Thermochemical and kinetic analysis on the reactions of O2 with products from OH addition to isobutene, 2-hydroxy-1,1-dimethylethyl, and 2-hydroxy-2-methylpropyl radicals: HO2 formation from oxidation of neopentane, Part II

Unimolecular dissociation of a neopentyl radical to isobutene and methyl radical is competitive with the neopentyl association with O2 ((3)Sigma(g)-) in thermal oxidative systems. Furthermore, both isobutene and the OH radical are important primary products from the reactions of neopentyl with O2. Consequently, the reactions of O2 with the 2-hydroxy-1,1-dimethylethyl and 2-hydroxy-2-methylpropyl radicals resulting from the OH addition to isobutene are important to understanding the oxidation of neopentane and other branched hydrocarbons. Reactions that correspond to the association of radical adducts with O2((3)Sigma(g)-) involve chemically activated peroxy intermediates, which can isomerize and react to form one of several products before stabilization. The above reaction systems were analyzed with ab initio and density functional calculations to evaluate the thermochemistry, reaction paths, and kinetics that are important in neopentyl radical oxidation. The stationary points of potential energy surfaces were analyzed based on the enthalpies calculated at the CBS-Q level. The entropies, S(degrees)298, and heat capacities, C(p)(T), (0 相似文献   

Unimolecular reactions in the CF3CH2Cl ↔ CF2ClCH2F system: isomerization by interchange of Cl and F atoms

The recombination of CF(2)Cl and CH(2)F radicals was used to prepare CF(2)ClCH(2)F* molecules with 93 ± 2 kcal mol(-1) of vibrational energy in a room temperature bath gas. The observed unimolecular reactions in order of relative importance were: (1) 1,2-ClH elimination to give CF(2)═CHF, (2) isomerization to CF(3)CH(2)Cl by the interchange of F and Cl atoms and (3) 1,2-FH elimination to give E- and Z-CFCl═CHF. Since the isomerization reaction is 12 kcal mol(-1) exothermic, the CF(3)CH(2)Cl* molecules have 105 kcal mol(-1) of internal energy and they can eliminate HF to give CF(2)═CHCl, decompose by rupture of the C-Cl bond, or isomerize back to CF(2)ClCH(2)F. These data, which provide experimental rate constants, are combined with previously published results for chemically activated CF(3)CH(2)Cl* formed by the recombination of CF(3) and CH(2)Cl radicals to provide a comprehensive view of the CF(3)CH(2)Cl* ? CF(2)ClCH(2)F* unimolecular reaction system. The experimental rate constants are matched to calculated statistical rate constants to assign threshold energies for the observed reactions. The models for the molecules and transition states needed for the rate constant calculations were obtained from electronic structures calculated from density functional theory. The previously proposed explanation for the formation of CF(2)═CHF in thermal and infrared multiphoton excitation studies of CF(3)CH(2)Cl, which was 2,2-HCl elimination from CF(3)CH(2)Cl followed by migration of the F atom in CF(3)CH, should be replaced by the Cl/F interchange reaction followed by a conventional 1,2-ClH elimination from CF(2)ClCH(2)F. The unimolecular reactions are augmented by free-radical chemistry initiated by reactions of Cl and F atoms in the thermal decomposition of CF(3)CH(2)Cl and CF(2)ClCH(2)F.     

Direct dynamics studies on hydrogen abstraction reactions of CH3CHFCH3 and CH3CH2CH2F with OH radicals

The hydrogen abstraction reactions of CH3CHFCH3 and CH3CH2CH2F with the OH radicals have been studied theoretically by a dual-level direct dynamics method. The geometries and frequencies of all the stationary points are optimized by means of the DFT calculation. There are complexes at the reactant side or exit route, indicating these reactions may proceed via indirect mechanisms. To improve the reaction enthalpy and potential barrier of each reaction channel, the single point energy calculation is performed by the MC-QCISD/3 method. The rate constants are evaluated by canonical variational transition state theory (CVT) with the small-curvature tunneling correction method (SCT) over a wide temperature range 200-2000 K. The canculated CVT/SCT rate constants are consistent with available experimental data. The results show that both the variation effect and the SCT contribution play an important role in the calculation of the rate constants. For reactions CH3CHFCH3 and CH3CH2CH2F with OH radicals, the channels of H-abstraction from -CHF- and -CH2- groups are the major reaction channels, respectively, at lower temperature. Furthermore, to further reveal the thermodynamics properties, the enthalpies of formation of reactants CH3CHFCH3, CH3CH2CH2F, and the product radicals CH3CFCH3, CH3CHFCH2, CH3CH2CHF, CH3CHCH2F, and CH2CH2CH2F are studied using isodesmic reactions.     

