y bonds reversibly. The addition of carbenes R2C: (C with a sextet) to X-H bonds generates stable compounds R2C(X)-H with an octet carbon center. The opposite reaction is an α-elimination or 1,1elimination.

α-Insertion/α-elimination
The number of VE is reduced by two when going from the reactant to the product in an α-insertion; the oxidation number of the metal is not changed (Z=O, NR', C(X)Y; R=H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

β-Insertion/β-elimination
The number of VE is reduced by two when going from the reactant to the product in an α-insertion; the oxidation number of the metal is not changed (Z=O, NR', C(X)Y; R=H, alkyl, alkenyl, aryl, R'O, Hal, etc.). The number of VE is reduced by two when going from reactant to product in the β-insertion; the oxidation number of the metal is not changed (R = H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

α-cycloinsertion/α-cycloelimination
The number of VE of the metal is reduced by two when going from reactant to product in the α-cycloinsertion; the oxidation number of the metal is increased by two by convention.

Oxidative cyclization/reductive fragmentation (β-cycloinsertion/β-cycloelimination)
The number of VE of the metal is reduced by two when going from reactant to product in the oxidative cyclization and the oxidation number of the metal increases by two by convention. The metal-catalyzed cycloinsertions can combine other unsaturated reactants besides alkenes.
The number of VE is reduced by two when going from reactant to product in the β-insertion; the oxidation number of the metal is not changed (R = H, alkyl, alkenyl, aryl, R'O, Hal, etc.). The number of VE is reduced by two when going from reactant to product in the β-insertion; the oxidation number of the metal is not changed (R = H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

α-cycloinsertion/α-cycloelimination
The number of VE of the metal is reduced by two when going from reactant to product in the α-cycloinsertion; the oxidation number of the metal is increased by two by convention.

Oxidative cyclization/reductive fragmentation (β-cycloinsertion/β-cycloelimination)
The number of VE of the metal is reduced by two when going from reactant to product in the oxidative cyclization and the oxidation number of the metal increases by two by convention. The metal-catalyzed cycloinsertions can combine other unsaturated reactants besides alkenes.
The number of VE of the metal is reduced by two when going from reactant to product in the α-cycloinsertion; the oxidation number of the metal is increased by two by convention.

Oxidative cyclization/reductive fragmentation (β-cycloinsertion/β-cycloelimination)
Catalysts 2022, 12, x FOR PEER REVIEW 19 of 33 The number of VE is reduced by two when going from reactant to product in the β-insertion; the oxidation number of the metal is not changed (R = H, alkyl, alkenyl, aryl, R'O, Hal, etc.).

α-cycloinsertion/α-cycloelimination
The number of VE of the metal is reduced by two when going from reactant to product in the α-cycloinsertion; the oxidation number of the metal is increased by two by convention.

Oxidative cyclization/reductive fragmentation (β-cycloinsertion/β-cycloelimination)
The number of VE of the metal is reduced by two when going from reactant to product in the oxidative cyclization and the oxidation number of the metal increases by two by convention. The metal-catalyzed cycloinsertions can combine other unsaturated reactants besides alkenes.
The number of VE of the metal is reduced by two when going from reactant to product in the oxidative cyclization and the oxidation number of the metal increases by two by convention. The metal-catalyzed cycloinsertions can combine other unsaturated reactants besides alkenes.

Reactions at the coordinated ligands
Catalysts 2022, 12, x FOR PEER REVIEW 20 of 33

