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.     

An electron localization function and catastrophe theory analysis on the molecular mechanism of gas-phase identity SN2 reactions

A set of four reactions, XCH₃+X^? (X=F, Cl, Br) and ClSiH₃+Cl^?, is investigated by means of the joint use of the electron localization function (ELF) and catastrophe theory (CT) analysis in order to obtain new insights into the bond breaking/forming processes for identity S_N2 gas-phase reactions. Using DFT calculations at the OLYP/6-311++G(d,p) level, the effect of nucleophile (F, Cl, and Br anions) and the role of reacting centers (C or Si) on the reaction mechanisms are investigated. The charge-shift character of carbon–halogen bonds is studied by determination of the weights of the Lewis resonance structures. In all S_N2 reactions at the carbon atom, there is a progressive reduction on the covalent character of the C–X bond from the reactant complex (0.41, 0.57, 0.58 for F, Cl, and Br, respectively) until the bond-breaking process, occurring before the transition structure is reached. On the other hand, the Si–Cl bond maintains its degree of covalent character (0.51) from the isolated fragments to the formation of a stable transition complex, presenting two silicon–chlorine charge-shifted bonds. The analysis of the ELF topology along the reaction path reveals that all reactions proceed via the same turning points of fold-type but the order is inverted for reactions taking place at C or Si atoms.     

Olefin epoxidation by molybdenum peroxo compound: molecular mechanism characterized by the electron localization function and catastrophe theory

The oxygen atom transfer reaction from the Mimoun-type complex MoO(η(2)-O(2))(2)OPH(3) to ethylene C(2)H(4) affording oxirane C(2)H(4)O has been investigated within the framework of the Bonding Evolution Theory in which the corresponding molecular mechanism is characterized by the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT). Topological analysis of ELF and electron density analysis reveals that all Mo-O bonds in MoO(η(2)-O(2))(2)OPH(3) and MoO(2)(η(2)-O(2))OPH(3) belong to closed-shell type interactions though negative values of total energy densities E(e)(r(BCP)) imply some covalent contribution. The peroxo O(i)-O(j) bonds are characterized as charge-shift or protocovalent species in which pairs of monosynaptic basins V(3)(O(i)), V(3)(O(j)) with a small electron population of ~0.25e each, are localized between core basins C(O(i)), C(O(j)). The oxygen transfer reaction from molybdenum diperoxo complex MoO(η(2)-O(2))(2)OPH(3) to C(2)H(4) system can be described by the following consecutive chemical events: (a) protocovalent peroxo O(2)-O(1) bond breaking, (b) reduction of the double C(1)=C(2) bond to single C(1)-C(2) bond in ethylene, (c) displacement of oxygen O(1) with two nonbonding basins, V(i=1,2)(O(1)), (d) increase of a number of the nonbonding basins to three (V(i=1,2,4)(O(1))); (e) reorganization and reduction in the number of nonbonding basis to two basins (V(i=1,4)(O(1))) resembling the ELF-topology of the nonbonding electron density in oxirane, (e) formation of the first O(1)-C(2) bond in oxirane, (f) C(2)-O(1)-C(2) ring closure, (g) formation of singular nonbonding basin V(O(2)) in new Mo=O(2) bond. The oxygen atom is transferred as an anionic moiety carrying a rather small electronic charge ranging from 0.5 to 0.7e.     

Characterisation of the reaction mechanism between ammonia and formaldehyde from the topological analysis of ELF and catastrophe theory perspective

Structural Chemistry - A prototypical reaction between ammonia and formaldehyde has been investigated at the DFT(M06)/6-311++G(d,p) computational level using the Bonding Evolution Theory (BET). BET...     

