The 1deltag dioxygen ene reaction with propene: a density functional and multireference perturbation theory mechanistic study

This study aims to determine whether a balance between concerted and non-concerted pathways exists, and in particular to ascertain the possible role of diradical/zwitterion or peroxirane intermediates. Three non-concerted pathways, via 1) diradical or 2) peroxirane intermediates, and 3) by means of hydrogen-abstraction/radical recoupling, plus one concerted pathway (4), are explored. The intermediates and transition structures (TS) are optimized at the DFT(MPW1K), DFT(B3LYP) and CASSCF levels of theory. The latter optimizations are followed by multireference perturbative CASPT2 energy calculations. (1) The polar diradical forms from the separate reactants by surmounting a barrier (deltaE(++)(MPW1K)=12, deltaE++(B3LYP)=14, and deltaE(++)(CASPT2)=16 kcal mol(-1) and can back-dissociate through the same TS, with barriers of 11 (MPW1K) and 8 kcal mol(-1) (B3LYP and CASPT2). The diradical to hydroperoxide transformation is easy at all levels (deltaE(++)(MPW1K)<4, deltaE(++)(B3LYP)=1 and deltaE(++)(CASPT2)=1 kcal mol(-1)). (2) Peroxirane is attainable only by passing through the diradical intermediate, and not directly, due to the nature of the critical points involved. It is located higher in energy than the diradical by 12 kcal mol(-1), at all theory levels. The energy barrier for the diradical to cis-peroxirane transformation (deltaE(++)=14-16 kcal mol(-1)) is much higher than that for the diradical transformation to the hydroperoxide. In addition, peroxirane can very easily back-transform to the diradical (deltaE(++)<3 kcal mol(-1)). Not only the energetics, but also the qualitative features of the energy hypersurface, prevent a pathway connecting the peroxirane to the hydroperoxide at all levels of theory. (3) The last two-step pathway (hydrogen-abstraction by (1)O(2), followed by HOO-allyl radical coupling) is not competitive with the diradical mechanism. (4) A concerted pathway is carefully investigated, and deemed an artifact of restricted DFT calculations. Finally, the possible ene/[pi2+pi2] competition is discussed.     

Quantum mechanical study of the ring-closing reaction of the hexatriene radical cation

The ring-closing reaction of hexatriene radical cation 1(*)(+) to 1,3-cyclohexadiene radical cation 2(*)(+) was studied computationally at the B3LYP/6-31G* and QCISD(T)/6-311G*//QCISD/6-31G* levels of theory. Both, concerted and stepwise mechanisms were initially considered for this reaction. Upon evaluation at the B3LYP level of theory, three of the possible pathways-a concerted C(2)-symmetric via transition structure 3(*)(+) and stepwise C(1)-symmetric pathways involving three-membered ring intermediate 5(*)(+) and four-membered ring intermediate 6(*)(+)-were rejected due to high-energy stationary points along the reaction pathway. The two remaining pathways were found to be of competing energy. The first proceeds through the asymmetric, concerted transition structure 4(*)(+) with an activation barrier E(a) = 16.2 kcal/mol and an overall exothermicity of -23.8 kcal/mol. The second pathway, beginning from the cis,cis,trans rotamer of 1(*)(+), proceeds by a stepwise pathway to the cyclohexadiene product with an overall exothermicity of -18.6 kcal/mol. The activation energy for the rate-determining step in this process, the formation of the intermediate bicyclo[3.1.0]hex-2-ene via transition structure 9(*)(+), was found to be 20.4 kcal/mol. More rigorous calculations of a smaller subsection of the potential energy hypersurface at the QCISD(T)//QCISD level confirmed these findings and emphasized the importance of conformational control of the reactant.     