Reactions at the coordinated ligands
One of the processes that generates a bond between two reactants is the β-insertion (Reaction (30), the opposite reaction being a β-elimination). For the insertion of a hydrogen atom, the model reaction is the corner-to-corner migration in Hcycloproponium ions that corresponds to a 1,3-hydrogen shift, as shown with reaction (29) [156]. The rearrangement involves a transition structure that is a C-cycloproponium ion or edge-protonated cyclopropane (Scheme 7). A priori, any R group can do such migration (β-insertion). After the β-insertion, the metallic center has lost two VE. For the reaction to occur, a ligand L must coordinate the unsaturated metallic center. After the β-insertion, a reductive elimination (Reaction (31)), occurs, forming the final product of hydrocarbation and an unsaturated metallic species that can return as the active catalyst for another oxidative addition with reactant R-H, or be stabilized by the coordination of a ligand molecule L of a solvent molecule (Scheme 8). The reductive elimination is the opposite reaction of the oxidative addition (e.g., Reaction (23)). If the 16-One of the processes that generates a bond between two reactants is the β-insertion (Reaction (30), the opposite reaction being a β-elimination). For the insertion of a hydrogen atom, the model reaction is the corner-to-corner migration in H-cycloproponium ions that corresponds to a 1,3-hydrogen shift, as shown with reaction (29) [156]. The rearrangement involves a transition structure that is a C-cycloproponium ion or edge-protonated cyclopropane (Scheme 7). A priori, any R group can do such migration (β-insertion). After the β-insertion, the metallic center has lost two VE. For the reaction to occur, a ligand L must coordinate the unsaturated metallic center.

Reactions at the coordinated ligands
One of the processes that generates a bond between two reactants is the β-insertion (Reaction (30), the opposite reaction being a β-elimination). For the insertion of a hydrogen atom, the model reaction is the corner-to-corner migration in Hcycloproponium ions that corresponds to a 1,3-hydrogen shift, as shown with reaction (29) [156]. The rearrangement involves a transition structure that is a C-cycloproponium ion or edge-protonated cyclopropane (Scheme 7). A priori, any R group can do such migration (β-insertion). After the β-insertion, the metallic center has lost two VE. For the reaction to occur, a ligand L must coordinate the unsaturated metallic center. After the β-insertion, a reductive elimination (Reaction (31)), occurs, forming the final product of hydrocarbation and an unsaturated metallic species that can return as the active catalyst for another oxidative addition with reactant R-H, or be stabilized by the coordination of a ligand molecule L of a solvent molecule (Scheme 8). The reductive elimination is the opposite reaction of the oxidative addition (e.g., Reaction (23)). If the 16-Scheme 7. β-insertions and β-eliminations in transition metal complexes are modeled by corner-tocorner migration in protonated cyclopropanes.
After the β-insertion, a reductive elimination (Reaction (31)), occurs, forming the final product of hydrocarbation and an unsaturated metallic species that can return as the active catalyst for another oxidative addition with reactant R-H, or be stabilized by the coordination of a ligand molecule L of a solvent molecule (Scheme 8). The reductive elimination is the opposite reaction of the oxidative addition (e.g., Reaction (23)). If the 16-VE metallic adduct intermediate is an allylmetal species, it may add to the unsaturated system in a metalla-ene reaction [157,158]. The other processes (α-insertion/α-elimination, α-cycloinsertion/α-cycloelimination, β-cycloinsertion/β-cycloelimination) induced by transition metal complexes are also modeled by reactions of carbocations, as summarized in Table 1 [156].