Thermochemical and kinetic analysis of the thermal decomposition of monomethylhydrazine: an elementary reaction mechanism

The reaction kinetics for the thermal decomposition of monomethylhydrazine (MMH) was studied with quantum Rice-Ramsperger-Kassel (QRRK) theory and a master equation analysis for pressure falloff. Thermochemical properties were determined by ab initio and density functional calculations. The entropies, S degrees (298.15 K), and heat capacities, Cp degrees (T) (0 < or = T/K < or = 1500), from vibrational, translational, and external rotational contributions were calculated using statistical mechanics based on the vibrational frequencies and structures obtained from the density functional study. Potential barriers for internal rotations were calculated at the B3LYP/6-311G(d,p) level, and hindered rotational contributions to S degrees (298.15 K) and Cp degrees (T) were calculated by solving the Schr?dinger equation with free rotor wave functions, and the partition coefficients were treated by direct integration over energy levels of the internal rotation potentials. Enthalpies of formation, DeltafH degrees (298.15 K), for the parent MMH (CH3NHNH2) and its corresponding radicals CH3N*NH2, CH3NHN*H, and C*H2NHNH2 were determined to be 21.6, 48.5, 51.1, and 62.8 kcal mol(-1) by use of isodesmic reaction analysis and various ab initio methods. The kinetic analysis of the thermal decomposition, abstraction, and substitution reactions of MMH was performed at the CBS-QB3 level, with those of N-N and C-N bond scissions determined by high level CCSD(T)/6-311++G(3df,2p)//MPWB1K/6-31+G(d,p) calculations. Rate constants of thermally activated MMH to dissociation products were calculated as functions of pressure and temperature. An elementary reaction mechanism based on the calculated rate constants, thermochemical properties, and literature data was developed to model the experimental data on the overall MMH thermal decomposition rate. The reactions of N-N and C-N bond scission were found to be the major reaction paths for the modeling of MMH homogeneous decomposition at atmospheric conditions.     

Addition-elimination in the reaction of alpha-hydroxyalkyl radicals with 3,5-pyridinedicarboxylic acid and nicotinic acid: example of inner sphere organic electron transfer

Reactions of alpha-hydroxyalkyl radicals with 3,5-pyridinedicarboxylic acid (3,5-PDCA) and nicotinic acid (NA) were studied at appropriate pHs in aqueous solutions by pulse radiolysis technique. At pH 1, CH(3)C*HOH and *CH(2)OH radicals were found to react with 3,5-PDCA by rate constants of 2.2 x 10(9) and 5.1 x 10(8) dm(3) mol(-1) s(-1), respectively, giving radical adduct species. The adduct species formed in the reaction of CH(3)C*HOH radicals with 3,5-PDCA underwent unimolecular decay (k = 9.8 x 10(4) s(-1)) giving pyridinyl radicals. Reaction of (CH(3))(2)C*OH, CH(3)C*HOH, and *CH(2)OH radicals with NA at pH 3.3 gave the adduct species which subsequently decayed to the pyridinyl radicals. At pH 1, wherein NA is present in the protonated form, (CH(3))(2)C*OH radicals directly transfer electrons to NA, whereas CH(3)C*HOH and *CH(2)OH radicals react with higher rate constants compared with those at pH 3.3, initially giving the adduct species which subsequently undergo elimination reaction giving pyridinyl radicals. Reactions of alpha-hydroxyalkyl radicals with 3,5-pyridinedicarboxylic acid and nicotinic acid are found to proceed by an addition-elimination pathway that provides one of the few examples of organic inner sphere electron-transfer reactions. Rate constant for the addition reaction as well as rate of elimination varies with the reduction potential of alpha-hydroxyalkyl radicals.     

