Symmetry‐Enthalpy Correlations in Diels–Alder Reactions

Woodward–Hoffmann (WH) rules provide strict symmetry selection rules: when they are obeyed, a reaction proceeds; when they are not obeyed, there is no reaction. However, the voluminous experimental literature provides ample evidence that strict compliance to symmetry requirements is not an obstacle for a concerted reaction to proceed, and therefore the idea has developed that it is enough to have a certain degree of the required symmetry to have reactivity. Here we provide quantitative evidence of that link, and show that as one deviates from the desired symmetry, the enthalpy of activation increases, that is, we show that concerted reactions slow down the further they are from the ideal symmetry. Specifically, we study the deviation from mirror symmetry (evaluated with the continuous symmetry measure (CSM)) of the [4+2] carbon skeleton of the transition state of a series of twelve Diels–Alder reactions in seven different solvents (and in the gas phase), in which the dienes are butadiene, cyclopentadiene, cyclohexadiene, and cycloheptadiene; the dienophiles are the 1‐, 1,1‐, and 1,1,2‐cyanoethylene derivatives; the solvents were chosen to sample a range of dielectric constants from heptane to ethanol. These components provide twenty‐four symmetry–enthalpy DFT‐calculated correlation lines (out of which only one case is a relatively mild exception) that show the general trend of increase in enthalpy as symmetry decreases. The various combinations between the dienophiles, cyanoethylenes, and solvents provide all kinds of sources for symmetry deviations; it is therefore remarkable that although the enthalpy of activation is dictated by various parameters, symmetry emerges as a primary parameter. In our analysis we also bisected this overall picture into solvent effects and geometry variation effects to evaluate under which conditions the electronic effects are more dominant than symmetry effects.     

Quantifying asymmetry in concerted reactions: solvents effect on a Diels-Alder cycloaddition

We propose the notion that if asymmetry characterizes a concerted reaction, a quantitative treatment in terms of continuous symmetry can bridge the gap between the Woodward-Hoffmann (WH) rules, originally formulated for symmetry-idealized unsubstituted reactants, and the fact that these rules hold for a much wider scope of reactions. Instead of focusing on symmetry conservation along the minimum energy path, we suggest that the distortion with respect to the original expected symmetry must attain a certain minimal value, not necessarily zero. To demonstrate this approach we studied the effect of solvents on the symmetry and reactivity of the classical [4 + 2] Diels-Alder cycloaddition of (E,E)-1,4-dimethoxy-1,3-butadiene with tetracyanoethylene, revealing the predictive value of this approach. Calculations of the enthalpy of activation and the charge separation at the transition state (TS) predict increased reactivity with the polarity of the solvent. The symmetry measure is in excellent correlation with the enthalpy of activation and the charge separation at the TS, indicating the higher reactivity of the more symmetric case, thus quantifying the main teaching of the WH rules. The advantages of using a global structural parameter that takes into account all geometrical parameters, i.e., the symmetry measure, over specific ones (e.g., asynchronicity) are discussed.     

A rationalization of the solvent effect on the Diels-Alder reaction in ionic liquids using multiparameter linear solvation energy relationships

The Diels-Alder reaction between cyclopentadiene and three dienophiles (acrolein, methyl acrylate and acrylonitrile) having different hydrogen bond acceptor abilities has been carried out in several ionic liquids and molecular solvents in order to obtain information about the factors affecting reactivity and selectivity. The solvent effects on these reactions are examined using multiparameter linear solvation energy relationships. The collected data provide evidence that the solvent effects are a function of both the solvent and the solute. For a solvent effect to be seen, the solute must have a complimentary character; selectivities and rates are determined by the solvent hydrogen bond donation ability (alpha) in the reactions of acrolein and methyl acrylate, but not of acrylonitrile.     

A Basis for Orbital Symmetry Rules

The influence of molecular symmetry on reaction rates is examined with an approach in which reactions are viewed as electronic transitions between states of reacants and products (described, in turn by quasiadiabatic potential surface). The moleculer Hamiltonian is used to derive selection rules for these transitions. The complete Hamilatonian has no useful symmetery. Neglect of non-Born-Oppenheimer and spin-orbit terms (and of other angular momentum coupling terms) leads to an apporixmate Hamiltonian and to selection rules which from the basis of the Woodward-Hoffmann rules. This apporch provides an alternative to the adiabatic potantial surfaces, reaction coordinates, and transition state theory used in more familiar discussions of the Woodward-Hoffmann rules. Further, it provides a particulary clear method for discussing violations of these symmetry rules, and for differentiating concerted and nonconcerted reactions.     