Review of the Fundamental Reactions of Simple Carbocations
The mass spectrum of methane (CH4) has peaks with mass/charge ratios m/Q = 12, 13, 14, 15, and 16 corresponding to the cations C •+ , HC + , H2C •+ , H3C + , and H4C •+ , respectively. The parent cation H4C •+ (or molecular ion) can dissociate into hydrogen radical H • and methyl cation H3C + , and so on. If there is sufficient pressure in the ionization chamber, the transfer of a proton (32) can take place (bimolecular reaction): In this case, a peak is observed in the mass spectrum of methane with a mass/charge ratio m/Q = 17, which corresponds to methonium ion, CH5 + , whose carbon atom is surrounded by an octet of valence electrons. It is much more stable (by 45 kcal mol −1 , Equilibrium (25)) than methyl cation, H3C + , whose carbon atom is surrounded by a sextet of valence electrons. Methonium ion is the prototype of carbonium ions. Methyl cation is the prototype of carbenium ions. The notation H4C •+ describes the methanium radicalcation, which has seven valence electrons [159,160].
The salts of methyl and ethyl cations cannot be observed as persistent species in solution. When CD3CH2F is allowed to react with an excess of SbF5/SO2 at −78°C, complete deuterium/hydrogen scrambling in the ethyl group of ethyl fluoride is observed by 1 H-NMR spectroscopy. However, when CH3CH2F is added to DSO3F/SbF5 or DF/SbF5 in SO2 at −78°C, no detectable incorporation of deuterium into the ethyl group occurs [161]. This demonstrates that scrambling takes place intramolecularly in the ethyl cation intermediate (Scheme 9). Quantum calculations predict similar stabilities for classical ethyl cations and the bridged πH-ethenium ions (Equilibrium (33)) [162,163], which has been confirmed by infrared spectroscopy of the ion in the gas phase [164,165]. The πHethenium ion is the smallest possible π-complex of an alkene. The other processes (α-insertion/α-elimination, α-cycloinsertion/α-cycloelimination, β-cycloinsertion/β-cycloelimination) induced by transition metal complexes are also modeled by reactions of carbocations, as summarized in Table 1 [156].

Review of the Fundamental Reactions of Simple Carbocations
The mass spectrum of methane (CH 4 ) has peaks with mass/charge ratios m/Q = 12, 13, 14, 15, and 16 corresponding to the cations C •+ , HC + , H 2 C •+ , H 3 C + , and H 4 C •+ , respectively. The parent cation H 4 C •+ (or molecular ion) can dissociate into hydrogen radical H • and methyl cation H 3 C + , and so on. If there is sufficient pressure in the ionization chamber, the transfer of a proton (32) can take place (bimolecular reaction): In this case, a peak is observed in the mass spectrum of methane with a mass/charge ratio m/Q = 17, which corresponds to methonium ion, CH 5 + , whose carbon atom is surrounded by an octet of valence electrons. It is much more stable (by 45 kcal mol −1 , Equilibrium (25)) than methyl cation, H 3 C + , whose carbon atom is surrounded by a sextet of valence electrons. Methonium ion is the prototype of carbonium ions. Methyl cation is the prototype of carbenium ions. The notation H 4 C •+ describes the methanium radical-cation, which has seven valence electrons [159,160].
The salts of methyl and ethyl cations cannot be observed as persistent species in solution. When CD 3 CH 2 F is allowed to react with an excess of SbF 5 /SO 2 at −78 • C, complete deuterium/hydrogen scrambling in the ethyl group of ethyl fluoride is observed by 1 H-NMR spectroscopy. However, when CH 3 CH 2 F is added to DSO 3 F/SbF 5 or DF/SbF 5 in SO 2 at −78 • C, no detectable incorporation of deuterium into the ethyl group occurs [161]. This demonstrates that scrambling takes place intramolecularly in the ethyl cation intermediate (Scheme 9). Quantum calculations predict similar stabilities for classical ethyl cations and the bridged πH-ethenium ions (Equilibrium (33)) [162,163], which has been confirmed by infrared spectroscopy of the ion in the gas phase [164,165]. The πH-ethenium ion is the smallest possible π-complex of an alkene. The other processes (α-insertion/α-elimination, α-cycloinsertion/α-cycloelimination, β-cycloinsertion/β-cycloelimination) induced by transition metal complexes are also modeled by reactions of carbocations, as summarized in Table 1 [156].