Reaction of singlet-excited 2,3-diazabicyclo[2.2.2]oct-2-ene and tert-butoxyl radicals with aryl-substituted benzofuranones

5,7-Di-tert-butyl-3-aryl-3H-benzofuran-2-ones are lactones with potential antioxidant activity, owing to their abstractable benzylic C-H hydrogens. The fluorescence quenching of the azoalkane 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO), an established probe for the hydrogen-donor propensity of chain-breaking antioxidants, was investigated for 16 aryl-substituted benzofuranone derivatives [m,m-(CF3)2, p-CN, m-CN, p-CF3, p-COOCH3, m-CF3, p-Cl, p-F, H, m-CH3, p-CH3, m,p-(CH3)2, p-OCH3, o-CH3, o-CF3, o,m-(CH3)2]. Analysis of the rate data in terms of a linear free energy relationship yielded a reaction constant of rho = +0.35. This implies that n,pi*-excited DBO acts as nucleophilic species. In contrast, hydrogen abstraction of tert-butoxyl radicals from the benzofuranones was accelerated by electron-donating substituents (rho = -0.23), in conformity with the electrophilic character of oxygen-centered alkoxyl radicals. Possible implications for the optimization of the hydrogen-donor propensity of antioxidants through structural variation are discussed.     

Reactions of hydrated electron with various radicals: spin factor in diffusion-controlled reactions

The reactions of hydrated electron (eaq-) with various radicals have been studied in pulse radiolysis experiments. These radicals are hydroxyl radical (*OH), sulfite radical anion (*SO3-), carbonate radical anion (CO3*-), carbon dioxide radical anion (*CO2-), azidyl radical (*N3), dibromine radical anion (Br2*-), diiodine radical anion (I2*-), 2-hydroxy-2-propyl radical (*C(CH3)2OH), 2-hydroxy-2-methyl-1-propyl radical ((*CH2)(CH3)2COH), hydroxycyclohexadienyl radical (*C6H6OH), phenoxyl radical (C6H5O*), p-methylphenoxyl radical (p-(H3C)C6H4O*), p-benzosemiquinone radical anion (p-OC6H4O*-), and phenylthiyl radical (C6H5S*). The kinetics of eaq- was followed in the presence of the counter radicals in transient optical absorption measurements. The rate constants of the eaq- reactions with radicals have been determined over a temperature range of 5-75 degrees C from the kinetic analysis of systems of multiple second-order reactions. The observed high rate constants for all the eaq- + radical reactions have been analyzed with the Smoluchowski equation. This analysis suggests that many of the eaq- + radical reactions are diffusion-controlled with a spin factor of 1/4, while other reactions with *OH, *N3, Br2*-, I2*-, and C6H5S* have spin factors significantly larger than 1/4. Spin dynamics for the eaq-/radical pairs is discussed to explain the different spin factors. The reactions with *OH, *N3, Br2*-, and I2*- have also been found to have apparent activation energies less than that for diffusion control, and it is suggested that the spin factors for these reactions decrease with increasing temperature. Such a decrease in spin factor may reflect a changing competition between spin relaxation/conversion and diffusive escape from the radical pairs.     

Comparison of activation parameters for ionization reactions within zeolites and in aqueous solution

Absolute rate constants for the ionization of chloride from the 2-chloro-1-(4-methoxyphenyl)ethyl radical are measured in aqueous methanol and in alkali-metal cation zeolites as a function of temperature. The absolute rate constants are very fast in the two distinct media. However, the activation parameters are considerably different. In solution, the reaction proceeds with low enthalpies of activation and large, negative entropies of activation, while in zeolites, the reaction is characterized by significantly higher activation enthalpies and large, positive entropies of activation. These differences reveal that the fundamental factors allowing for such rapid reactions are not the same in the two media.     

5-氟胞嘧啶气相及水助质子转移异构化的理论研究

采用密度泛函B3LYP/6-311G**方法,对6种5-氟胞嘧啶异构体孤立分子的稳定性及质子转移引起的酮式-烯醇式、氨基式-亚胺式互变异构反应机理进行了计算研究,获得了零点能、吉布斯自由能及质子转移过程的反应焓、活化能、活化吉布斯自由能和速率常数等参数.计算结果表明,气相中烯醇-氨基式FC4是最稳定的异构体.分子内质子转移设计了FC1→FC2和FC1→FC6两条通道,分别标记为P(1)和P(2),各通道速控步骤的活化能和速率常数分别为155.9 kJ·mol-1,4.70×10-15 s-1和173.1 kJ·mol-1,1.41×10-18 s-1.水助催化时,相应通道P(3) 和P(4) 速控步骤的活化能和速率常数分别为51.0 kJ·mol-1,1.41×103 s-1和88.2 kJ·mol-1,4.53×10-3 s-1.可见,水分子的加入极大地降低了质子转移的活化能垒.另外发现,水分子参与形成协同的双质子转移机理比水助单质子转移机理更利于降低活化能垒.     

