Direct Calculation of Reaction Rates

We test several approximate theories of thermal rate constants against accurate quantal equilibrium rate constants for collinear bimolecular reactions governed by given potential energy surfaces. The systems considered are F+H2 and F+D2 for the Muckerman potential energy surface no. 5 at 200–1200 K and H+F2, D+F2, and T+F2 for potential surface II of Jonathan, Okuda, and Timlin at 233–1260 K. For F+H2, conventional transition state theory overestimates the accurate rate constant by factors of 2.9–3.4, with the largest errors at the lowest and highest temperatures. Vibrationally adiabatic transmission coefficients or variational transition state theory decrease the error to factors of 1.2–1.3 at the lowest temperature and to a factor of 3.2 at the highest temperature. The unified statistical model reduces the errors to a factor of 1.1 at the lowest temperature and a factor of 2.7 at the highest temperature. For F+D2 the trends are similar but the errors in all the methods are smaller at all temperatures. For H+F2 conventional transition state theory underestimates the rate constants by a factor of 0.56 at the lowest temperature with the error decreasing to 2% at the highest temperature. Various formulations of vibrationally adiabatic transmission coefficients, in conjunction with either conventional or variational transition state theory, reduce the error to factors of 0.84–0.96 at the lowest temperature while not destroying the good agreement at the highest temperature. The unified statistical theory seems to overestimate the recrossing correction for this reaction, though only by about 10%. The results are similar for D+F2 and T+F2 except that the low-temperature underestimates of the calculations without tunneling are not as severe. The best theory, improved canonical variational theory with the Marcus–Coltrin path semiclassical adiabatic ground-state transmission coefficient, reproduces the accurate quantal results for H+F2, D+F2, and T+F2 within 5% or better in every case for the whole temperature range.

Reactions of β-hydroxypropyl radicals with O2 on the HOC3H6OO• potential energy surfaces: A theoretical study

In the present work, the reaction mechanisms for thermal decomposition of cyclohexane in the gas phase have been investigated using quantum chemical calculations and transition-state theory. Three series of reaction schemes containing 38 elementary reactions are proposed. The geometry optimization and vibrational frequencies of reactants, transition states, and products are determined at the BH&HLYP/cc-pVDZ level, while energies are calculated at the CCSD(T)/cc-pVDZ level. The rate constants for the reactions without transition states, including the initial steps of cyclohexane decomposition (C–C bond scission or C–H bond scission), are obtained by the canonical variational transition-state theory (CVT), while the rate constants for the other reactions with saddle-point transition states are obtained by the conventional transition-state theory (TST) in the temperature range of 300–3000 K. The rate constants are in good agreement with data available from the literature. The kinetic parameters in the modifi...

The kinetics of chemical reactions characterizes the rates of chemical processes, i.e. distribution of all reactants, intermediates and products over time. This information is of vital importance for all areas of chemistry: chemical technology to control organic or inorganic syntheses, chemical construction of nanomaterials, as well as for the investigation of biochemical processes. The chemical kinetics data provide a possibility to investigate the effect of different chemical, physical and environmental factors on the rate of a reaction, final products and by-products distribution, and even the direction of a chemical process. In the first part of the chapter the general introduction to the kinetics of chemical reactions is given. The classical kinetics of chemical reactions uses the outcome from experimental measurement of reaction rates. However, currently available reliable computational ab initio methods provide an alternative efficient way for estimation of the rate constants even for stepwise and multidirectional reactions. Another benefit of the computational investigations is the possibility to simulate a wide range of processes with duration from picoseconds to hours, days, or even for much longer time scales. Contemporary ab initio methods have been used for estimation and prediction of reaction rates for a number of different chemical reactions. Until recently most of the theoretical studies on kinetic parameters have not been extended beyond the calculations of the rate constants of chemical reactions. In the present review we describe the simulation of the chemical kinetics of proton transfer (tautomerization) in nucleic acid bases and their complexes with metal ions, also in the presence of water molecules. The considered models are based on the ab initio calculated rate constants of chemical reactions. Then, such predicted rate constants are used for further kinetic simulations. Biological consequences of investigated processes are also discussed.KeywordsChemical reactivityGas-phase experimentsNucleobasesLaser desorptionTautomerizationPoint mutations

A variant of the Kac-Zwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a double-well external potential and coupled to N free particles through linear springs. While the Kac-Zwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a two-state Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems.

Variational transition state theory is a powerful tool for tackling the problem of activated barrier crossing in condensed phases, enabling the exact reduction of infinite-dimensional problems to much more tractable few-dimensional problems. Variational transition state theory may be used to go beyond Kramers’ theory and consider the effects of memory friction and solute nonlinearities on the rate of barrier crossing. In addition, since variational transition state theory is a Hamiltonian based formalism, it is not tied to the limitations of generalized Langevin equation dynamics; thus it can be used to treat nonlinear solute-solvent interactions. Other recent advances include the development of new formalisms for improved optimization of the transition state dividing surface, the incorporation of intramolecular solute modes, and the development of centroid-based quantum transition state theory analogs.

Transition state theory (TST) is revisited, as well as evolutions upon TST such as variational TST in which the TST dividing surface is optimized so as to minimize the rate of recrossing through this surface and methods which aim at computing dynamical corrections to the TST transition rate constant. The theory is discussed from an original viewpoint. It is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be well-separated metastable sets corresponding to long-lived conformation states (as necessary to obtain the actual transition rate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient kappaS of the TST dividing surface are given, and it is shown that the relative error on kappaS scales as 1/square root(kappaS) when kappaS is small. This implies that dynamical corrections to the TST rate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient kappaS which is not too small. In particular, the TST dividing surface must be optimized upon (for otherwise kappaS is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum kappaS, but this coefficient may still be very small).