Review of the Fundamental Reactions of Simple Carbocations
The mass spectrum of methane (CH4) has peaks with mass/charge ratios m/Q = 12, 13, 14, 15, and 16 corresponding to the cations C •+ , HC + , H2C •+ , H3C + , and H4C •+ , respectively. The parent cation H4C •+ (or molecular ion) can dissociate into hydrogen radical H • and methyl cation H3C + , and so on. If there is sufficient pressure in the ionization chamber, the transfer of a proton (32) can take place (bimolecular reaction): In this case, a peak is observed in the mass spectrum of methane with a mass/charge ratio m/Q = 17, which corresponds to methonium ion, CH5 + , whose carbon atom is surrounded by an octet of valence electrons. It is much more stable (by 45 kcal mol −1 , Equilibrium (25)) than methyl cation, H3C + , whose carbon atom is surrounded by a sextet of valence electrons. Methonium ion is the prototype of carbonium ions. Methyl cation is the prototype of carbenium ions. The notation H4C •+ describes the methanium radicalcation, which has seven valence electrons [159,160].
The 1 H-NMR spectrum of the but-2-yl cation (s-Bu + ) in SbF 5 /SO 2 ClF solution measured below −120 • C indicates a very fast proton interchange due to Equilibrium (37) [170,171]. Between −100 and −40 • C, all the hydrogen atoms in s-Bu + are scrambled with an activation energy E a =7.5 ± 0.1 kcal mol −1 (logA = 12.3 ± 0.1). If a series of 1,2-hydride shifts were responsible for the proton interchange, formation of a n-butyl (but-1-yl) cation intermediate (n-Bu + ) would be required (Scheme 12). However, by analogy with the isopropyl cation (Equilibria (34) and (35)), the formation of n-Bu + would be expected to require an activation energy higher than 15 kcal mol −1 . Hence, a more facile process involving formation of a protonated methylcyclopropane and degenerate hydrogen shifts via an edge-protonated cyclopropane intermediate or transition state is more probable (Equilibrium (38)). When heated to −40 • C, the but-2-yl cation rearranges irreversibly into a t-butyl cation with an activation energy of 18 kcal mol −1 . The similarity of this energy barrier with that observed for the isopropyl n-propyl cation rearrangement (E a ∼ = 16 kcal mol −1 ) indicates that the reaction takes place via the primary carbenium ion intermediate isobutyl cation, i-Bu + , although this species is undoubtedly bridged by H or methyl in its minimum energy structure. were responsible for the proton interchange, formation of a n-butyl (but-1-yl) cation intermediate (n-Bu + ) would be required (Scheme 12). However, by analogy with the isopropyl cation (Equilibria (34) and (35)), the formation of n-Bu + would be expected to require an activation energy higher than 15 kcal mol −1 . Hence, a more facile process involving formation of a protonated methylcyclopropane and degenerate hydrogen shifts via an edge-protonated cyclopropane intermediate or transition state is more probable (Equilibrium (38)). When heated to −40°C, the but-2-yl cation rearranges irreversibly into a t-butyl cation with an activation energy of 18 kcal mol −1 . The similarity of this energy barrier with that observed for the isopropyl ⇄ n-propyl cation rearrangement (Ea ≅ 16 kcal mol −1 ) indicates that the reaction takes place via the primary carbenium ion intermediate isobutyl cation, i-Bu + , although this species is undoubtedly bridged by H or methyl in its minimum energy structure.
Two different types of hydrogen exchange processes have been observed in the 1 H-NMR spectrum of the t-amyl cation (2-methylbut-2-yl cation) (Scheme 14) [173]. One involves the interchange of the two types of methyl group protons, not affecting the methylene group (Equilibrium (40)). On the NMR time scale, this process occurs at temperatures above 0 °C and has an activation energy of Ea ≅ 15 kcal mol −1 (logA ≅ 13.2). The rearrangement first involves a 1,2-sigmatropic shift of hydrogen generating a secondary alkyl cation intermediate (3-methylbut-2-yl cation). This is followed by a 1,2sigmatropic shift of a methyl group (Wagner-Meerwein rearrangement) that generates another secondary alkyl cation intermediate (3-methylbut-2-yl cation). The latter undergoes a quick 1,2-sigmatropic shift of a hydrogen-producing t-amyl cation via a protonated dimethylcyclopropane (as intermediate or transition state). Since degenerate Wagner-Meerwein shifts of both hydrogen and methyl groups are very fast (Ea < 4 kcal/mol, see e.g., Equilibrium (37)) when no change in the degree of chain branching of the carbenium ion occurs, the major part of the activation energy for this rearrangement (15 kcal mol −1 ) must be due to the formation of the secondary ion intermediate (3methylbut-2-yl cation) from an t-amyl cation (2-methylbut-2-yl cation) [173]. The second process (41) occurs above 80 °C on the NMR time scale. It causes the scrambling of all the hydrogen atoms in a t-amyl cation. It has an activation energy Ea = 18.8 ± 1 kcal mol −1 (logA = 13.2 ± 0.5). A mechanism involving reversible hydride shifts to primary carbenium ion intermediates (e.g., 2-methylbut-1-yl cation) can be rejected on the basis that such species would have energies well above (ca. 30 kcal mol −1 ) that of the starting tertiary cation (t-amyl cation). In the alternative mechanism shown with Equilibrium (41), the hydrogen atom interchange involves corner-to-corner hydrogen shifts in the protonated dimethylcyclopropane intermediates. Thus, this process, which involves an overall change in the degree of chain branching, has an energy barrier 3 kcal Scheme 13. Protonated cyclobutane is much less stable than protonated methylcyclopropane.