Theoretical analysis of the initial stages of the thermal decomposition of trinitromethane

The hybrid method B3LYP/6-311G* of density functional theory is used to optimize the geometries of nitroform and some intermediates of its decomposition (CH(NO₂)₂, CH(NO₂)₂ONO, CH(NO₂), and HC(O)NO) and to locate the transition states of the dissociation and isomerization reactions involving these species. The heat of formation of nitroform and of the intermediates of its decomposition and the Gibbs energies of activation of the reactions examined are calculated using the modern ab initio multilevel procedures G2M(CC5) and G2. The high-pressure limits of the rate constants of these reactions in the temperature range 300–2000 K are calculated using transition state theory or its variational analogue.     

Intramolecular reactions of free radicals formed from artemisinin

Two cyclic alkoxyl radicals are formed as a result of peroxide bridge scission in artemisinin. Intramolecular reactions of these radicals induce the cascade of reactions of isomerization, decyclization, and decomposition of formed free radicals. It includes 14 reactions of intramolecular free radical hydrogen transfer, 17 reactions of decyclization of alkoxyl and alkyl radicals, and 4 reactions of decomposition of alkoxyl, acyl, and carboxyl radicals. The enthalpies of these 35 reactions are calculated. Using intersection parabolas method, activation energies and rate constants of all these reactions are calculated. The most rapid reactions are selected for every intermediate free radical. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 554–565, 2005     

黄嘌呤异构体质子转移异构化反应机理的理论研究

采用量子化学密度泛函B3LYP/6-31G(d,p)和M06-2X/6-311++G(d,p)方法对黄嘌呤两种酮式异构体X(1,3,7)与X(1,3,9)间质子转移引起的互变异构反应机理进行了计算研究,获得了异构化反应过程的反应焓﹑活化吉布斯自由能和质子转移反应的速率常数等参数。水相计算采用极化连续(PCM)模型。结果表明,由于可能的氢迁移顺序差异,分子内由X(1,3,7)向X(1,3,9)异构化可能共有16条反应通道,涉及11个中间体和20个过渡态,其主反应通道速控步骤的活化吉布斯自由能为183.10k J/mol,速率常数为5.17×10-20s-1,其余各通道速控步骤活化吉布斯自由能均较高,而且整体水溶剂效应不利于质子转移的发生。     

两个4,4'-二甲基-2,2'-联吡啶锰(Ⅱ)配合物切割DNA的动力学研究

对2个4,4'-二甲基-2,2'-联吡啶锰(Ⅱ)配合物在生理条件及H2O2的存在下对DNA切割的动力学进行了研究.结果表明,这2个配合物分别存在下的DNA切割反应具有相似的动力学反应特征.其中对超螺旋DNA切割成缺口DNA步骤,均表现为三级反应,即反应速率分别与底物DNA的浓度、配合物的浓度和H2O2的浓度的一次方成正比;同时得到了2个反应的速率常数、活化能(Ea)、活化焓(△H≠)和活化熵(△S≠)等动力学参数,并根据这些结果提出了一个可能的氧化切割反应机理.     

Theoretical kinetic study of thermal unimolecular decomposition of cyclic alkyl radicals

Whereas many studies have been reported on the reactions of aliphatic hydrocarbons, the chemistry of cyclic hydrocarbons has not been explored extensively. In the present work, a theoretical study of the gas-phase unimolecular decomposition of cyclic alkyl radicals was performed by means of quantum chemical calculations at the CBS-QB3 level of theory. Energy barriers and high-pressure-limit rate constants were calculated systematically. Thermochemical data were obtained from isodesmic reactions, and the contribution of hindered rotors was taken into account. Classical transition state theory was used to calculate rate constants. The effect of tunneling was taken into account in the case of CH bond breaking. Three-parameter Arrhenius expressions were derived in the temperature range of 500-2000 K at atmospheric pressure, and the CC and CH bond breaking reactions were studied for cyclic alkyl radicals with a ring size ranging from three to seven carbon atoms, with and without a lateral alkyl chain. For the ring-opening reactions, the results clearly show an increase of the activation energy as the pi bond is being formed in the ring (endo ring opening) in contrast to the cases in which the pi bond is formed on the side chain (exo ring opening). These results are supported by analyses of the electronic charge density that were performed with Atoms in Molecules (AIM) theory. For all cycloalkyl radicals considered, CH bond breaking exhibits larger activation energies than CC bond breaking, except for cyclopentyl for which the ring-opening and H-loss reactions are competitive over the range of temperatures studied. The theoretical results compare rather well with the experimental data available in the literature. Evans-Polanyi correlations for CC and CH beta-scissions in alkyl and cycloalkyl free radicals were derived. The results highlight two different types of behavior depending on the strain energy in the reactant.     