Nature of the ring-closure process along the rearrangement of octa-1,3,5,7-tetraene to cycloocta-1,3,5-triene from the perspective of the electron localization function and catastrophe theory

We analyze the behavior of the energy profile of the ring‐closure process for the transformation of (3Z,5Z)‐octa‐1,3,5,7‐tetraene 5 to (1Z,3Z,5Z)‐cycloocta‐1,3,5‐triene 6 through a combination of electron localization function (ELF) and catastrophe theory (CT). From this analysis, concepts such as bond breaking/forming processes, formation/annihilation of lone pairs, and other electron pair rearrangements arise naturally through the reaction progress simply in terms of the different ways of pairing up the electrons. A relationship between the topology and the nature of the bond breaking/forming processes along this rearrangement is reported. The different domains of structural stability of the ELF occurring along the intrinsic reaction path have been identified. The reaction mechanism consists of six steps separated by fold and cusp catastrophes. The transition structure is observed in the third step, d(C1? C8) = 2.342 Å, where all bonds have topological signature of single bonds (C? C). The “new” C1? C8 single bond is not formed in transition state and respective catastrophe of the ELF field (cusp) is localized in the last step, d(C1? C8) ≈ 1.97 Å, where the two monosynaptic nonbonding basins V(C1) and V(C8) are joined into single disynaptic bonding basin V(C1,C8). The V(C1,C8) basin corresponds to classical picture of the C1? C8 bond in the Lewis formula. In cycloocta‐1,3,5‐triene 6 the single C1? C8 bond is characterized by relatively small basin population 1.72e, which is much smaller than other single bonds with 2.03 and 2.26e. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A joint study based on the electron localization function and catastrophe theory of the chameleonic and centauric models for the Cope rearrangement of 1,5-hexadiene and its cyano derivatives

A novel interpretation of the chameleonic and centauric models for the Cope rearrangements of 1,5-hexadiene (A) and different cyano derivatives (B: 2,5-dicyano, C: 1,3,4,6-tetracyano, and D: 1,3,5-tricyano) is presented by using the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) on the reaction paths calculated at the B3LYP/6-31G(d,p) level. The progress of the reaction is monitorized by the changes of the ELF structural stability domains (SSD), each being change controlled by a turning point derived from CT. The reaction mechanism of the parent reaction A is characterized by nine ELF SSDs. All processes occur in the vicinity of the transition structure and corresponding to a concerted formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, respectively, together with an accumulation of charge density onto C(2) and C(5) atoms. Reaction B presents the same number of ELF SSDs as A, but a different order appears; the presence of 2,5-dicyano substituents favors the formation of C(1)-C(6) bonds over the breaking of C(3)-C(4) bond process, changing the reaction mechanism from a concerted towards a stepwise, via a cyclohexane biradical intermediate. On the other side, reaction C presents the same type of turning points but two ELF SSD less than A or B; there is an enhancement of the C(3)-C(4) bond breaking process at an earlier stage of the reaction by delocalizing the electrons from the C(3)-C(4) bond among the cyano groups. In the case of competitive effects of cyano subsituents on each moiety, as it is for reaction D, seven different ELF SSDs have been identified separated by eight turning points (two of them occur simultaneously). Both processes, formation/breaking of C(1)-C(6) and C(3)-C(4) bonds, are slightly favored with respect to the parent reaction (A), and the TS presents mixed electronic features of both B and C. The employed methodology provides theoretical support for the centauric nature (half-allyl, half-radical) for the TS of D.     

A theoretical study on the mechanism and diastereoselectivity of the Kulinkovich hydroxycyclopropanation reaction

A detailed mechanism for the Kulinkovich hydroxycyclopropanation reaction has been explored with density functional theory calculations on the reactions between R(1)COOMe and Ti(OMe)(2)(CH(2)CHR(2)) (R(1) and R(2) are hydrogen and alkyl groups). Addition of ester to titanacyclopropane is found to be fast, exothermic, and irreversible. It has a preference for the alpha-addition manifold over the beta-addition manifold in which its cycloinsertion transition states suffer from the steric repulsion between the R(2) and ester. The following intramolecular methoxy migration step is also exothermic with reasonable activation energy. The cyclopropane-forming step is the rate-determining step, which affords the experimentally observed cis-R(1)/R(2) diastereoselectivity in the alpha-addition manifold by generating cis-R(1)/R(2) 1,2-disubstituted cyclopropanol when R(1) is primary alkyl groups. On the contrary, the unfavored beta-addition manifold offers the diastereoselectivity contradicting the experimental observations. The effects of R(1) and R(2) on the regio- and stereoselectivity are also discussed.     