Two different types of hydrogen exchange processes have been observed in the 1 H-NMR spectrum of the t-amyl cation (2-methylbut-2-yl cation) (Scheme 14) [173]. One involves the interchange of the two types of methyl group protons, not affecting the methylene group (Equilibrium (40)). On the NMR time scale, this process occurs at temperatures above 0 • C and has an activation energy of E a ∼ = 15 kcal mol −1 (logA ∼ = 13.2). The rearrangement first involves a 1,2-sigmatropic shift of hydrogen generating a secondary alkyl cation intermediate (3-methylbut-2-yl cation). This is followed by a 1,2-sigmatropic shift of a methyl group (Wagner-Meerwein rearrangement) that generates another secondary alkyl cation intermediate (3-methylbut-2-yl cation). The latter undergoes a quick 1,2-sigmatropic shift of a hydrogen-producing t-amyl cation via a protonated dimethylcyclopropane (as intermediate or transition state). Since degenerate Wagner-Meerwein shifts of both hydrogen and methyl groups are very fast (E a < 4 kcal/mol, see e.g., Equilibrium (37)) when no change in the degree of chain branching of the carbenium ion occurs, the major part of the activation energy for this rearrangement (15 kcal mol −1 ) must be due to the formation of the secondary ion intermediate (3-methylbut-2-yl cation) from an t-amyl cation (2-methylbut-2-yl cation) [173]. Two different types of hydrogen exchange processes have been observed in the 1 H-NMR spectrum of the t-amyl cation (2-methylbut-2-yl cation) (Scheme 14) [173]. One involves the interchange of the two types of methyl group protons, not affecting the methylene group (Equilibrium (40)). On the NMR time scale, this process occurs at temperatures above 0 °C and has an activation energy of Ea ≅ 15 kcal mol −1 (logA ≅ 13.2). The rearrangement first involves a 1,2-sigmatropic shift of hydrogen generating a secondary alkyl cation intermediate (3-methylbut-2-yl cation). This is followed by a 1,2sigmatropic shift of a methyl group (Wagner-Meerwein rearrangement) that generates another secondary alkyl cation intermediate (3-methylbut-2-yl cation). The latter undergoes a quick 1,2-sigmatropic shift of a hydrogen-producing t-amyl cation via a protonated dimethylcyclopropane (as intermediate or transition state). Since degenerate Wagner-Meerwein shifts of both hydrogen and methyl groups are very fast (Ea < 4 kcal/mol, see e.g., Equilibrium (37)) when no change in the degree of chain branching of the carbenium ion occurs, the major part of the activation energy for this rearrangement (15 kcal mol −1 ) must be due to the formation of the secondary ion intermediate (3methylbut-2-yl cation) from an t-amyl cation (2-methylbut-2-yl cation) [173].
The second process (41) occurs above 80 °C on the NMR time scale. It causes the scrambling of all the hydrogen atoms in a t-amyl cation. It has an activation energy Ea = 18.8 ± 1 kcal mol −1 (logA = 13.2 ± 0.5). A mechanism involving reversible hydride shifts to primary carbenium ion intermediates (e.g., 2-methylbut-1-yl cation) can be rejected on the basis that such species would have energies well above (ca. 30 kcal mol −1 ) that of the starting tertiary cation (t-amyl cation). In the alternative mechanism shown with Equilibrium (41), the hydrogen atom interchange involves corner-to-corner hydrogen shifts in the protonated dimethylcyclopropane intermediates. Thus, this process, which involves an overall change in the degree of chain branching, has an energy barrier 3 kcal Scheme 14. Hydrogen-and carbon-atom scrambling in 2-methylbut-2-yl (tertioamyl) salt in a superionizing medium (SbF 5 /SO 2 ClF).
The second process (41) occurs above 80 • C on the NMR time scale. It causes the scrambling of all the hydrogen atoms in a t-amyl cation. It has an activation energy E a = 18.8 ± 1 kcal mol −1 (logA = 13.2 ± 0.5). A mechanism involving reversible hydride shifts to primary carbenium ion intermediates (e.g., 2-methylbut-1-yl cation) can be rejected on the basis that such species would have energies well above (ca. 30 kcal mol −1 ) that of the starting tertiary cation (t-amyl cation). In the alternative mechanism shown with Equilibrium (41), the hydrogen atom interchange involves corner-to-corner hydrogen shifts in the protonated dimethylcyclopropane intermediates. Thus, this process, which involves an overall change in the degree of chain branching, has an energy barrier 3 kcal mol −1 higher than those for related processes not involving such a change [155,174] The secondary cyclopentyl cation is stable in SbF5/SO2ClF solution up to -20°C [176]. It undergoes a fast, degenerate 1,2-hydride shift (equilibrium (42), Ea < 4.5 kcal mol -1 ), but no ring contraction (equilibrium (43)) has ever been detected (Scheme 16). Considering an energy difference of 15 kcal mol −1 for the isomerization of a secondary alkyl cation to a primary isomer and the ring strain difference of 20 kcal mol −1 between cyclopentane and cyclobutene, one estimates the cyclobutylmethyl cation to be less stable than the cyclopentyl cation by ca. 35 kcal mol −1 . Contrary to the cyclopropylmethyl cation, which is highly stabilized [177,178], the cyclobutylmethyl cation does not enjoy the same hyperconjugative stabilization [179,180]. Scheme 16. The cyclobutylmethyl cation is not a stable primary carbenium ion.