Competition between mono-and bimolecular reactions of artemisinin alkoxyl radicals

The competition between intramolecular and bimolecular reactions of alkoxyl radicals formed from artemisinin was theoretically analyzed. The enthalpies of these reactions were calculated. The activation energies and rate constants of reactions of intramolecular hydrogen atom transfer, decyclization, and decomposition of alkoxyl radicals of artemisinin and several its derivatives, as well as the activation energies and rate constants of reactions of these radicals with the C-H, S-H, and O-H bonds in biological substrates and their analogs were calculated by the intersecting parabolas method The fastest reactions of artemisinin alkoxyl radicals were identified. The full kinetic scheme of transformation of these radicals was proposed. Artemisinin radicals with the free valence on the carbon atom are predominantly formed due to the transformation of the artemisininoxyl radicals. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1502–1510, September, 2006.     

Electron-transfer reduction of dinuclear copper peroxo and bis-μ-oxo complexes leading to the catalytic four-electron reduction of dioxygen to water

The four-electron reduction of dioxygen by decamethylferrocene (Fc*) to water is efficiently catalyzed by a binuclear copper(II) complex (1) and a mononuclear copper(II) complex (2) in the presence of trifluoroacetic acid in acetone at 298 K. Fast electron transfer from Fc* to 1 and 2 affords the corresponding Cu(I) complexes, which react at low temperature (193 K) with dioxygen to afford the η(2):η(2)-peroxo dicopper(II) (3) and bis-μ-oxo dicopper(III) (4) intermediates, respectively. The rate constants for electron transfer from Fc* and octamethylferrocene (Me(8)Fc) to 1 as well as electron transfer from Fc* and Me(8)Fc to 3 were determined at various temperatures, leading to activation enthalpies and entropies. The activation entropies of electron transfer from Fc* and Me(8)Fc to 1 were determined to be close to zero, as expected for outer-sphere electron-transfer reactions without formation of any intermediates. For electron transfer from Fc* and Me(8)Fc to 3, the activation entropies were also found to be close to zero. Such agreement indicates that the η(2):η(2)-peroxo complex (3) is directly reduced by Fc* rather than via the conversion to the corresponding bis-μ-oxo complex, followed by the electron-transfer reduction by Fc* leading to the four-electron reduction of dioxygen to water. The bis-μ-oxo species (4) is reduced by Fc* with a much faster rate than the η(2):η(2)-peroxo complex (3), but this also leads to the four-electron reduction of dioxygen to water.     

Addition reactions of alkyl and carboxyl radicals to vinylidene fluoride

The addition reactions of alkyl radicals CF3* and CH3* and carboxyl radicals C2H5O*, C2H5OCOO*, CF3COO*, and CH3COO* to a vinylidene fluoride (VDF) molecule are studied using ab initio calculations. These radicals were selected because they are intermediate or final products of diacyl peroxides decomposition in the initiation reactions of VDF polymerization. Two combinations of methods for energetics and structure optimization are applied: QCISD/6-311G(d,p)//HF/6-31G(d) and B3LYP/6-311G+(3df, 2p)//B3LYP/6-31G(d). It is found that the formed bond length of the product, the forming bond length of the transition state, and the attack angle of the product structures are not sensitive to the level of theory even though the attack angle of the transition state structures is. Early transition states are obtained upon attack at both high-substituted and nonsubstituted carbon atom VDF ends. Kinetic and thermodynamic control rules play different roles on governing the reactivity of the addition with the studied radicals. Both theoretical methods yield the same trends for the preferential attack site in terms of regioselectivity, barrier energies, and reaction enthalpies. It is shown that the addition reactions of the intermediate radicals C2H5OCOO*, CF3COO*, and CH3COO* of the decomposition of diethyl peroxydicarbonate, trifluoroacetyl peroxide, and diacetyl peroxide initiators yield smaller energy barriers than the additions of the corresponding final radicals, C2H5O*, CF3*, and CH3*; therefore, the reactions of the intermediate radicals should not be ignored when analyzing the initiation process of the VDF polymerization using those initiators.     

