Understanding reaction mechanisms in organic chemistry from catastrophe theory applied to the electron localization function topology

Thom's catastrophe theory applied to the evolution of the topology of the electron localization function (ELF) gradient field constitutes a way to rationalize the reorganization of electron pairing and a powerful tool for the unambiguous determination of the molecular mechanisms of a given chemical reaction. The identification of the turning points connecting the ELF structural stability domains along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a chemical transformation, such as multiple bond forming/breaking processes, ring closure processes, creation/annihilation of lone pairs, transformations of C-C multiple bonds into single ones. The reaction mechanism of some relevant organic reactions: Diels-Alder, 1,3-dipolar cycloaddition and Cope rearrangement are reviewed to illustrate the potential of the present approach.     

Electron delocalization and bond formation under the ELF framework

A first approach to the relationship between the electron localization function (ELF) and electronic delocalization upon bond formation is provided. We show from first principles the ability of ELF at the bond critical points to act as an index of the electron reorganization involved in chemical bonding. Simultaneously, this index, that we shall call ELF delocalization index (EDI), constitutes a good measure of electron delocalization. We will show how the core of ELF is proportional to the Wiberg index under the valence bond approach. This relationship will be exploited for some representative examples where EDI is able to identify the stages of bond formation. Furthermore, a maximum in EDI along this process has been found to correlate with the molecular equilibrium configuration, allowing for a formulation of a ??maximal localization principle?? for the stable structure of covalent compounds in terms of ELF.     

Evidence of an unexpectedly long C-C bond (>2.7 A) in 1,3-metalladiyne complexes [Cp2MCCR]2 (M = Ti, Zr): QTAIM and ELF analyses

Topological analyses of the electron density using the quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) have been carried out, at the B3LYP/DGVZVP and MP2/DGVZVP theoretical levels, on different 1,3-metalladiyne cyclic compounds [Cp2M(CCR)]2, (M = Ti, Zr; R = F, CH3, H, SiH3). The QTAIM results indicate the presence of an extraordinarily long C-C bond (in a 2.7-3.0 A range) connecting the CCR moieties, contrary to the common geometrical assumption of a M-M bond in similar metallacycles. The existence of this C-C bond is also supported by the distinct consequences on the reaction profiles for the Ti and Zr complexes, the CC oxidative coupling reactions being favored only for the Ti complexes. Moreover, the consequences of this bonding in the coupling/cleavage reactions of these metallacyclic complexes are reported and analyzed, revealing the transcendence of these long-range bonds in the overall behavior of these compounds.     

Bond ionicity and the strength of carbon-carbon bonds

A simple VB analysis is used to illustrate that the greater stability of geminally disubstituted ethanes and ethylenes compared to their vicinally substituted counterparts is due to the strength of the central C-C bond and not to the stability of the radical and carbene fragments that compose the molecule. The qualitative arguments are supported by MO calculations. The implications to the additivity rules for the estimation of heats of formation are discussed.     

Understanding the mechanism of non-polar Diels-Alder reactions. A comparative ELF analysis of concerted and stepwise diradical mechanisms

The electron-reorganization along the concerted and stepwise pathways associated with the non-polar Diels-Alder reaction between cyclopentadiene (Cp, 1) and ethylene (2) has been studied using the topological analysis of the electron localization function (ELF) at the B3LYP/6-31G(d) level of theory. ELF results for the concerted mechanism stresses that the electron-reorganization demanded on the diene and ethylene reagents to reach two pseudo-diradical structures is responsible for the high activation energy. A comparative ELF analysis of some relevant points of the non-polar Diels-Alder reaction between Cp and styrene (10) suggests that these concerted mechanisms do not have a pericyclic electron-reorganization.     