In the gas phase, the doubly 13 C-labelled cyclopentyl cations 11 and 12 generated from the doubly 13 C-labelled bromides 7-10 undergo degenerate carbon scrambling (Equilibrium (44)) prior to elimination of ethylene (Fragmentation (45)). The complete carbon scrambling can, in principle, proceed via either the cyclobutylmethyl cation intermediate (Equilibrium (43)) or the "non-classical" pyramidal cation 13 (Equilibrium (44)), as calculations have suggested that they have similar energies [181,182]. Cation 13 can be viewed as a π-complex between ethylene and a cyclopropyl cation (cornerprotonated spiropentane) or as a double π-complex between two ethylene units and the methylidynium ion, :CH + (Scheme 17). The fragmentation of the cyclopentyl cation into the allyl cation and ethylene (Fragmentation (45)) may also involve cation 13 as an intermediate. The dissociation of an ethylene unit from 13 via transition state 14 is Scheme 15. The 2-norbornyl cation is a stable corner-protonated cyclopropane derivative (nonclassical carbonium ion).
The secondary cyclopentyl cation is stable in SbF 5 /SO 2 ClF solution up to -20 • C [176]. It undergoes a fast, degenerate 1,2-hydride shift (equilibrium (42), E a < 4.5 kcal mol -1 ), but no ring contraction (equilibrium (43)) has ever been detected (Scheme 16). Considering an energy difference of 15 kcal mol −1 for the isomerization of a secondary alkyl cation to a primary isomer and the ring strain difference of 20 kcal mol −1 between cyclopentane and cyclobutene, one estimates the cyclobutylmethyl cation to be less stable than the cyclopentyl cation by ca. 35 kcal mol −1 . Contrary to the cyclopropylmethyl cation, which is highly stabilized [177,178], the cyclobutylmethyl cation does not enjoy the same hyperconjugative stabilization [179,180]. The secondary cyclopentyl cation is stable in SbF5/SO2ClF solution up to -20°C [176]. It undergoes a fast, degenerate 1,2-hydride shift (equilibrium (42), Ea < 4.5 kcal mol -1 ), but no ring contraction (equilibrium (43)) has ever been detected (Scheme 16). Considering an energy difference of 15 kcal mol −1 for the isomerization of a secondary alkyl cation to a primary isomer and the ring strain difference of 20 kcal mol −1 between cyclopentane and cyclobutene, one estimates the cyclobutylmethyl cation to be less stable than the cyclopentyl cation by ca. 35 kcal mol −1 . Contrary to the cyclopropylmethyl cation, which is highly stabilized [177,178], the cyclobutylmethyl cation does not enjoy the same hyperconjugative stabilization [179,180]. Scheme 16. The cyclobutylmethyl cation is not a stable primary carbenium ion.
In the gas phase, the doubly 13 C-labelled cyclopentyl cations 11 and 12 generated from the doubly 13 C-labelled bromides 7-10 undergo degenerate carbon scrambling (Equilibrium (44)) prior to elimination of ethylene (Fragmentation (45)). The complete carbon scrambling can, in principle, proceed via either the cyclobutylmethyl cation intermediate (Equilibrium (43)) or the "non-classical" pyramidal cation 13 (Equilibrium (44)), as calculations have suggested that they have similar energies [181,182]. Cation 13 can be viewed as a π-complex between ethylene and a cyclopropyl cation (cornerprotonated spiropentane) or as a double π-complex between two ethylene units and the methylidynium ion, :CH + (Scheme 17). The fragmentation of the cyclopentyl cation into the allyl cation and ethylene (Fragmentation (45)) may also involve cation 13 as an intermediate. The dissociation of an ethylene unit from 13 via transition state 14 is Scheme 16. The cyclobutylmethyl cation is not a stable primary carbenium ion.
In the gas phase, the doubly 13 C-labelled cyclopentyl cations 11 and 12 generated from the doubly 13 C-labelled bromides 7-10 undergo degenerate carbon scrambling (Equilibrium (44)) prior to elimination of ethylene (Fragmentation (45)). The complete carbon scrambling can, in principle, proceed via either the cyclobutylmethyl cation intermediate (Equilibrium (43)) or the "non-classical" pyramidal cation 13 (Equilibrium (44)), as calculations have suggested that they have similar energies [181,182]. Cation 13 can be viewed as a π-complex between ethylene and a cyclopropyl cation (corner-protonated spiropentane) or as a double π-complex between two ethylene units and the methylidynium ion, :CH + (Scheme 17). The fragmentation of the cyclopentyl cation into the allyl cation and ethylene (Fragmentation (45)) may also involve cation 13 as an intermediate. The dissociation of an ethylene unit from 13 via transition state 14 is expected to give an allyl cation and ethylene. This process would be analogous to the gas phase fragmentation of the corner-protonated cyclopropane into molecular hydrogen and allyl cations. Mechanisms similar to those presented with Equilibrium (44) have been proposed to rationalize the complete hydrogen and carbon atom scrambling in the gaseous cyclohexyl methylcyclopentyl cation equilibrium that occurs prior to monomolecular elimination of ethylene [183]. Cation 13 is also formed upon protonation of spiropentane. In the gas phase, its lifetime exceeds 7 × 10 −9 s. Cation 13 is separated from the cyclopentyl cation by 30 kcal mol −1 [184,185].
Catalysts 2022, 12, x FOR PEER REVIEW 26 of 33 expected to give an allyl cation and ethylene. This process would be analogous to the gas phase fragmentation of the corner-protonated cyclopropane into molecular hydrogen and allyl cations. Mechanisms similar to those presented with Equilibrium (44) have been proposed to rationalize the complete hydrogen and carbon atom scrambling in the gaseous cyclohexyl ⇄ methylcyclopentyl cation equilibrium that occurs prior to monomolecular elimination of ethylene [183]. Cation 13 is also formed upon protonation of spiropentane. In the gas phase, its lifetime exceeds 7 × 10 −9 s. Cation 13 is separated from the cyclopentyl cation by 30 kcal mol −1 [184,185].