Variational analysis of the phenyl + O2 and phenoxy + O reactions

Variational transition state analysis was performed on the barrierless phenyl + O2 and phenoxy + O association reactions. In addition, we also calculated rate constants for the related vinyl radical (C2H3) + O2 and vinoxy radical (C2H3O) + O reactions and provided rate constant estimates for analogous reactions in substituted aromatic systems. Potential energy scans along the dissociating C-OO and CO-O bonds (with consideration of C-OO internal rotation) were obtained at the O3LYP/6-31G(d) density functional theory level. The CO-O and C-OO bond scission reactions were observed to be barrierless, in both phenyl and vinyl systems. Potential energy wells were scaled by G3B3 reaction enthalpies to obtain accurate activation enthalpies. Frequency calculations were performed for all reactants and products and at points along the potential energy surfaces, allowing us to evaluate thermochemical properties as a function of temperature according to the principles of statistical mechanics and the rigid rotor harmonic oscillator (RRHO) approximation. The low-frequency vibrational modes corresponding to R-OO internal rotation were omitted from the RRHO analysis and replaced with a hindered internal rotor analysis using O3LYP/6-31G(d) rotor potentials. Rate constants were calculated as a function of temperature (300-2000 K) and position from activation entropies and enthalpies, according to canonical transition state theory; these rate constants were minimized with respect to position to obtain variational rate constants as a function of temperature. For the phenyl + O2 reaction, we identified the transition state to be located at a C-OO bond length of between 2.56 and 2.16 A (300-2000 K), while for the phenoxy + O reaction, the transition state was located at a CO-O bond length of 2.00-1.90 A. Variational rate constants were fit to a three-parameter form of the Arrhenius equation, and for the phenyl + O2 association reaction, we found k(T) = 1.860 x 1013T-0.217 exp(0.358/T) (with k in cm3 mol-1 s-1 and T in K); this rate equation provides good agreement with low-temperature experimental measurements of the phenyl + O2 rate constant. Preliminary results were presented for a correlation between activation energy (or reaction enthalpy) and pre-exponential factor for heterolytic O-O bond scission reactions.     

Reactivity of tris(trimethylsilyl)silane toward diarylaminyl radicals

Absolute rate constants for the reaction of tri-tert-butylphenoxyl radical (ArO*) with (TMS)(3)SiH were measured spectrophotometrically in the temperature range 321-383 K. Rate constants for the hydrogen abstraction from (TMS)(3)SiH by diarylaminyl radicals of type (4-X-C(6)H(4))(2)N* were determined by using a method in which the corresponding amines catalyze the reaction of ArO* with (TMS)(3)SiH. At 364.2 K, rate constants are in the range of 2-50 M(-)(1) s(-)(1) for X = H, CH(3), CH(3)O, and Br, whereas the corresponding value for ArO* is 3 orders of magnitude lower. A common feature of these reactions is the low preexponential factor [log(A/M(-1)s(-1)) of 4.4 and 5.2 for ArO* and Ph(2)N*, respectively], which reflects high steric demand in the transition state. A semiempirical approach based on intersecting parabolas suggests that the observed reactivity is mainly related to the enthalpy of the reaction and allowed to estimate activation energies for the reaction of (4-X-C(6)H(4))(2)N* and ArO* radicals with a variety of silicon hydrides.     

A Theoretical Study of Ene Reactions in Solution: A Solution‐Phase Translational Entropy Model

Several density functional theory (DFT) methods, such as CAM‐B3LYP, M06, ωB97x, and ωB97xD, are used to characterize a range of ene reactions. The Gibbs free energy, activation enthalpy, and entropy are calculated with both the gas‐ and solution‐phase translational entropy; the results obtained from the solution‐phase translational entropies are quite close to the experimental measurements, whereas the gas‐phase translational entropies do not perform well. For ene reactions between the enophile propanedioic acid (2‐oxo‐1,3‐dimethyl ester) and π donors, the two‐solvent‐involved explicit+implicit model can be employed to obtain accurate activation entropies and free‐energy barriers, because the interaction between the carbonyl oxygen atom and the solvent in the transition state is strengthened with the formation of C?C and O?H bonds. In contrast, an implicit solvent model is adequate to calculate activation entropies and free‐energy barriers for the corresponding reactions of the enophile 4‐phenyl‐1,2,4‐triazoline‐3,5‐dione.