A predictive model for unimolecular reactions: Reactions of unsaturated carbonium ions

The major slow unimolecular reactions undergone by C₄H₇⁺, C₅H₉⁺ and C₆H⁺₁₁ are discussed in terms of a potential surface approach and the organic chemist's concept of mechanism. It is shown that the observed decompositions which do not involve σ-bond formation in the dissociation step are precisely those expected from the model. Further use of the model correctly predicts the slow reactions of C₇H⁺₁₃ which have not previously been reported. The approach also permits useful limits to be set on the transition state energies for reactions involving σ-bond formation in the dissociation step (H₂,CH₄ loss). It is concluded that stepwise addition of ethylene to the allyl cation is preferred to a concerted 4-electron process which is symmetry forbidden.     

Development of predictive tools for optimizing organic reactions

Although microwave chemistry and its applications have undergone rapid growth over the last decade, the technology is not yet employed routinely in all synthetic laboratories. A significant obstacle to implementation concerns the empirical work required to adapt established conditions into alternatives employing higher temperatures. We now have established predictive tools to translate reaction conditions from conventional heated (ambient pressure) to elevated temperature (ambient or elevated pressure). We have studied 45 reactions (including published literature examples) and made in excess of 200 estimations for specific yield or conversion, with a high degree of accuracy. Linear regression analysis of estimated vs. experimental conversion or yield was 0.90 (first iteration) and 0.98 (second iteration).     

A fitting formula for the falloff curves of unimolecular reactions

A fitting formula is proposed to approximate the falloff curves of the pressure‐ and temperature‐dependent unimolecular reaction rate constants. Compared with the widely used Troe's formula, the present expression has the potential to substantially reduce the computation time in its evaluation because of the mathematical simplicity. Four testing reactions from the VariFlex program package were used to examine the accuracy of the present formula, showing improved performance as compared with previous expressions. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 727–734, 2009     

SCF perturbation theory for unimolecular reactions

A CNDO/2 SCF perturbation theory is presented for interpreting the form of CNDO/2 potential energy surfaces of unimolecular reactions. The analysis is performed by calculating the energy change E arising from a distortion of the molecular geometry along the reaction coordinate. E is decomposed into different perturbational contributions which are appropriate for an interpretation of the perturbation energy E. Moreover, E is resolved into energy parts arising from a single occupied orbital and contributions due to pairwise orbital interactions. In this way one evaluates numerically how the form of the occupied and unoccupied orbitals determines the magnitude of E. If the distortion occurs along a definite symmetry coordinate, group-theoretical arguments can be applied to discuss the magnitude of characteristic components of the perturbation energy. The SCF perturbation theory is used to analyze the isomerization of ethylene, cis-2-butene and cis-2-butenenitrile.This work was partially supported by Nato-Grant No. 1072     

Solution of the master equation for unimolecular reactions

A method is given for computing the rate coefficient of a unimolecular reaction as an eigenvalue solution of an integral master equation, based on Nesbet's algorithm, which overcomes computational difficulties associated with this problem. An illustrative fit to pressure-dependent data on the pyrolysis of azoethane is presented.     

Potential energy profiles for unimolecular reactions of organic ions: [C3H8N]+ and [C3H7O]+

The unimolecular decompositions of two isomers of [C₃H₈N]⁺, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} {\rm CH} = \mathop {\rm N}\limits^ + {\rm H}_2 $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H = CH}_{\rm 2} $\end{document}, are discussed in terms of the potential energy profile over which reaction may be considered to occur. The energy needed to promote slow (metastable) dissociations of either ion is found to be less than that required to cause isomerization to the other structure. This finding is supported by the observation of different decomposition pathways, different metastable peak shapes for C₂H₄ loss, the results of ²H labelling studies, and energy measurements on the two ions. The corresponding potential energy profile for decomposition of the oxygen analogues, \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 3} {\rm CH}_{\rm 2} {\rm CH =\!= }\mathop {\rm O}\limits^ + {\rm H} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm O}\limits^ + {\rm = CH}_{\rm 2} $\end{document}, is compared and contrasted with that proposed for the [C₃H₈N]⁺ isomers. This analysis indicates that for the oxygen analogues, the energy needed to decompose either ion is very similar to that required to cause isomerization to the other structure. Consequently, dissociation of either ion is finely balanced with rearrangement to the other and similar reactions are observed. Detailed mechanisms are proposed for loss of H₂O and C₂H₄ from each ion and it is shown that these mechanisms are consistent with ²H and ¹³C labelling studies, the kinetic energy release associated with each decomposition channel, the relative competition between H₂O and C₂H₄ loss and energy measurements.     