Scheme 17.
In the gas phase, the cyclopentyl cation equilibrates with the corner-protonated spiropentane intermediate, which permits its carbon-atom scrambling and fragmentation into ethylene and an allyl cation.

Conclusions
The inventor of new processes can predict equilibrium constants and reaction rates by applying simple rules of thermodynamics and using published thermochemical data. Organic chemistry today offers a fantastic panoply of new reactions, especially catalytic reactions, that render the exploration of chemical space faster and more facile. Very important and sustainable processes are available, especially when atom economical processes are engaged, such as pericyclic reactions and direct hydrocarbation of unsaturated compounds. Catalysts can be invented that permit these reactions to be run under smooth conditions (no cooling, no heating, no solvent or in harmless solvents such as water, ethanol, ethyl acetate, or 2-methyltetrahydrofuran). There is a catalyst for any kind of reaction that permits energy savings and reduces the co-production of waste. The Vogel-Houk book has been written to help engineers and inventors realize a more sustainable world and to quickly generate a large number of new molecules that our civilization needs or will need. It also illustrates how fundamental concepts of chemical reactivity are based on thermodynamics. In this review, we have extracted a few models that help to show the analogies that exist between reactions of organic compounds and transition organometallic compounds. They help to understand a large number of catalyzed processes. Scheme 17. In the gas phase, the cyclopentyl cation equilibrates with the corner-protonated spiropentane intermediate, which permits its carbon-atom scrambling and fragmentation into ethylene and an allyl cation.

