A method for computer analysis of kinetics of competing first- and second-order reactions

Competing first- and second-order reactions of transient molecular species (e.g., triplet states and free radicals) are a common occurrence in kinetic studies such as flash photolysis and pulse radiolysis. We have developed a method for analyzing the decay kinetics of any species (Y) whose disappearance is described by ?dY/dt = k₁Y + k₂Y². The computer program (written in time-sharing BASIC) employs an iterative technique to obtain the least-squares estimates of the three parameters in the integrated rate equation.     

Kinetics of the thermal gas phase isomerization of bicyclo[4.1.0]heptane

The kinetics of the gas-phase decomposition of bicyclo[4.1.0]heptane has been studied over the temperature range of 708–769 K at pressures between 1 and 17 torr. Isomerization to 1-methylcyclohex-1-ene, methylenecyclohexane, and cycloheptene accounts for 96–98% of the primary reaction products and occurs by first-order, homogeneous, nonradical processes.      

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Theoretical calculation of rate constants for the thermal isomerization from 1,2-butadiene to 1,3-butadiene

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Understanding supported reactions in spherical compartments: a general algorithm to model and determine rate constants, diffusion coefficients, and spatial product distributions

A general algorithm allowing the numerical modeling of the time and space dependence of product formation in spherical reaction volumes is described. The algorithm is described by the complete set of mass balance equations. On the basis of these equations, the effects of the diffusion coefficient, reaction rate, bead size, reagent excess, and packing density of the resin beads on the overall reaction rates are determined for second-order reactions. Experimental data of reaction progress are employed to calculate reaction rates and diffusion coefficients in polymer-supported reactions. In addition, the conditions for shell-like product formation are determined, and various strategies for the radial patterning of resin beads are compared. The effect of diffusion on polymer-supported enzyme-catalyzed reactions of the Michaelis-Menten type is treated, as well. Finally, the effects of typical nonideal solid-phase phenomena, namely, the inhomogeneity of rate constants and the concentration dependence of diffusion coefficients, on overall rates are discussed.     

A differential modification of the thermal maximum method for evaluating the enthalpies and rate constants of homogeneous reactions

Both the change of enthalpy associated with a reaction and the rate constant of the reaction can be found from the dependence on time of the difference between the temperatures of a reaction mixture and a reference solution contained in identical non-insulated vessels submerged in a thermostat. Heats of dilution and fluctuations of the temperature of the thermostat are cancelled by the differential arrangement, and the heat-transfer constant for the reaction vessel need not be known or measured separately, which is an important advantage over the classical thermal maximum method. For half-times between about 9 and 30 s and overall changes of temperature between 25 and 90 mK, relative standard deviations of a few per cent in both ΔH and k are easily attainable.     

Kinetics of some reactions of vinyl and isopropyl radicals in the gas phase

Vinyl and isopropyl radicals were generated by the pyrolysis of azoisopropane in the presence of acrolein at 473–563 K. Reaction products were analyzed by gas chromatography. Rate constant ratios k₂/k₁ = 0.02 ± 0.01 and k₄/k₃ = 0.01 ± 0.005 are suggested for the following reactions: The rate constant ratio of reactions (7) and (c) obeys the Arrhenius equation The Arrhenius equation was derived for (k₈ + k₉).     

The thermal decomposition of diimide in the gas phase: Kinetics and stoichiometry

The kinetics and stoiehiometry of the decomposition of N₂H₂ and N₂D₂ have been studied as a function of sample size, pressure, and temperature. The reaction follows a single first order kinetic expression over most of its time course. It is suggested that the rate-determining step in the mechanism is a first-order homogeneous gas-phase isomerization of trans-diimide with rate constants:k = 1.8 exp (-4.2 kcal/mol/RT) sec^?1 and k = 1 exp (-4.4 kcal/mol/RT) sec^?1. The detailed mechanism of this isomerization, however, is not evident. At temperatures above room temperature, self-heating has been observed which leads to an initial fast decay. At room temperature the reaction exhibits autocatalysis with the rate increasing as the reaction proceeds. This has been attributed to enhancement by a surface decay process involving adsorbed hydrazine. The only significant products from the decomposition of N₂H₂ are N₂, H₂, and N₂H₄, and the results are interpreted in terms of two parallel reactions: The decomposition of N₂D₂ occurs almost completely by the single reaction giving N₂ + N₂D₄. No azide formation has been detected from either N₂D₂, or N₂D₂, and limits have been put on the yield of ammonia. Extinction coefficients at 365 nm of 3.9 ± 0.2 for N₂H₂ and 3.3 ± 0.1 for N₂D₂ have been measured. Both the rate of decay and the stoichiometry of products show pressure dependence below 150 torr, and this is suggested to be due to direct decomposition of cis-N₂H₂ on the surface.     