The arrhenius factors for some six-center unimolecular reactions

The Pyrolysis of ethyl formate has been carried out in the temperature range 557°–630° and the rate expression k = 10^12.34 e^{?48,100±500/RT} sec^?1 was obtained, in agreement with the prediction of O'Neal and Benson [1]. Calculated Arrhenius A-factors and experimental rate constants have been used to obtain the activation energies for the decomposition of the following compounds by the six-center molecular mechanism (in kcal/mole): 2-pentanone 59; methoxyacetone, 58; 2,4-pentanedione, 51; methyl butyrate, ≥ 70; 1-heptene, 54, and 4-methyl-1-hexene, 54–55.     

Gas-phase reactions of organic radicals and diradicals with ions

Reactions of polyatomic organic radicals with gas phase ions have been studied at thermal energy using a flowing afterglow-selected ion flow tube (FA-SIFT) instrument. A supersonic pyrolysis nozzle produces allyl radical (CH2CHCH2) and ortho-benzyne diradical (o-C6H4) for reaction with ions. We have observed: [CH2CHCH2 + H3O+ --> C3H6+ + H2O], [CH2CHCH2 + HO- --> no ion products], [o-C6H4 + H3O+ --> C6H5+ + H2O], and [o-C6H4 + HO- --> C6H3- + H2O]. The proton transfer reactions with H3O+ occur at nearly every collision (kII approximately with 10(-9) cm3 s(-1)). The exothermic proton abstraction for o-C6H4 + HO- is unexpectedly slow (kII approximately with 10(-10) cm3 s(-1)). This has been rationalized by competing associative detachment: o-C6H4 + HO- --> C6H5O + e-. The allyl + HO- reaction proceeds presumably via similar detachment pathways.     

Towards A qualitative rationalisation of the fragmentation reactions of organic negative molecular ions

A set of axioms is formulated which provides a means for the qualitative rationalization and prediction of the fragmentation modes of organic molecular anions.     

Revisiting falloff curves of thermal unimolecular reactions

Master equations for thermal unimolecular reactions and the reverse thermal recombination reactions are solved for a series of model reaction systems and evaluated with respect to broadening factors. It is shown that weak collision center broadening factors F(cent) (wc) can approximately be related to the collision efficiencies β(c) through a relation F(cent) (wc) ≈ max {β(c) (0.14), 0.64(±0.03)}. In addition, it is investigated to what extent weak collision falloff curves in general can be expressed by the limiting low and high pressure rate coefficients together with central broadening factors F(cent) only. It is shown that there cannot be one "best" analytical expression for broadening factors F(x) as a function of the reduced pressure scale x = k(0)∕k(∞). Instead, modelled falloff curves of various reaction systems, for given k(0), k(∞), and F(cent), fall into a band of about 10% width in F(x). A series of analytical expressions for F(x), from simple symmetric to more elaborate asymmetric broadening factors, are compared and shown to reproduce the band of modelled broadening factors with satisfactory accuracy.     

Metal ions dramatically enhance the enantioselectivity for lipase-catalysed reactions in organic solvents

We propose a simple and a powerful method to enhance the enantioselectivity for lipase-catalysed transformations in organic solvents by an addition of metal ion-containing water to the reaction mixture. In this paper, various metal ions such as LiCl or MgCl2 are tested to improve the enantioselectivity for the model reactions. The enantioselectivities obtained are dramatically enhanced, the E values of which are about 100-fold as compared with the ordinary conditions without a metal ion, for example, E = 200 by addition of LiCl. Furthermore, lowering the reaction temperature led to an almost perfect enantioselectivity of lipase in the presence of a metal ion, for example, E = 1,300 by addition of LiCl. Also, a mechanism for the drastic enhancement by metal ions is discussed briefly on the basis of the EPR spectroscopic study and the initial rate for each enantiomer of the substrate.     

Evaluation of unimolecular rate constants for some outer-sphere electrochemical reactions

Unimolecular rate constants, k_et (s^?1), and transfer coefficients, α_cet, for the outer-sphere electroreduction of several Co(III) ammine and ethylenediamine complexes have been evaluated by electrostatically adsorbing the reactants at silver electrodes coated with chloride or bromide monolayers. Sufficiently strong diffuse-layer adsorption is thereby produced so to enable k_cet and α_cet to be determined by means of linear sweep voltammetry, employing sufficiently fast sweep rates (10–100 V s^?1) and dilute reactant concentrations (≤ 50 μM) so that the bulk solution reactant contributes negligibly to the observed faradaic transients. Comparison with corresponding rate constants and transfer coefficients for the solution reactants enables the influence of precursor-state stability upon the latter rate parameters to be assessed.     