Conformational selectivity in the diels-alder cycloaddition: predictions for reactions of s-trans-1,3-butadiene

Diels-Alder cycloaddition of s-trans-1,3-butadiene (1) should yield trans-cyclohexene (7), just as reaction of the s-cis conformer gives cis-cyclohexene (9). Investigation of this long-overlooked process with Hartree-Fock, Moller-Plesset, CASSCF, and DFT methods yielded in every case a C(2)-symmetric concerted transition state. At the B3LYP/6-31G (+ZPVE) level, this structure is predicted to be 42.6 kcal/mol above reactants, while the overall reaction is endothermic by 16.7 kcal/mol. A stepwise diradical process has been studied by UBLYP/6-31G theory and found to have barriers of 35.5 and 17.7 kcal/mol for the two steps. Spin correction lowers these values to 30.1 and 13.0 kcal/mol. The barrier to pi-bond rotation in cis-cyclohexene (9) is predicted (B3LYP theory) to be 62.4 kcal/mol, with trans-cyclohexene (7) lying 53.3 kcal/mol above cis isomer 9. Results suggest that pi-bond isomerization and concerted reaction may provide competitive routes for Diels-Alder cycloreversion. It is concluded that full understanding of the Diels-Alder reaction requires consideration of both conformers of 1,3-butadiene.     

A cornucopia of cycloadducts: theoretical predictions of the mechanisms and products of the reactions of cyclopentadiene with cycloheptatriene

The potential cycloaddition reactions between cyclopentadiene and cycloheptatriene have been explored theoretically. B3LYP/6-31G was used to locate the transition states, intermediates, and products for concerted pathways and stepwise pathways passing through diradical intermediates. Interconversions of various cycloadducts through sigmatropic shifts were also explored. CASPT2/6-31G single point calculations were employed to obtain independent activation energy estimates. MM3 was also used to compute reaction energetics. Several bispericyclic cycloadditions in which two cycloadducts are linked by a sigmatropic shift have been identified. B3LYP predicts, in line with frontier molecular orbital predictions, that the [6+4] cycloaddition is the favored concerted pathway, but an alternative [4+2] pathway is very close in energy. By contrast, CASPT2 predicts that a [4+2] cycloaddition is the preferred pathway. B3LYP predicts that the lowest energy path to many of the cycloadducts will involve diradical intermediates, whereas CASPT2 predicts that each of the products of orbital symmetry allowed reactions will be reached most readily by closed shell processes-concerted cycloadditions and sigmatropic shift rearrangements of cycloadducts.     

Transition states for the dimerization of 1,3-cyclohexadiene: a DFT, CASPT2, and CBS-QB3 quantum mechanical investigation

Quantum mechanical calculations using restricted and unrestricted B3LYP density functional theory, CASPT2, and CBS-QB3 methods for the dimerization of 1,3-cyclohexadiene (1) reveal several highly competitive concerted and stepwise reaction pathways leading to [4 + 2] and [2 + 2] cycloadducts, as well as a novel [6 + 4] ene product. The transition state for endo-[4 + 2] cycloaddition (endo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 28.7 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 19.0 kcal/mol) is not bis-pericyclic, leading to nondegenerate primary and secondary orbital interactions. However, the C(s) symmetric second-order saddle point on the B3LYP energy surface is only 0.3 kcal/mol above endo-2TS. The activation enthalpy for the concerted exo-[4 + 2] cycloaddition (exo-2TS, DeltaH(double dagger)(B3LYP(0K)) = 30.1 kcal/mol and DeltaH(double dagger)(CBS-QB3(0K)) = 21.1 kcal/mol) is 1.4 kcal/mol higher than that of the endo transition state. Stepwise pathways involving diallyl radicals are formed via two different C-C forming transition states (rac-5TS and meso-5TS) and are predicted to be competitive with the concerted cycloaddition. Transition states were located for cyclization from intermediate rac-5 leading to the endo-[4 + 2] (endo-2) and exo-[2 + 2] (anti-3) cycloadducts. Only the endo-[2 + 2] (syn-3) transition state was located for cyclization of intermediate meso-5. The novel [6 + 4] "concerted" ene transition state (threo-4TS, DeltaH(double dagger)(UB3LYP(0K)) = 28.3 kcal/mol) is found to be unstable with respect to an unrestricted calculation. This diradicaloid transition state closely resembles the cyclohexadiallyl radical rather than the linked cyclohexadienyl radical. Several [3,3] sigmatropic rearrangement transition states were also located and have activation enthalpies between 27 and 31 kcal/mol.     

The reaction of cyclopentyne with ethene: concerted vs stepwise mechanism?