Transition states and mechanisms of the hetero-Diels-Alder reactions of hyponitrous acid, nitrosoalkanes, nitrosoarenes, and nitrosocarbonyl compounds.

The transition states and energetics of Diels-Alder reactions for a variety of nitroso compounds with dienes were explored with density functional theory using the B3LYP functional and 6-31G basis set. The reactions involve HNO, various nitrosoalkanes and arenes (RNO and ArNO), and nitrosoformaldehyde (CHONO) as dienophiles with butadiene and a series of 1- and 2-substituted dienes. The mechanisms, activation energies, energies of reaction, stereoselectivities, and regioselectivities are predicted for these reactions. These predictions are compared to available experimental data. The mechanism is found to be concerted but involves highly asynchronous transition states. Although it is not evident in the products, we find that the endo path is very strongly favored over the exo alternative due to repulsion between the diene and nitrogen's lone pair. A range of experimental regioselectivities are reproduced by calculations and are found to hinge on a very sensitive balance between FMO interactions, electrostatics, and steric effects. A series of generalizations for predicting regioselectivity for untried diene-dienophile pairs are made.     

The effect of transition state bond order on sigmatropic shifts and cycloaddition reactions

A recently developed classical model for the calculation of activation free energies of chemical reactions is applied to the study of sigmatropic shifts and cycloaddition reactions. The model does not require the consideratlon of parallel or perpendicular effects along the reaction coordinate to interpret substituent effects. These reactions can be treated as any other ordinary chemical reation, and the effect of substituents is explained in terms of an increase in the bond order of the transition state, n³, due to an increase in the electronic charge produced by the substituents on the carbon skeleton. Secondary isotope effects are also explained in terms of n³. The model estimates absolute ΔG³ for the main reactions in good agreement with experiment, under the assumption that the processes are concerted and synchronous and consequently n³ = O.5. The nonlinear character of the free energy relationships for these reactions is attributed to the variation of n³ upon substitution. Some of the apparent violations of the Woodward-Hoffmann rules on the conservation of orbital symmetry in concerted reactions can be treated in a similar way. The synchronism of these reactions is also discussed.     

亚硝基化合物与甲醛的反应机理和溶剂效应的理论研究

采用密度泛函方法B3LYP/6-311++G(d,p)研究了亚硝基苯C₆H₅-NO和2-甲基-2-亚硝基丙烷(CH₃)₃C-NO与甲醛分别在气相和溶剂中的反应机理. 在气相中均找到两条反应通道, 即协同机理和分步机理, 均生成实验产物氧肟酸, 而且分步机理均为优势通道; 除2-甲基-2-亚硝基丙烷的反应没有协同途径外, 在溶剂中反应机理与气相中的类似. 采用导电极化连续介质模型分别研究了在乙腈与水溶液中反应的溶剂化效应, 发现这些溶剂可降低反应的活化能, 但降低的程度比较小, 反应速率变化不大.     

Reevaluation of donor number using titration calorimetry

Many empirical parameters have been suggested to measure solvent effects in chemical reactions. Gutmann's donor number has been a successful parameter to quantify the electron-donating property of the solvent molecule; it is defined as the enthalpy change of the addition reaction of solvent molecule to SbCl(5) in 1,2-dichloroethane. Calorimetric measurements can be applied to determine the quantity. Because the existence of water is critical for reactions in organic solvents, we have analyzed the enthalpy change using the titration calorimetry while considering the complexation with water. The determined donor numbers of formamide, N,N-dimethylformamide (DMF), dimethyl sulfoxide (DMSO), and 1,1,3,3-tetramethylurea (TMU) are 22.4, 26.5, 30.0, and 40.4, respectively. The values of DMF and DMSO are in perfect agreement with those of Gutmann. A reliable value for TMU is obtained for the first time on the basis of the enthalpy change for the addition reaction.     