Deuterium kinetic isotope effects and mechanism of the thermal isomerization of bicyclo[4.2.0]oct-7-ene to 1,3-cyclooctadiene

The thermal conversion of cis-bicyclo[4.2.0]oct-7-ene to cis,cis-1,3-cyclooctadiene might involve a direct disrotatory ring opening, or it might possibly take place by way of cis,trans-1,3-cyclooctadiene. This cis,trans-diene might possibly form the more stable cis,cis isomer through a [1,5] hydrogen shift or a trans-to-cis isomerization about the trans double bond. Deuterium kinetic isotope effect determinations for the isomerizations of 2,2,5,5-d(4)-bicyclo[4.2.0]oct-7-ene and 7,8-d(2)-bicyclo[4.2.0]oct-7-ene rule out these two alternatives because the observed effects are much smaller than would be anticipated for these mechanisms: k(H)/k(D)(d(4)) at 250 degrees C is 1.17 (1.04 per D), and k(H)/k(D)(d(2)) at 238 degrees C is 1.20 (1.10 per D). The direct disrotatory ring opening route remains the preferred mechanism.     

Kinetics of partly diffusion-controlled reaction XXI: A simple algorithm for computing the apparent rate of reaction

Starting from Smoluchowski's hypothesis, a simple algorithm is developed in order to obtain the apparent rate constant at large values of time, t, with some physical and chemical processes, as in the case of diffusion controlled reactions. Some practical examples are illustrated, assuming nonuniform distribution function, space-dependent diffusion coefficient or short-range interaction leading to an asymptotic analytical expression of the form α + β/√t, where α and β are constants function of the system of interest.     

Kinetics and mechanism of the thermal decomposition reaction of acetone cyclic diperoxide in the gas phase

The kinetics of the thermal decomposition reaction of gaseous 3,3,6,6-tetramethyl-1,2,4,5-tetroxane (ACDP) in the presence of n-octane was studied in the 403.2–523.2 K temperature range. This reaction yields acetone as the organic product. Under optimum conditions, first-order kinetics were observed, included when the S/V ratio of the Pyrex reaction vessel was increased by a nearly six-fold factor. In the range 443.2–488.2 K the temperature dependence of the rate constants for the unimolecular reaction in conditioned vessels is given by In k₁/(s^?1) = (31.8 ± 2.5) ? [(39.0 ± 2.5)/RT]. The value of the energy of activation in kcal/mol correspond to one O? O bond homolysis of the ACDP molecule in a stepwise biradical initiated decomposition mechanism. At the lower reaction temperatures as well in preliminary experiments participation of a surface catalyzed ACDP decomposition process could be detected. © 1994 John Wiley & Sons, Inc.     

Kinetics and mechanism of the thermal reactions of endo- and exo-5-cyanobicyclo[2.2.2]oct-2-ene and methyl-substituted derivatives in the gas phase

The thermal reactions of endo- and exo-5-cyanobicyclo-[2.2.2]oct-2-ene and their trans- and cis-6-methyl-substituted derivatives have been investigated in the gas phase between 518 and 630 K. Each product decomposes by two parallel first-order retro-Diels-Alder reactions, a main one with formation of cyclohexa-1,3-diene and a minor one with elimination of ethene. Slight isomerizations are also observed. The kinetic results can be explained in terms of a biradical mechanism. The rate-determining step is shown to depend on the amount of resonance energy in the biradical. Heats of formation and entropies of the bicyclo[2.2.2]oct-2-enes studied are estimated.     