Angular momentum conservation in multichannel unimolecular reactions

A recently developed solution of the master equation for unimolecular and recombination reactions is extended to give new means for incorporating angular momentum (J) conservation in the fall-off regime for multichannel reactions. The calculated pressure dependence of a typical multichannel unimolecular dissociation reaction (thermal dissociation of 1-iodopropane) shows that if one of the channels has a transition state with a moment of inertia (I?) significantly different from that of the parent molecule (I) (e.g., a “simple-fission” type), neglect of angular momentum conservation causes the predicted branching ratio to be grossly in error at lower pressures. Specifically, if I? > I the rate coefficient is underestimated whereas if I? < I the rate coefficient is overestimated.     

Molecular beam measurements of small specific rate constants for unimolecular reactions

The investigation of unimolecular reactions with small rate constants is difficult owing to competing processes (inelastic collisions and bimolecular reactions) and the diffusion of reactant and product molecules out of the detection volume. For this reason, a new experimental approach for the measurement of specific rate constants in a molecular beam experiment has been exploited; instead of monitoring the temporal change of intensity as in a cell experiment, we monitor the spatial change along the molecular beam axis after laser excitation. For a given particle velocity the flight path between excitation and detection region defines the reaction time. By varying the distance the specific rate constant can be determined directly both from the decrease in the number density of reactant molecules as well as from the increase in product molecules. As a model system, the laser-induced (λ = 193 nm) photodissociation of mesitylene (trimethylbenzene) is studied. Previous experiments on the specific rate constant of mesitylene at this excitation energy differ between each other by about a factor of ten. By combining the new results with measurements at higher excitation energies, rate constants over a range of two orders of magnitude are now available for this reaction. The differences between the various experimental results are discussed within the framework of a statistical theory.     

A fitting formula for the falloff curves of unimolecular reactions,II: Tunneling effects

By taking into account effects of tunneling on the shape of the falloff curves of unimolecular reaction rate constants based on Troe's weak collision integral, a fitting formula for these curves is developed and then examined for several tunneling‐affected reactions. It is demonstrated that, compared to the widely used Troe's formula, the present expression not only substantially enhances the accuracy in fitting for tunneling‐affected reactions, but it is also computationally more efficient in its evaluation. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 31–42, 2011     

Modeling unimolecular reactions in photoelectron photoion coincidence experiments

A computer program has been developed to model and analyze the data from photoelectron photoion coincidence (PEPICO) spectroscopy experiments. This code has been used during the past 12 years to extract thermochemical and kinetics information for almost a hundred systems, and the results have been published in over forty papers. It models the dissociative photoionization process in the threshold PEPICO experiment by calculating the thermal energy distribution of the neutral molecule, the energy distribution of the molecular ion as a function of the photon energy, and the resolution of the experiment. Parallel or consecutive dissociation paths of the molecular ion and also of the resulting fragment ions are modeled to reproduce the experimental breakdown curves and time‐of‐flight distributions. The latter are used to extract the experimental dissociation rates. For slow dissociations, either the quasi‐exponential fragment peak shapes or, when the mass resolution is insufficient to model the peak shapes explicitly, the center of mass of the peaks can be used to obtain the rate constants. The internal energy distribution of the fragment ions is calculated from the densities of states using the microcanonical formalism to describe consecutive dissociations. Dissociation rates can be calculated by the RRKM, SSACM or VTST rate theories, and can include tunneling effects, as well. Isomerization of the dissociating ions can also be considered using analytical formulae for the dissociation rates either from the original or the isomer ions. The program can optimize the various input parameters to find a good fit to the experimental data, using the downhill simplex algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Energy transfer in unimolecular reactions at high temperatures

The application of modern theories of energy transfer to unimolecular reactions taking place at very high temperatures is discussed. It is shown that the efficiency of energy transfer for both reactant–reactant and reactant–inert diluent collisions may be substantially smaller than the values determined experimentally at lower temperatures. Consequently at high temperatures unimolecular falloff effects, particularly in some shock-tube measurements, may be greater than has been believed hitherto. The application of these calculations to the unimolecular reactions of cyclopropane, cyclobutane, and cyclohexene at temperatures around 1300°K is discussed, and it is shown that under shock-tube conditions the apparent first-order rate coefficient may be at least ten times less than the high-pressure limiting value.     

Electron-impact-induced rearrangements of organic ions VIUnimolecular reactions of isomeric[C8H9]+ions

Metastable ion spectra and deuterium labelling have been used to investigate a series of gaseous [C₈H₉]+ ions of isomeric structures. The similarity of the intensities of their metastable loss of hydrogen, acetylene and ethylene molecules and metastable reactions of specifically labelled ions, suggests that the [C₈H₉]+ reacting ions, formed initially with different structures, isomerise to a common structure or mixture of structures via deep-seated rearrangement reactions which render all hydrogen atoms equivalent. The isomerisation process involved is controlled by a conversion of a vinyl bond into an allyl-type bond, thus destroying the aromatic moiety.