硅杂苯与亲二烯体的Diels-Alder反应

采用密度泛函理论(DFT)在B3LYP/6-311G(d,p)水平上研究了硅杂苯与一些亲二烯体的两类可能的Diels-Alder反应的微观机理、势能剖面、取代基效应和溶剂化效应. 计算结果表明, 所研究反应均以协同的方式进行. 亲二烯体分子碳原子上的苯基取代基对两个新键形成的非同步性和反应的活化能垒的影响取决于苯基在产物中的相对位置, 而硅杂苯分子中硅原子上的CCl3取代基有利于杂Diels-Alder反应的进行. 形成一个C—Si键的杂Diels-Alder反应在热力学和动力学上均远比相应的全碳Diels-Alder反应容易进行, 实验观察到的杂Diels-Alder反应中的区域选择性由动力学因素所控制. 硅杂苯与烯烃的反应比与相应炔烃的反应在动力学上容易进行一些, 但在热力学上后者远比前者容易进行. 苯溶剂对所研究反应的势能剖面影响较小.     

Lewis碱稳定的硼代苯与亲二烯体的Diels-Alder反应的理论研究

采用密度泛函理论方法在B3LYP/6-31G(d)水平上研究了Lewis碱稳定的硼代苯与一些亲二烯体的两种可能的Diels-Alder反应的微观机理和势能剖面, 并研究了反应的溶剂效应和取代基效应. 计算结果表明, 一部分反应以直接的近同步的协同方式进行, 而在另一部分反应中, 两个反应物分子先形成分子间复合物, 然后再经过协同的过渡态生成产物. 与气相中相比, 二氯甲烷溶剂使所研究的大部分反应的活化能垒有所增加. 在乙炔或乙烯分子中分别引入吸电子基团CO2Me或CN能显著降低反应的活化能垒. 形成一个C—B键的杂Diels-Alder反应都比相应的Diels-Alder反应在热力学和动力学上容易进行, 这与实验结果一致.     

High-pressure rate rules for alkyl + O2 reactions. 2. The isomerization, cyclic ether formation, and β-scission reactions of hydroperoxy alkyl radicals

The unimolecular reactions of hydroperoxy alkyl radicals (QOOH) play a central role in the low-temperature oxidation of hydrocarbons as they compete with the addition of a second O(2) molecule, which is known to provide chain-branching. In this work we present high-pressure rate estimation rules for the most important unimolecular reactions of the β-, γ-, and δ-QOOH radicals: isomerization to RO(2), cyclic ether formation, and selected β-scission reactions. These rate rules are derived from high-pressure rate constants for a series of reactions of a given reaction class. The individual rate expressions are determined from CBS-QB3 electronic structure calculations combined with canonical transition state theory calculations. Next we use the rate rules, along with previously published rate estimation rules for the reactions of alkyl peroxy radicals (RO(2)), to investigate the potential impact of falloff effects in combustion/ignition kinetic modeling. Pressure effects are examined for the reaction of n-butyl radical with O(2) by comparison of concentration versus time profiles that were obtained using two mechanisms at 10 atm: one that contains pressure-dependent rate constants that are obtained from a QRRK/MSC analysis and another that only contains high-pressure rate expressions. These simulations reveal that under most conditions relevant to combustion/ignition problems, the high-pressure rate rules can be used directly to describe the reactions of RO(2) and QOOH. For the same conditions, we also address whether the various isomers equilibrate during reaction. These results indicate that equilibrium is established between the alkyl, RO(2), and γ- and δ-QOOH radicals.     

High-pressure rate rules for alkyl + O2 reactions. 1. The dissociation, concerted elimination, and isomerization channels of the alkyl peroxy radical

The reactions of alkyl peroxy radicals (RO(2)) play a central role in the low-temperature oxidation of hydrocarbons. In this work, we present high-pressure rate estimation rules for the dissociation, concerted elimination, and isomerization reactions of RO(2). These rate rules are derived from a systematic investigation of sets of reactions within a given reaction class using electronic structure calculations performed at the CBS-QB3 level of theory. The rate constants for the dissociation reactions are obtained from calculated equilibrium constants and a literature review of experimental rate constants for the reverse association reactions. For the concerted elimination and isomerization channels, rate constants are calculated using canonical transition state theory. To determine if the high-pressure rate expressions from this work can directly be used in ignition models, we use the QRRK/MSC method to calculate apparent pressure and temperature dependent rate constants for representative reactions of small, medium, and large alkyl radicals with O(2). A comparison of concentration versus time profiles obtained using either the pressure dependent rate constants or the corresponding high-pressure values reveals that under most conditions relevant to combustion/ignition problems, the high-pressure rate rules can be used directly to describe the reactions of RO(2).     