Computational study of the reactions of methanol with the hydroperoxyl and methyl radicals. 2. Accurate thermal rate constants

Multistructural canonical variational-transition-state theory with multidimensional tunneling (MS-CVT/MT) is employed to calculate thermal rate constants for the abstraction of hydrogen atoms from both positions of methanol by the hydroperoxyl and methyl radicals over the temperature range 100-3000 K. The M08-HX hybrid meta-generalized gradient approximation density functional and M08-HX with specific reaction parameters, both with the maug-cc-pVTZ basis set, were validated in part 1 of this study (Alecu, I. M.; Truhlar, D. G. J. Phys. Chem. A2011, 115, 2811) against highly accurate CCSDT(2)(Q)/CBS calculations for the energetics of these reactions, and they are used here to compute the properties of all stationary points and the energies, gradients, and Hessians of nonstationary points along each considered reaction path. The internal rotations in some of the transition states are found to be highly anharmonic and strongly coupled to each other, and they generate multiple structures (conformations) whose contributions are included in the partition function. It is shown that the previous estimates for these rate constants used to build kinetic models for the combustion of methanol, some of which were based on transition state theory calculations with one-dimensional tunneling corrections and harmonic-oscillator approximations or separable one-dimensional hindered rotor treatments of torsions, are appreciably different than the ones presently calculated using MS-CVT/MT. The rate constants obtained from the best MS-CVT/MT calculations carried out in this study, in which the important effects of corner cutting due to small and large reaction path curvature are captured via a microcanonical optimized multidimensional tunneling (μOMT) treatment, are recommended for future refinement of the kinetic model for methanol combustion.     

A simple method relating specific rate constants k(E,J) and Thermally averaged rate constants k(infinity)(T) of unimolecular bond fission and the reverse barrierless association reactions

This work describes a simple method linking specific rate constants k(E,J) of bond fission reactions AB --> A + B with thermally averaged capture rate constants k(cap)(T) of the reverse barrierless combination reactions A + B --> AB (or the corresponding high-pressure dissociation or recombination rate constants k(infinity)(T)). Practical applications are given for ionic and neutral reaction systems. The method, in the first stage, requires a phase-space theoretical treatment with the most realistic minimum energy path potential available, either from reduced dimensionality ab initio or from model calculations of the potential, providing the centrifugal barriers E(0)(J). The effects of the anisotropy of the potential afterward are expressed in terms of specific and thermal rigidity factors f(rigid)(E,J) and f(rigid)(T), respectively. Simple relationships provide a link between f(rigid)(E,J) and f(rigid)(T) where J is an average value of J related to J(max)(E), i.e., the maximum J value compatible with E > or = E0(J), and f(rigid)(E,J) applies to the transitional modes. Methods for constructing f(rigid)(E,J) from f(rigid)(E,J) are also described. The derived relationships are adaptable and can be used on that level of information which is available either from more detailed theoretical calculations or from limited experimental information on specific or thermally averaged rate constants. The examples used for illustration are the systems C6H6+ <==> C6H5+ + H, C8H10+ --> C7H7+ + CH3, n-C9H12+ <==> C7H7+ + C2H5, n-C10H14+ <==> C7H7+ + C3H7, HO2 <==> H + O2, HO2 <==> HO + O, and H2O2 <==> 2HO.     

Structure and isomerization of arenonium ions of dichlorobenzenes in the gas phase. A theoretical study

Ab initio MP2 calculations of all isomeric arenoium ions (AI) ofortho-, meta-, andpara-dichlorobenzenes in the gas phase were carried out with full optimization of geometry with the 6–31 G^* basis set. The calculated proton affinities depend substantially on the position of geminal center in the corresponding dichlorobenzenonium ion and decrease in the series 1,2-dichloro-4H-benzenonium>1,2-dichloro-3H-benzenonium>1,2-dichloro-2H-benzenonium; 1,3-dichloro-4H-benzenonium>1,2-dichloro-3H-benzenonium >1,3-dichloro-5H-benzenonium>1,3-dichloro-3H-benzenonium; 1,4-dichloro-2H-benzenonium >1,4-dichloro-4H-benzenonium. The structures of transition states and activation energies (E _a) of almost all 1,2-shifts of H and Cl atoms in Al were determined. The activation energies of migrations of H atoms are about 6 kcal mol⁻¹ less than those of migrations of Cl atoms in similar structures. The isomerization routes and relations between the rate constants for isomerization of dichlorobenzenes through Al were established. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1726–1731, September, 1998.