Conclusions
The inventor of new processes can predict equilibrium constants and reaction rates by applying simple rules of thermodynamics and using published thermochemical data. Organic chemistry today offers a fantastic panoply of new reactions, especially catalytic reactions, that render the exploration of chemical space faster and more facile. Very important and sustainable processes are available, especially when atom economical processes are engaged, such as pericyclic reactions and direct hydrocarbation of unsaturated compounds. Catalysts can be invented that permit these reactions to be run under smooth conditions (no cooling, no heating, no solvent or in harmless solvents such as water, ethanol, ethyl acetate, or 2-methyltetrahydrofuran). There is a catalyst for any kind of reaction that permits energy savings and reduces the co-production of waste. The Vogel-Houk book has been written to help engineers and inventors realize a more sustainable world and to quickly generate a large number of new molecules that our civilization needs or will need. It also illustrates how fundamental concepts of chemical reactivity are based on thermodynamics. In this review, we have extracted a few models that help to show the analogies that exist between reactions of organic compounds and transition organometallic compounds. They help to understand a large number of catalyzed processes.
Author Contributions: Conceptualization, P.V. and K.N.H.; writing-original draft preparation, P.V.; writing-review and editing, P.V. and K.N.H. All authors have read and agreed to the published version of the manuscript.

Funding:
The writing of this review was supported by the Basic Science Faculty of the "Ecole Polytechnique Fédérale de Lausanne" (EPFL) and by the Department of Chemistry and Biochemistry, University of California (UCLA), Los Angeles.