A theoretical study on the mechanism and thermodynamics of ozone-water gas phase reaction

Ozone water reaction including a complex was studied at the MP2/6-311++G(d,p) and CCSD/6-311++G(2df,2p)//MP2/6-311++G(d,p) levels of theory. The interaction between water oxygen and central oxygen of ozone produces stable H₂O-O₃ complex with no barrier. With decomposition of this complex through H-abstraction by O₃ and O-abstraction by H₂O, three possible product channels were found. Intrinsic reaction coordinate, topological analyses of atom in molecule, and vibrational frequency calculation have been used to confirm the preferred mechanism. Thermodynamic data at T = 298.15 K and atmospheric pressure have been calculated. The results show that the production of hydrogen peroxide is the main reaction channel with ΔG = ?21.112 kJ mol^-1.     

Better understanding of the ring-cleavage process of cyanocyclopropyl anionic derivatives. A theoretical study based on the electron localization function

[reaction: see text] Theoretical calculations at the B3LYP/6-31+G(d), MP2/6-31+G(d), and G3(MP2) levels have been carried out to understand the alternative reaction pathways (the cyclopropyl ring cleavage (RC) and the retrocycloaddition reaction (rCA)) of a constrained tricyanocyclopropyl anionic derivative. The more energetically favorable path is found to be the RC process, a formally "forbidden" rearrangement (Leiviers, M.; Tam, I.; Groves, K.; Leung, D.; Xie, Y.; Breslow, R. Org. Lett. 2003, 5, 19, 3407) yielding an allylic anion system via a concerted transition structure, in agreement with experimental outcomes. rCA is more energetically favorable along a two-stage mechanism, via an intermediate, than a synchronous concerted process. By using isodesmic reactions, we have found that B3LYP presents limitations when it calculates carbon-carbon bond-breaking processes along the present rCA reaction. A detailed analysis of the nature of the topology of the reactive potential energy surface for the RC process points out the presence of a valley-ridge inflection point in the uphill part. An explanation for the low-energy barrier associated with RC is furnished on the analysis of the evolution of the twisting (dis-/conrotatory) motions of cyano substituents in the cyclopropyl ring as well as on the number and type of electron pairs provided by the electron localization function (ELF).     

A theoretical study on the mechanism of the addition reaction between carbene and epoxyethane

The mechanism of addition reaction between carbene and epoxyethane has been investigated employing the MP2 and B3LYP/6-311+G* levels of theory. Geometry optimization, vibrational analysis, and energy property for the involved stationary points on the potential energy surface have been calculated. Based on the calculated results at the MP2/6-311+G* level of theory, it can be predicted that there are two reaction mechanisms (1) and (2). In the first reaction carbene attacks the atom O of epoxyethane to form an intermediate 1a (IM1a), which is a barrier-free exothermic reaction. Then, IM1a can isomerize to IM1b via a transition state 1a (TS1a), where the potential barrier is 48.6 kJ/mol. Subsequently, IM1b isomerizes to a product epoxypropane (Pro1) via TS1b with a potential barrier of 14.2 kJ/mol. In the second carbene attacks the atom C of epoxyethane firstly to form IM2 via TS2a. Then IM2 isomerizes to a product allyl alcohol (Pro2) via TS2b with a potential barrier of 101.6 kJ/mol. Correspondingly, the reaction energies for the reactions (1) and (2) are −448.4 and −501.6 kJ/mol, respectively. Additionally, the orbital interactions are also discussed for the leading intermediate. The results based on the B3LYP/6-311+G* level of theory are paralleled to those on the MP2/6-311+G* level of theory. Furthermore, the halogen and methyl substituent effects of H₂C: on the two reaction mechanisms have been investigated. The calculated results indicate that the introductions of halogen or methyl make the addition reaction difficult to proceed.     