The cycloaddition of cyclopentyne with ethene was examined using (U)B3LYP and CASSCF methods to discern the reaction mechanism. (U)B3LYP/6-31G* and (U)B3LYP/6-311+G* slightly favor the concerted pathway, whereas CASSCF(4,4)/6-31G* and CASCF(6,6)/6-31G* favor the diradical pathway. MRMP2 using the CASSCF(4,4) wave function also favors the diradical mechanism. In the context of a diradical pathway, the experimentally observed complete retention of stereochemistry for this reaction is understood in terms of stereochemical control resulting from dynamic effects.     

One-bond, two-bond, and three-bond mechanisms in thermal deazetizations of 2,3-diazabicyclo[2.2.2]oct-2-enes, trans-azomethane, and 2,3-diazabicyclo[2.2.1]hept-2-ene

The thermal deazetizations of a series of substituted 2,3-diazabicyclo[2.2.2]oct-2-enes and some simpler model systems have been studied using the UB3LYP/6-31G(d) and CASPT2 methods, with a variety of active spaces. A fused cyclopropane exerts unique control on the mechanism and rate of deazetization. When the Walsh sigma-orbitals are appropriately aligned in an exo orientation, a pericyclic three-bond cleavage occurs. For an endo-fused cyclopropane, sequential one-bond cleavages occur to take advantage of orbital overlap with the Walsh orbitals. In systems lacking strongly directing substituents, concerted two-bond cleavage pathways to form diradical intermediates have a small enthalpic advantage (DeltaH(0K)++) over sequential one-bond cleavage pathways. However, the one-bond mechanism has an entropic advantage over the two-bond; consequently, at 400-500 K where decomposition occurs, one-bond and two-bond diradical cleavages both occur simultaneously. The thermal decompositions of trans-azomethane and 2,3-diazabicyclo[2.2.1]hept-2-ene are also studied, and the results are compared to extensive computational studies in the literature. Comparisons of UB3LYP, CASSCF, and CASPT2 surfaces for these reactions are made.     

Computational study of the aminolysis of 2-benzoxazolinone

Three possible mechanisms (zwitterionic, neutral stepwise, and neutral concerted) of the ring-opening reaction of 2-benzoxazolinone (BO) upon aminolysis with methylamine were studied at the B3LYP/6-31G* level. In the gas phase, the neutral concerted mechanism is shown to be most favorable, which proceeds via a rate-determining barrier of 28-29 kcal/mol. The transition state, CTS, associated with this barrier is a four-centered one, where 1,2-addition of the N[bond]H of methylamine to the C[bond]O of BO ring occurs. The rate-determining barrier of the neutral stepwise pathway is found to be ca. 42 kcal/mol. The inclusion of solvent effects by a polarizable continuum model (PCM) does not change the conclusions based on the gas-phase study; the barrier at CTS is reduced to 20, 20, and 22 kcal/mol in water, ethanol, and acetonitrile, respectively.     

Theoretical analysis of concerted and stepwise mechanisms of Diels-Alder reactions of butadiene with silaethylene and disilene

The concerted and the stepwise mechanisms of the Diels-Alder reactions of butadiene with silaethylene and disilene were studied by ab initio MO methods. For the reaction of butadiene and silaethylene, an asymmetric concerted process that is almost stepwise and two stepwise processes were located. For the first step of the stepwise process, the C-Si bond formation is more favorable than the C-C bond formation. The activation energy barrier of the concerted transition state is only 0.89 kcal/mol lower than that of the first-step transition state of the C-Si bond formation for the stepwise process by the CASPT2 calculation level. For the reaction of butadiene and disilene, the activation energy barrier of the concerted-type transition state constrained with Cs symmetry is about 9 kcal/mol higher than that of the stepwise transition state by the CASSCF method. The energy barrier of the first step of the stepwise reaction disappears at the CASPT2/6-311++G(d,p) calculation level including the nondynamical correlation energy, although the reaction of the butadiene with disilene occurs through the stepwise-like process.     