Visual valence bond rules for chemical reactions

A symmetry-adaptation rule of the valence bond structure for concerted reactions was developed within the bonded tableau valence bond formalism. According to a symmetry analysis of the valence bond structure segments accounting for the reaction, one can predict whether a chemical process is favored or unfavored. This method is based on conceptual resonance theory and the visual valence bond approach, without carrying out any explicitly theoretical calculations to know orbital details. Furthermore, by imposing a phase factor on each bonding pair, namely, the phase alternation postulate, the mechanisms of the concerted reactions can be easily outlined. These rules have been applied to organic and inorganic reactions including the participation of biradicals and species with multi-reference character. Received: 7 September 1998 / Accepted: 9 November 1998 / Published online: 1 February 1999     

Retro-[3 + 2]-cycloaddition reactions in the decomposition of five-membered nitrogen-containing heterocycles

Nitrogen-containing heterocycles form the basis for a new generation of high-energy density materials, and they serve as model compounds for nitrogen-containing fuels, such as coal and biomass, and they form the backbone of ionic liquids. A novel retro-[3 + 2]-cycloaddition to a three-membered diene and a two-membered dienophile, analogous to a retro-Diels-Alder reaction, may constitute an important initial reaction step in the thermal decomposition of these heterocyclic compounds. We investigate the kinetics and thermodynamics of these reactions for the heterocycles pyrrole, pyrazole, imidazole, 1,2,3-triazole, 1,2,4-triazole, 1,2,5-triazole, 1,3,4,-triazole, 1H-tetrazole, and 2H-tetrazole, using theoretical computational chemistry. The retro-cycloadditions are shown to form one of the three-membered products: hydrazoic acid (NH=N=N), nitrilimine (NH=N=CH), carbodiimide (NH=C=NH), or ketenimine (NH=C=CH2) plus one of the two-membered products acetylene, hydrogen cyanide, or N2. Accurate enthalpies of formation are calculated for the reaction products using the high-level W1 computational protocol, providing the previously undetermined enthalpy values of 70.09, 88.75, 35.03, and 44.28 kcal mol(-1) for hydrazoic acid, nitrilimine, carbodiimide, and ketenimine, respectively. We apply a variable-order form of the Marcus equation to the dissociation reactions in correlating the enthalpy of reaction with the activation enthalpy. Typical molecular elimination reactions from the heterocycles proceed with an intrinsic activation enthalpy of 36.8 kcal mol(-1) and intrinsic activation free energy of 42.1 kcal mol(-1). However, dissociation reactions resulting in the formation of either NH=C=NH or NH=C=CH2 demonstrate intrinsic barriers ca. 30 kcal mol(-1) higher, as a result of a concerted intramolecular hydrogen shift. Rate constants calculated between 300 and 3000 K indicate that the proposed dissociation reactions should be important in the decomposition of tetrazole and 1,2,3-triazole. This is confirmed by comparison with available experimental data. Decomposition of 1,2,4-triazole to HCN + nitrilimine may also be important at high temperatures. From extrapolation of our Marcus equation relationship, we predict pentazole to decompose to N2 + NHNN with an activation enthalpy of 19.5 kcal mol-1 and a half-life of only 14 s at 298 K.     

Copper(II)-catalyzed room temperature aerobic oxidation of hydroxamic acids and hydrazides to acyl-nitroso and azo intermediates, and their Diels-Alder trapping

CuCl(2), in the presence of a 2-ethyl-2-oxazoline ligand, is an effective catalyst for the room temperature, aerobic oxidation of hydroxamic acids and hydrazides, to acyl-nitroso and azo dienophiles respectively, which are efficiently trapped in situ via both inter- and intramolecular hetero-Diels-Alder reactions with dienes. Both inter- and intramolecular variants of the Diels-Alder reaction are suitable under the reaction conditions using a variety of solvents. Under the same conditions, an acyl hydrazide was also oxidized to give an acyl-azo dienophile which was trapped intramolecularly by a diene.     