A quantitative measure of bond polarity from the electron localization function and the theory of atoms in molecules

 A quantitative measure of the polarity of a bond can be obtained through combining the two complementary topological partitionings of the electron density obtained from the atoms in molecules theory, on the one hand, and the electron localization function, on the other. This requires an integration of the electron density in the atomic subbasins of a common bond electron localization basin. We present the first numerical application of the resulting topological definition of bond polarity to a set of small linear systems consisting of the FCN, HF, HCl, HBr, and NaCl molecules and the NeAr van der Waals dimer. It is shown that the findings are essentially in line with common expectation for these simple molecules, thus confirming the potential value of the novel bond polarity index for the analysis of controversial bonding situations. Additional insight is provided through the detailed investigation of fluctuations in the basin populations. Received: 10 January 2001 / Accepted 12 February 2001 / Published online: 22 May 2001     

A theoretical study on the mechanism of a novel one-carbon unit transfer reaction

The mechanism of one-carbon unit transfer reaction between tetrahydrofolate coenzymes model compound (e.g., benzimidazolium) and Grignard reagent has been investigated employing the DFT and B3LYP/6-31G* levels of theory. Three consecutive reactions leading to major products N,N′-dimethyl-ophenylenediamine and acetone have been proposed and discussed. For these reactions, the structure parameters, vibrational frequencies, and energies for each stationary point have been calculated, and the corresponding reaction mechanism has been given by the potential energy surface, which is drawn according to the relative energies. The calculated results show that the corresponding major products N,N′-dimethyl-ophenylenediamine and acetone are in agreement with experimental findings, which provided a new illustration and guidance for these reactions.     

A study on the mechanism of reaction between BNAH and chloranil:Evidence for electron transfer

The reaction between chloranil and N-benzyldihydronicotinamide(BNAH)in boratebuffer/DMF was investigated.The reaction mixture gave a strong esr signal,which is consistentwith that of chloranil anion radical,and tetrachlorohydrophenol(QH_2)and N-benzylnicotinamide(BNA~+)were obtained as the sole products.When the reaction was run in benzene solution,a greencoloured charge-transfer complex between the reactants could be isolated,which decomposed in polarsolvents to give BNA-+ and QH_2.Based on kinetic studies by esr spectroscopy by the stopped-flowtechnique,a two-step electron-transfer mechanism for the reactionis proposed in contrast to thehydride-transfer mechanism reported in the literature.     

单线态卡宾衍生物与臭氧反应机理的密度泛函数理论研究

用密度泛函理论中B3LYP方法,在6-31G(d)水平上优化了单线态卡宾衍生物(CX~2,X=F,Cl,Br)与臭氧反应过程中驻点的几何构型,通过振动分析对反应过渡态和中间体构型进行确认,对单点进行了CCSD(T)/6-31G(d)计算,并进行了零点能(ZPE)校正,同时对反应绝对速率常数进行了理论计算,研究结果表明：相对CF~2和CCl~2而言CBr~2对臭氧的损耗较大,卡宾衍生物与臭氧反应过程均为强放热反应。     

Electronic fluxes during diels‐alder reactions involving 1,2‐benzoquinones: mechanistic insights from the analysis of electron localization function and catastrophe theory

By means of the joint use of electron localization function (ELF) and Thom's catastrophe theory, a theoretical analysis of the energy profile for the hetero‐Diels‐Alder reaction of 4‐methoxy‐1,2‐benzoquinone 1 and methoxyethylene 2 has been carried out. The 12 different structural stability domains obtained by the bonding evolution theory have been identified as well as the bifurcation catastrophes (fold and cusp) responsible for the changes in the topology of the system. This analysis permits finding a relationship between the ELF topology and the evolution of the bond breaking/forming processes and electron pair rearrangements through the reaction progress in terms of the different ways of pairing up the electrons. The reaction mechanism corresponds to an asynchronous electronic flux; first, the O1? C5 bond is formed by the nucleophilic attack of the C5 carbon of the electron rich ethylene 2 on the most electrophilically activated carbonyl O1 oxygen of 1 , and once the σ bond has been completed, the formation process of the second O4? C6 bond takes place. In addition, the values of the local electrophilicity and local nucleophilcity indices in the framework of conceptual density functional theory accounts for the asychronicity of the process as well as for the observed regioselectivity. © 2012 Wiley Periodicals, Inc.     