Heat of hydrogenation of 1,5-dehydroquadricyclane. A computational and experimental study of a highly pyramidalized alkene

The radical anion of the highly pyramidalized alkene 1,5-dehydroquadricyclane (1) was generated in the gas phase from the Squires reaction of 1,5-bis(trimethylsilyl)quadricyclane with F-/F2. The electron binding energy and proton affinity of 1*- were determined by bracketing experiments to be 0.6 +/- 0.1 eV and 386 +/- 5 kcal/mol, respectively. These values are in good agreement with values predicted by density functional theory (B3LYP/6-31+G*) and ab initio (CASPT2/6-31+G*) calculations. The experimental heat of hydrogenation of 1, obtained from a thermochemical cycle, was found to be 91 +/- 9 kcal/mol. This value of deltaH(H2) leads to values of 67 +/- 9 kcal/mol for the olefin strain energy (OSE) of 1, 172 +/- 9 kcal/mol for its heat of formation, and 23 +/- 9 kcal/mol for its pi bond dissociation enthalpy. Since the retro-Diels-Alder reaction of neutral 1 is computed to be highly exothermic, the finding that 1*- apparently does not undergo a retro-Diels-Alder reaction is of particular interest. The B3LYP/6-31+G* optimized geometry of 1 suggests that the bonding in this alkene is partially delocalized, presumably because the highly pyramidalized double bond in 1 interacts with the distal cyclopropane bonds in a manner that eventually leads to a retro-Diels-Alder reaction. The good agreement of the B3LYP and (2/2)CASPT2 values for the heat of hydrogenation and OSE of 1 with the experimentally derived values provides indirect evidence for the correctness of the B3LYP prediction that the equilibrium geometry of 1 lies part way along the reaction coordinate to the transition structure for the retro-Diels-Alder reaction.     

Molecule-induced alkane homolysis with dioxiranes.

The mechanisms of C-H and C-C bond activations with dimethyldioxirane (DMD) were studied experimentally and computationally at the B3LYP/6-311+G**//B3LYP/6-31G* density functional theory level for the propellanes 3,6-dehydrohomoadamantane (2) and 1,3-dehydroadamantane (3). The sigma(C-C) activation of 3 with DMD (Delta G(*) = 23.9 kcal mol(-1) and Delta G(r) = -5.4 kcal mol(-1)) is the first example of a molecule-induced homolytic C-C bond cleavage. The C-H bond hydroxylation observed for 2 is highly exergonic (Delta G(r) = -74.4 kcal mol(-1)) and follows a concerted pathway (Delta G(*) = 34.8 kcal mol(-1)), in contrast to its endergonic molecule-induced homolysis (Delta G(*) = 28.8 kcal mol(-1) and Delta G(r) = +9.2 kcal mol(-1)). The reactivities of 2 and 3 with CrO(2)Cl(2), which follow a molecule-induced homolytic activation mechanism, parallel the DMD results only for highly reactive 3, but differ considerably for more stable propellanes such as 4-phenyl-3,6-dehydrohomoadamantane (1) and 2.     

CASSCF and CASPT2 calculations on the cleavage and ring inversion of bicyclo[2.2.0]hexane find that these reactions involve formation of a common twist-boat diradical intermediate.

(6/6)CASSCF and CASPT2/6-31G calculations have been performed to understand the experimental finding of Goldstein and Benzon (J. Am. Chem. Soc. 1972, 94, 5119) that exo-bicyclo[2.2.0]hexane-d(4) (1b) undergoes ring inversion to form endo-bicyclo[2.2.0]hexane-d(4) (4b) faster than it undergoes cleavage to form cis,trans-1,5-hexadiene-d(4) (3b). Goldstein and Benzon also found that the latter reaction, which must occur via a chairlike transition structure (TS), is much faster than cleavage of 1b to trans,trans-1,5-hexadiene-d(4) (2b) via a boatlike TS. Our calculations reveal that all three of these reactions involve ring opening of 1, through a boat diradical TS (BDTS), to form a twist-boat diradical intermediate (TBDI). TBDI can reclose to 4 via a stereoisomeric boat diradical TS (BDTS'), or TBDI can cleave, either via a half-chair diradical TS (HCDTS) to form 3 or via a boat TS (BTS) to form 2. The calculated values of DeltaH(++) = 34.6 kcal/mol, DeltaS(++) = -1.6 eu, and DeltaH(++) = 35.2 kcal/mol, DeltaS(++) = 2.0 eu for ring inversion of 1 to 4 and cleavage of 1 to 3, respectively, are in excellent agreement with the values measured by Goldstein and Benzon. The higher value of DeltaH(++) = 37.6 kcal/mol, computed for cleavage of TBDI to 2, is consistent with the experimental finding that very little 2b is formed when 1b is pyrolyzed. The relationships between BDTS, HCDTS, and BTS and the chair and boat Cope rearrangement TSs (CCTS and BCTS) are discussed.     