New findings on the Diels-Alder reactions. An analysis based on the bonding evolution theory

Two Diels-Alder type reactions, i.e., normal electron demand (NED) between 1,3-butadiene (BD) and acrolein (Acr) and inverse electron demand (IED) between 2,4-pentadienal (PDA) and methyl vinyl ether (MVE), have been investigated using the bonding evolution theory (BET). BET combines topological analysis of the electron localization function (ELF) and catastrophe theory. Catalyst effect has been incorporated through Lewis acid BH3. The B3LYP hybrid HF/DFT method along with 6-31G(d), 6-311++G(d,p) basis sets have been used. All reactions yield two-stage mechanism and there is no topological evidence that they might be concerted with two bonds partially formed during transition structure. A formation of six-membered ring requires 10 (or 11) steps separated by two types of catastrophes: fold and cusp. The first "intermolecular" bond (C1-C6) is formed at 1.93, 1.92 A (NED) and 1.92, 1.97 A (IED). The six-membered ring is "closed" at 2.11, 2.13 A (NED) and 2.5, 2.6 A (IED) via formation of the second bond C4-C5. All reactions begin with "reduction" of C=C bonds to single C-C (cusp catastrophes). Subsequently, the nonbonding electron density is concentrated (fold catastrophes) on terminal C atoms. Finally the new bonds, C1-C6 and C4-C5, are established (cusp catastrophes). Both magnitude and regularity of the electron redistribution, happening during reactions enable us to distinguish two effects: (1) the "ring effect", where a large amount of electron density is regularly transferred from double C=C bonds to intermolecular regions and single C-C bonds, (2) the "side chain effect"--usually weaker and irregular--involving substituents' bonds. In the transition structure, well formed bonding basin V(C1,C6), is observed only for the PDA...BH3/MVE reaction. For other reactions only the nonbonding basins: V(C1) and V(C6), are found in the interaction region C1...C6.     

Understanding the mechanism of the intramolecular stetter reaction. A DFT study

The mechanism of the N-heterocyclic carbene (NHC)-catalyzed intramolecular Stetter reaction of salicylaldehyde 1 to yield chromanone 3 has been theoretically studied at the B3LYP/6-31G** level. This NHC-catalyzed reaction takes place through six elementary steps, which involve: (i) formation of the Breslow intermediate IN2; (ii) an intramolecular Michael-Type addition in IN2 to form the new C-C s bond; and (iii) extrusion of the NHC catalyst from the Michael adduct to yield chromanone 3. Analysis of the relative free energies in toluene indicates that while formation of Breslow intermediate IN2 involves the rate-determining step of the catalytic process, the intramolecular Michael-type addition is the stereoselectivity determining step responsible for the configuration of the stereogenic carbon a to the carbonyl of chromanone 3. An ELF analysis at TSs and intermediates involved in the Michael-type addition allows for the characterization of the electronic changes along the C-C bond-formation.     

Catalytic C-C bond cleavage and C-Si bond formation in the reaction of RCN with Et3SiH promoted by an iron complex

Catalytic C-C bond cleavage of acetonitrile and C-Si bond formation have been attained in the photoreaction of MeCN with Et3SiH in the presence of an iron complex, Cp(CO)2FeMe. This catalytic system can be applied for arylnitrile C-C bond cleavage.     

The surprising and stereoselective formation of P2C10 cages by the reduction of Cp*PCl2

Reactions of Cp*PCl2 with Group 13 reducing agents result in a cascade of P-C, P-P and C-C bond forming reactions and the stereoselective formation of P2C10 cages.     

Removing electrons can increase the electron density: a computational study of negative Fukui functions

Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.     