甲基三氯硅烷水解反应机理的密度泛函研究

采用量子化学密度泛函方法研究了甲基三氯硅烷的结构性质和水解反应机理,发现水的O原子进攻Si原子取代Cl原子的同时,水的另一个H原子逐渐与Cl结合形成相应的羟基硅烷和HCl.甲基三氯硅烷水解按亲核取代--消除的协同反应机理完成.     

Oxidation reaction by xanthine oxidase: theoretical study of reaction mechanism

The oxidation process by molybdenum-containing enzyme, xanthine oxidase, is theoretically studied with a model complex representing the reaction center and a typical benchmark substrate, formamide. Comparisons were systematically made among reaction mechanisms proposed previously. In the concerted and stepwise mechanisms that were theoretically discussed previously, the oxidation reaction takes place with a moderate activation barrier. However, the product is less stable than the reactant complex, which indicates that these mechanisms are unlikely. Moreover, the product of the concerted mechanism is not consistent with the isotope experimental result. In addition to those mechanisms, another mechanism initiated by the deprotonation of the active site was newly investigated here. In the transition state of this reaction, the carbon atom of formamide interacts with the oxo ligand of the Mo center and the hydrogen atom is moving from the carbon atom to the thioxo ligand. This reaction takes place with a moderate activation barrier and considerably large exothermicity. Furthermore, the product by this mechanism is consistent with the isotope experimental result. Also, our computations clearly show that the deprotonation of the active site occurs with considerable exothermicity in the presence of glutamic acid and substrate. The intermediate of the stepwise mechanism could not be optimized in the case of the deprotonated active site. From all these results, it should be concluded that the one-step mechanism with the deprotonated active site is the most plausible.     

A theoretical study of the inner-sphere disproportionation reaction mechanism of the pentavalent actinyl ions

The inner-sphere mechanisms of the disproportionation reactions of U(V), Np(V), and Pu(V) ions have been studied using a quantum mechanical approach. The U(V) disproportionation proceeds via the formation of a dimer (a cation-cation complex) followed by two successive protonations at the axial oxygens of the donor uranyl ion. Bond lengths and spin multiplicities indicate that electron transfer occurs after the first protonation. A solvent water molecule then breaks the complex into solvated U(OH)2(2+) and UO2(2+) ions. Pu(V) behaves similarly, but Np(V) appears not to follow this path. The observations from quantum modeling are consistent with existing experimental data on actinyl(V) disproportionation reactions.     

New insights on the bridge carbon-carbon bond in propellanes: a theoretical study based on the analysis of the electron localization function

The nature of the bonding between bridgehead carbon atoms (Ca, Ca') as well as the ring strain in a family of 10 propellanes formed by three-, four-, or five-member rings: [1.1.1] (I), [2.1.1] (II), [3.1.1] (III), [2.2.1] (IV), [3.2.1] (V), [2.2.2] (VI), [3.3.1] (VII), [3.2.2] (VIII), [3.3.2] (IX), and [3.3.3] (X) are studied by means of the electron localization function (ELF) at the DFT level (B3LYP/cc-pVTZ). The ELF analysis of smaller propellanes (I, II, and III) reveals the coexistence of two resonance forms: one with a nonbonding electron pair partially delocalized between Ca and Ca' atoms outside the cage (ionic) and the other with a bridge bond between the same atoms (covalent). The weights of each form are calculated according to the ELF-basin populations, yielding 94, 88, and 53% for the ionic structure of I, II, and III, respectively, while larger propellanes (IV-X) present only the covalent form. The question of the s-character of the bridge bond is addressed by dissecting the bridge-bond ELF basin into the molecular orbital contributions. Finally, sigma-aromaticity associated to surface electron delocalization has been analyzed by means of nucleus-independent chemical shift (NICS) calculations. The results point out that the stability of the fused ring structure of propellanes I, II, and III, can be assigned to the remarkable sigma-aromaticity of the involved three-member rings.