DFT and CASPT2 study of two thermal reactions of nitromethane: C–N bond cleavage and nitro-to-nitrite isomerization. An example of the inverse symmetry breaking deficiency in density functional calculations of an homolytic dissociation

The reaction paths of nitromethane leading to the dissociation products or isomerization to methyl nitrite have been computationally investigated at the CAS-SCF and DFT levels of theory. Additionally, the CAS-SCF wave functions were used as reference in a second-order perturbation treatment, CASPT2, in order to obtain a good estimate for the activation energy of each reaction path. Both methods predict the isomerization as a concerted reaction. However, the behavior of the two approximations with respect to dissociation is rather different; while CASPT2 predicts a barrier height of (≈59 kcal/mol) in good accordance with the experimental activation energy (59.0 kcal/mol), B3-LYP/6-31G^* calculations overestimate the barrier for more than 30 kcal/mol. The DFT prediction of the dissociation channel exhibits inverse symmetry breaking, dissociating to the unphysical absurd CH₃^δ+ plus NO₂^δ−.     

Novel pathways for oxygen insertion into unactivated C-H bonds by dioxiranes. Transition structures for stepwise routes via radical pairs and comparison with the concerted pathway

The oxygen insertion into C-H bonds (of methane, isobutane, and acetone) by dioxiranes (parent dioxirane and dimethyldioxirane) to give alcohols was studied with the DFT theory, using both restricted and unrestricted B3LYP methods, and 6-31G(d) and 6-311+G(d,p) basis sets to evaluate the feasibility of stepwise mechanisms and their competition with the concerted counterpart. Confirming previous results by other authors, we have located, with the RB3LYP method, concerted TSs in which the oxygen bound to be inserted interacts very strongly with the hydrogen atom and very weakly with the carbon atom of the C-H bond. These TSs nicely explain all the experimental observations (e.g., configuration retention at the chiral centers), but all of them exhibit an RHF --> UHF wave function instability that preclude considering them as genuine transition structures. We also were able to characterize, with UB3LYP methods, two alternative two-step processes that can lead to final products (alcohol + carbonyl compound) via singlet radical pair intermediates. For the first step of both processes we located genuine diradicaloid TSs, namely, TSs rad,coll and TSs rad,perp, that have stable wave functions. In TSs rad,coll the alkane C-H bond tends to be collinear with the breaking O(1)- - -O(2) bond while in TSs rad,perp the alkane C-H bond is almost perpendicular to the O(1)- - -O(2) bond. The first step, of both processes, can represent an example of a "molecule induced homolysis" reaction: collision between alkane and dioxirane brings about the homolytic cleavage of the dioxirane O-O bond and the hydrogen abstraction follows afterward to produce the diradicaloid TS that then falls down to a singlet radical pair. This hypothesis was fully confirmed by IRC analysis in the case of TSs rad,coll. The possible pathways that lead from the intermediate radical pair to final products are discussed as well as the hypothesis that the radical collinear TSs may collapse directly to products in a "one-step nonconcerted" process. However, diradical mechanisms cannot explain the experimental data as satisfactorily as the concerted pathway does. As for computational predictions about competition of diradical vs concerted mechanisms, they strongly depend (i) on the alkane C-H type, (ii) on whether gas phase or solution is considered, and (iii) on the basis set used for calculations. In short, the concerted TS benefits, with respect to the corresponding diradicaloid TSs, of alkyl substitution at the C-H center, solvation effects, and basis set extension. Actually, in the case of DMD reactions with methane and acetone, the diradicaloid TSs are always (both in gas phase and in solution and with both the basis sets used) strongly favored over their concerted counterpart. In the case of DMD reaction with isobutane tertiary C-H bond the large favor for the diradicaloid TSs over the concerted TS, predicted in gas phase by the B3LYP/6-31G(d) method, progressively decreases as a result of basis set extension and introduction of solvent effects: the higher theory level [B3LYP/6-311+G(d,p)] suggests that in acetone solution TS conc has almost the same energy as TS rad,perp while TS rad,coll resides only 2 kcal/mol higher.     