A density functional theory study on the Diels‐Alder reactions with vinylallenes as dienes

The Diels‐Alder (DA) reactions of vinylallenes (VA) with ethylenes were investigated using the global electrophilicity and nucleophilicity of the corresponding reactants as global reactivity indexes defined within the conceptual density functional theory. The reactivity and regioselectivity of these reactions were predicted by analysis of the energies, geometries, and electronic nature of the transition‐state structures. In general, substitution by the electron‐accepting acetyl group favors the reaction, whereas substitution by the electron‐releasing methoxy group provides the opposite effect, regardless of being on VA or ethylene. However, the substitution effect in ethylene is apparently greater than that in VA. It has also been disclosed that substitution by electron‐accepting group on both reactants accelerates the reaction, and the reaction may give different regioselectivity from that between VA and acetyl‐substituted ethylene. This has also been verified by our experiments. It seems that the DA reactions with VAs as the diene components can generally be classified as nonpolar asynchronous with the endo product formation (wherever possible) being more pronounced. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Bond Fukui functions as descriptor of the electron density reorganization in π conjugated systems

The bond Fukui function is introduced and tested as a new reactivity index capable of predicting the evolution of bond breaking and formation processes during an organic reaction involving π conjugated systems. As an illustration, we examine many cases where substituted ethylenes and dienes may respond to different reagents to yield cycloaddition, Michael addition, and other reactions at double bonds.     

Revealing carbocations in highly asynchronous concerted reactions: The ene-type reaction between dithiocarboxylic acids and alkenes

The ene-type reaction between (dithio)carboxylic acids and alkenes has been studied computationally by DFT and topological (analysis of the electron localization function, ELF) methods. The reaction proceeds under kinetic control and the observed differences in regioselectivity are well-explained by the relative stability of the different transition structures. In agreement with experimental observations, electron-rich alkenes lead to Markownikoff adducts while electron-poor alkenes lead to Michael adducts. In all cases the reaction proceeds through an only transition structure (one kinetic step) although a different synchronicity was observed depending on the alkene electronics. The ELF analysis of the reactions corroborates the existence of a transient carbocation (hidden intermediate) in the reactions with electron-rich alkenes. On the other hand, electron-poor alkenes proceed through a more synchronous concerted mechanism. It can be predicted that with electron-rich alkenes bearing highly donating the transient carbocations might be captured by a nucleophile.     

Electron microscopic imaging of a single Group 8 metal atom catalyzing C-C bond reorganization of fullerenes

Heating a bulk sample of [60]fullerene complexes, (η(5)-C(5)H(5))MC(60)R(5) (M = Fe, Ru, R = Me, Ph), produces small hydrocarbons because of coupling of R and C(5)H(5) via C-C and C-H bond activation. Upon observation by transmission electron microscopy, these complexes, encapsulated in single-walled carbon nanotubes, underwent C-C bond reorganization reactions to form new C-C bond networks, including a structure reminiscent of [70]fullerene. Quantitative comparison of the electron dose required to effect the C-C bond reorganization of fullerenes and organofullerenes in the presence of a single atom of Ru, Fe, or Ln and in the the absence of metal atoms indicated high catalytic activity of Ru and Fe atoms, as opposed to no catalytic activity of Ln. Organic molecules such as hydrocarbons and amides as well as pristine [60]fullerene maintain their structural integrity upon irradiation by ca. 100 times higher electron dose compared to the Ru and Fe organometallics. The results not only represent a rare example of direct observation of a single-metal catalysis but also have implications for the use of single metal atom catalysis in Group 8 metal heterogeneous catalysis.     

Reactions of C5H5M (M = Fe, Ni) with substituted thiophenes

The ion molecule reactions between C₅H₅M⁺ (M = Fe, Ni) with some substituted thiophenes have been studied in an ion trap mass spectrometer. The reactions of halogen substituted thiophenes lead to the formation of a new C-C bond between the cyclopentadiene ring and the thiophene with the loss of a neutral HX. The reaction mechanism has been investigated by means of DFT calculations and it was found that the insertion of the metal atom in the C-X bond is the key step in the process.     