Intramolecular hetero-Diels-Alder reactions of imine and iminium dienophiles: quantum mechanical exploration of mechanisms and stereoselectivities

A series of intramolecular hetero-Diels-Alder reactions of iminium and imine dienophiles has been explored with density functional theory using the B3LYP functional and 6-31+G* basis set. Aqueous solvation energies were calculated with the CPCM method. DFT predicts that these reactions are concerted but involve highly asynchronous transition states. Stereochemical preferences of imine cycloaddition transition states arise from electron repulsion of the nitrogen lone pair with electron density from the butadiene moiety. Protonation of the nitrogen leads to a highly asynchronous transition state. The iminium dienophiles are predicted to have a 17 kcal/mol lower barrier than the corresponding imines, even in aqueous solution.     

Diels-Alder reactions in the presence of a minimal amount of water

Abstract

Diels-Alder reactions of neat reactive dienes and dienophiles are frequently vigorous and have a limited preparative value. It is possible to control the temperature of multi-gram scale Diels-Alder reactions by adding a minimal amount of water to neat reactants. In addition, the presence of water resulted in an increased reaction rate and formation of a higher purity product. The use of minimal amounts of other solvents, with lower heat capacities, did not give good results. Furthermore, some dienophiles, e.g. maleic anhydride, reacted poorly in a dilute water suspension or solution, but worked well in the presence of a minimal amount of water. This is an environmentally friendly, practical and efficient approach to preparation of Diels-Alder adducts on a multi-gram scale.     

Electron transfer and bond breaking: Recent advances

After a reminder of concerted/stepwise mechanistic dichotomy and other basic concepts and facts in the field, a series of recent advances is discussed. Particular emphasis is laid on the interactions between the fragments formed upon bond cleavage. These interactions may persist even in polar solvents and have important consequences on dissociative electron transfer kinetics and on the competition between concerted and stepwise pathways. Cleavage of ion radicals and its reverse reaction are examples of single electron transfer reactions concerted with bond cleavage and bond formation, respectively. The case of aromatic carbon–heteroatom bonds is particularly worth examination since symmetry restrictions impose circumventing a conical intersection. Reductive dehalogenases are involved in ‘dehalorespiration’ of anaerobic bacteria in which the role of dioxygen in aerobic organisms is played by major polychloride pollutants such as tetrachloroethylene. They offer an interesting illustration of how the coupling of electron transfer with bond breaking may be an important issue in natural processes. Applications of dissociative electron transfer concepts and models to mechanistic analysis in this class of enzymes will be discussed.     

Propensity rules for inelastic electron tunneling spectroscopy of single-molecule transport junctions

Using a perturbative approach to simple model systems, we derive useful propensity rules for inelastic electron tunneling spectroscopy (IETS) of molecular wire junctions. We examine the circumstances under which this spectroscopy (that has no rigorous selection rules) obeys well defined propensity rules based on the molecular symmetry and on the topology of the molecule in the junction. Focusing on conjugated molecules of C(2h) symmetry, semiquantitative arguments suggest that the IETS is dominated by a(g) vibrations in the high energy region and by out of plane modes (a(u) and b(g)) in the low energy region. Realistic computations verify that the proposed propensity rules are strictly obeyed by medium to large-sized conjugated molecules but are subject to some exceptions when small molecules are considered. The propensity rules facilitate the use of IETS to help characterize the molecular geometry within the junction.     

An easy and general protocol for multicomponent coupling reactions of aldehydes, amides, and dienophiles

An improved procedure for the three-component coupling reaction of aldehydes, amides, and dienophiles (AAD-reaction) has been developed. The use of microwave technology enables the endo-selective synthesis of N-acyl cyclohexenylamines via condensation of readily available aldehydes and amides, and subsequent Diels-Alder reaction with electron-deficient dienophiles in significantly improved yields. Advantageously, there is no need of employing additional solvents and reaction times are drastically reduced compared to similar thermal reactions.