Computational studies of the thermal fragmentation of P-arylphosphiranes: have arylphosphinidenes been generated by this method?

CASSCF, CASPT2, CCSD(T), and (U)B3LYP electronic structure calculations have been performed in order to investigate the thermal fragmentation of P-phenylphosphirane (1) to phenylphosphinidene (PhP) and ethylene. The calculations show that generation of triplet PhP via a stepwise pathway is 21 kcal mol(-1) less endothermic and has a 12 kcal mol(-1) lower barrier height than concerted fragmentation of 1 to give singlet PhP. The formation of singlet PhP via a concerted pathway is predicted to be stereospecific, whereas formation of triplet PhP is predicted to occur with complete loss of stereochemistry. However, calculations on fragmentation of anti-cis-2,3-dimethyl-P-mesitylphosphirane (cis-1Me) to triplet mesitylphosphinidene (MesP) indicate that this reaction should be more stereospecific, in agreement with the experimental results of Li and Gaspar. Nevertheless, with a predicted free energy of activation of 42 kcal mol(-1), the formation of MesP from cis-1Me is not likely to have occurred in an uncatalyzed reaction at the temperatures at which this phosphirane has been pyrolyzed.     

Benzylic cations with triplet ground states: computational studies of aryl carbenium ions, silylenium ions, nitrenium ions, and oxenium ions substituted with meta pi donors

Density functional theory (B3LYP/6-31G(d,p)) was used to predict the effect of meta substitution on aryl cationic (Ar-X+) species, including aryloxenium ions, arylsilylenium ions, arylnitrenium ions, and arylcarbenium ions. Multireference second-order perturbation theory (CASPT2) calculations were used to benchmark the quantitative accuracy of the DFT calculations for representative systems. Substituting the meta positions on these species with pi donors stabilizes a pi,pi* diradical state analogous to the well-known m-xylylene diradical. Notably, the 3,5-bis(N,N-dimethylamino)benzyl cation is predicted to have a triplet ground state by 1.9 kcal/mol by DFT and to have essentially degenerate singlet-triplet states at the CASPT2(10,9) level of theory. Adding electron-withdrawing CF3 groups to the exocyclic carbon of this meta-disubstituted benzyl cation further increases the predicted singlet-triplet gap in favor of the triplet. Other aryl cationic species substituted with strong pi electron-donating groups in the meta positions are predicted to have low-energy or ground-state triplet states. Systems analogous to the naphthaquinodimethane diradicals are also reported.     

The Curtius rearrangement of cyclopropyl and cyclopropenoyl azides. A combined theoretical and experimental mechanistic study

A combined experimental and theoretical study addresses the concertedness of the thermal Curtius rearrangement. The kinetics of the Curtius rearrangements of methyl 1-azidocarbonyl cycloprop-2-ene-1-carboxylate and methyl 1-azidocarbonyl cyclopropane-1-carboxylate were studied by (1)H NMR spectroscopy, and there is close agreement between calculated and experimental enthalpies and entropies of activation. Density functional theory (DFT) calculations (B3LYP/6-311+G(d,p)) on these same acyl azides suggest gas phase barriers of 27.8 and 25.1 kcal/mol. By comparison, gas phase activation barriers for the rearrangement of acetyl, pivaloyl, and phenyl azides are 27.6, 27.4, and 30.0 kcal/mol, respectively. The barrier for the concerted Curtius reaction of acetyl azide at the CCSD(T)/6-311+G(d,p) level exhibited a comparable activation energy of 26.3 kcal/mol. Intrinsic reaction coordinate (IRC) analyses suggest that all of the rearrangements occur by a concerted pathway with the concomitant loss of N2. The lower activation energy for the rearrangement of methyl 1-azidocarbonyl cycloprop-2-ene-1-carboxylate relative to methyl 1-azidocarbonyl cyclopropane-1-carboxylate was attributed to a weaker bond between the carbonyl carbon and the three-membered ring in the former compound. Calculations on the rearrangement of cycloprop-2-ene-1-oyl azides do not support pi-stabilization of the transition state by the cyclopropene double bond. A comparison of reaction pathways at the CBS-QB3 level for the Curtius rearrangement versus the loss of N2 to form a nitrene intermediate provides strong evidence that the concerted Curtius rearrangement is the dominant process.     