1,3-Dipolar cycloadditions of electrophilically activated benzonitrile N-oxides. Polar cycloaddition versus oxime formation

The reactions of electrophilically activated benzonitrile N-oxides (BNOs) toward 3-methylenephthalimidines (MPIs) have been studied using density functional theory (DFT) at the B3LYP/6-31G* level. For these reactions, two different channels allowing the formation of the [3 + 2] cycloadducts and two isomeric (E)- and (Z)-oximes have been characterized. The 1,3-dipolar cycloadditions take place along concerted but highly asynchronous transition states, while formation of the oximes is achieved through a stepwise mechanism involving zwitterionic intermediates. Both reactions are initiated by the nucleophilic attack of the methylene carbon of the MPIs to the carbon atom of the electrophilically activated BNOs. The analysis based on the natural bond orbital (NBO) and the topological analysis of the electron localization function (ELF) at the transition structures and intermediates explains correctly the polar nature of these reactions. Solvent effects considered by the PCM model allow explaining the low incidence of the solvent polarity on the rate and composition of the reactions.     

Different C-C coupling reactions of permethyltitanocene and permethylzirconocene with disubstituted 1,3-butadiynes

Herein we describe different C-C coupling reactions of permethyltitanocene and -zirconocene with disubstituted 1,3-butadiynes. The outcomes of these reactions vary depending on the metals and the diyne substituents. The reduction of [Cp2*MCl2] (Cp* = C5Me5; M = Ti, Zr) with Mg in the presence of disubstituted butadiynes RC triple bond C-C triple bond CR' is suitable for the synthesis of different C-C coupling products of the diyne and the permethylmetallocenes, and provides a new method for the generation of functionalized pentamethyl-cyclopentadienyl derivatives. For M = Zr and R = R' = tBu, the reaction gives, by a twofold activation of one pentamethylcyclopentadienyl ligand, the complex [Cp*Zr[-C(=C=CHtBu)-CHtBu-CH2-eta5-C5Me3-CH2-]] (3), containing a fulvene ligand that is coupled to the modified substrate (allenic subunit). When using the analogous permethyltitanocene fragment "Cp2*Ti", the reaction depends strongly on the substituents R and R'. The coupling product of the butadiyne with two methyl groups of one of the pentamethylcyclopentadienyl ring systems, [Cp*Ti[eta5-C5Me3-(CH2-CHR-eta2-C2-CHR'-CH2)]], is obtained with R = R' = tBu (4) and R = tBu, R' = SiMe3 (5). In these complexes one pentamethylcyclopentadienyl ligand is annellated to an eight-membered ring with a C-C triple bond, which is coordinated to the titanium center. A different activation of both pentamethylcyclopentadienyl ligands is observed for R = R' = Me, resulting in the complex [[eta5-C5Me4(CH2)-]Ti[-C(=CHMe)-C(=CHMe)-CH2-eta5-C5Me4]] (6), which displays a fulvene as well as a butadienyl-substituted pentamethylcyclopentadienyl ligand. The influence exerted by the size of the metal is illustrated in the reaction of [Cp2*ZrCl2] with MeC triple bond C-C triple bond CMe. Here the five-membered metallacyclocumulene complex [Cp2*Zr(eta4-1,2,3,4-MeC4Me)] (7) is obtained. The reaction paths found for R = R' = Me are identical to those formerly described for R = R' = Ph.     

The substituent effect in ethylenes and acetylenes – AIM analysis

The calculations on disubstituted ethylenes YCHCHX with Y = Li, H, F and X = H, F, Li, Na, OH, BeH, NH₂, BH₂, NO₂ were performed at MP2/6-311++G(d,p) level of theory. The analysis of bond lengths and atoms in molecules based theory (AIM) topological parameters such as the characteristics of bond critical points (electron densities and their Laplacians) and atomic radii leads to the conclusion that the AIM parameters are much more sensitive to the action of intramolecular perturbations like substituents than traditional structural parameters such as bond lengths. A comparison of substituted ethylenes with the previously analyzed substituted acetylenes is also given.