Transition state stabilization and substrate strain in enzyme catalysis: ab initio QM/MM modelling of the chorismate mutase reaction

To investigate fundamental features of enzyme catalysis, there is a need for high-level calculations capable of modelling crucial, unstable species such as transition states as they are formed within enzymes. We have modelled an important model enzyme reaction, the Claisen rearrangement of chorismate to prephenate in chorismate mutase, by combined ab initio quantum mechanics/molecular mechanics (QM/MM) methods. The best estimates of the potential energy barrier in the enzyme are 7.4-11.0 kcal mol(-1)(MP2/6-31+G(d)//6-31G(d)/CHARMM22) and 12.7-16.1 kcal mol(-1)(B3LYP/6-311+G(2d,p)//6-31G(d)/CHARMM22), comparable to the experimental estimate of Delta H(++)= 12.7 +/- 0.4 kcal mol(-1). The results provide unequivocal evidence of transition state (TS) stabilization by the enzyme, with contributions from residues Arg90, Arg7, and Arg63. Glu78 stabilizes the prephenate product (relative to substrate), and can also stabilize the TS. Examination of the same pathway in solution (with a variety of continuum models), at the same ab initio levels, allows comparison of the catalyzed and uncatalyzed reactions. Calculated barriers in solution are 28.0 kcal mol(-1)(MP2/6-31+G(d)/PCM) and 24.6 kcal mol(-1)(B3LYP/6-311+G(2d,p)/PCM), comparable to the experimental finding of Delta G(++)= 25.4 kcal mol(-1) and consistent with the experimentally-deduced 10(6)-fold rate acceleration by the enzyme. The substrate is found to be significantly distorted in the enzyme, adopting a structure closer to the transition state, although the degree of compression is less than predicted by lower-level calculations. This apparent substrate strain, or compression, is potentially also catalytically relevant. Solution calculations, however, suggest that the catalytic contribution of this compression may be relatively small. Consideration of the same reaction pathway in solution and in the enzyme, involving reaction from a 'near-attack conformer' of the substrate, indicates that adoption of this conformation is not in itself a major contribution to catalysis. Transition state stabilization (by electrostatic interactions, including hydrogen bonds) is found to be central to catalysis by the enzyme. Several hydrogen bonds are observed to shorten at the TS. The active site is clearly complementary to the transition state for the reaction, stabilizing it more than the substrate, so reducing the barrier to reaction.     

Concerted vs stepwise mechanism in 1,3-dipolar cycloaddition of nitrone to ethene, cyclobutadiene, and benzocyclobutadiene. A computational study

The problem of competition between concerted and stepwise diradical mechanisms in 1,3-dipolar cycloadditions was addressed by studying the reaction between nitrone and ethene with DFT (R(U)B3LYP/6-31G) and post HF methods. According to calculations this reaction should take place via the concerted cycloaddition path. The stepwise process is a viable but not competitive alternative. The R(U)B3LYP/6-31G study was extended to the reaction of the same 1, 3-dipole with cyclobutadiene and benzocyclobutadiene. The very reactive antiaromatic cyclobutadiene has an electronic structure that is particularly disposed to promote stepwise diradical pathways. Calculations suggest that its reaction with nitrone represents a borderline case in which the stepwise process can compete with the concerted one on similar footing. Attenuation of the antiaromatic character of the dipolarophile, i.e., on passing from cyclobutadiene to benzocyclobutadiene, causes the concerted 1,3-dipolar cycloaddition to become once again prevalent over the two-step path. Thus, our results suggest that, in 1,3-dipolar cycloadditions that involve normal dipolarophiles, the concerted path (Huisgen's mechanism) should clearly overwhelm its stepwise diradical (Firestone's mechanism) counterpart.