We have carried out ab initio calculations for the reaction OH+CH4→H2O+CH3 using second-order Mo/ller–Plesset perturbation theory, employing a very large basis set and scaling all correlation energy for the final energy calculation, but optimizing the equilibrium and transition state structures without scaling (MP-SAC2//MP2). We found that inclusion of correlation energy has an important effect on the geometry, barrier height, and vibrational frequencies of the transition state. The final calculated values for the forward and reverse classical barrier heights are 7.4 and 20.6 kcal/mol, respectively. We have used these with interpolated canonical variational transition state theory and the centrifugal-dominant small-curvature tunneling approximation, including information at the reactants, products, transition state, and two other points along the minimum energy path, to predict the rate constants for the above reaction in the temperature range from 223 to 2400 K. The calculated rate constants agree well with experiment over a wide temperature range.

Four implicit potential energy surfaces (PESs) with specific-reaction-parameters (SRP) are developed and tested for the reaction CH4+H→CH3+H2. The first is called MPW60 and is based on the modified Perdew–Wang hybrid density-functional method with the percentage of the Hartree–Fock exchange equal to 60%. The other three PESs are constructed with multi-coefficient correlation methods (MCCMs). The second is called MCOMP2-SRP, and the third is called MC-QCISD-SRP. Both of them are parametrized for this specific reaction by starting with their corresponding global parameters. The fourth is called MCG3-SRP and is based on the MCG3-CHO semiglobal parametrization with further refinement for this specific reaction. All four SRP surfaces have a classical forward barrier height of 14.8 kcal/mol, and all three MCCM SRP surfaces have a classical endoergicity of 3.3 kcal/mol. The stationary point geometries, vibrational frequencies, and zero-point-energies are reported for several standard single-level methods and MCCMs with global parameters as well as for the four new SRP surfaces. Direct dynamics calculations are carried out using variational transition state theory with multidimensional tunneling contributions on the proposed SRP surfaces. We calculate forward reaction rate constants for the title reaction from 250 to 2400 K and compare them with the latest re-analyzed experimental results over the temperature range from 348 to 1950 K. The calculated rate constants using canonical variational theory with the small-curvature tunneling approximation carried out on the MPW60, MC-QCISD-SRP, and MCG3-SRP surfaces show good agreement with the experimental results.

It is shown that there occur dispersion and absorption of sound owing to chemical reaction in a liquid which is in general chemical equilibrium aA+bB+···[open phi]qQ+rR+···. From the acoustic characteristic equation, the velocity and the absorption coefficient of sound are derived, and the characteristics of the dispersion and absorption curves are examined. The velocity and the absorption coefficient of sound in liquid are derived in terms of the density, the static isothermal compressibility, the thermal expansion coefficient, the partial molar volume, the equilibrium constant, that is, the composition, the reaction heat at constant volume, the molar heat at constant volume, and the rate constant of chemical reaction. By measuring the velocity and the absorption of sound, it is possible to determine the rate constant of chemical reaction, the reaction heat, and the volume change. The application to solutions, especially to electrolyte solutions is shown, and in this case the activity coefficients may be used. As special cases, chemical reactions which are not accompanied by reaction heat or volume change are treated, and the results of Freedman and Manes are compared with the present one, and the differences are pointed out. Several examples of the general formulas are shown. Since it is easy to increase the frequency of sound, the method of measuring the velocity and the absorption coefficient of sound is adequate for determining the rate of a very fast reaction in the equilibrium state.

Analytic continuation of real-time correlation functions to obtain thermal rate constants for chemical reaction

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe Effect of Pressure on the Rate and Equilibrium Constants of Chemical Reactions. The Calculation of Activation Volumes by Application of the Tait EquationSidney W. Benson and Jerome A. BersonCite this: J. Am. Chem. Soc. 1962, 84, 2, 152–158Publication Date (Print):January 1, 1962Publication History Published online1 May 2002Published inissue 1 January 1962https://doi.org/10.1021/ja00861a005RIGHTS & PERMISSIONSArticle Views299Altmetric-Citations34LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (725 KB) Get e-Alerts Get e-Alerts

Canonical variational transition state theory, microcanonical variational transition state theory, and Miller's unified statistical theory were used in an attempt to correct two major deficiencies of the conventional transition state theory. These are: (1) the necessity of extra assumptions to include quantum mechanical tunneling effects and (2) the fundamental assumption that trajectories crossing a dividing surface in phase space proceed directly to products. The accuracy of these approximate methods were tested by performing calculations for several collinear reactions of hydrogen, deuterium, chlorine, or iodine, with five isotopes of hydrogen molecules and comparison of these results with those from accurate quantitative calculations of the reaction probabilities as functions of energy and of the thermal rate constants as functions of temperature. 49 references, 28 figures, 17 tables.

The large-curvature ground-state model for the transmission coefficient of generalized transition state theory [presented in a previous paper by B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400(1983)] is tested against accurate quantal calculations of the rate coefficients for collinear reactions with very large inertial effects, namely Cl+HCl→ClH+Cl, Cl+DCl→ClD+Cl, and Cl+MuCl→ClMu+Cl. The tests cover the temperature range 200–2400 K. The accurate rate calculations are based on reaction probabilities obtained by a new numerical method for solving Schrödinger’s equation in Delves’ coordinates. Improved canonical variational transition state theory predicts rate coefficients 5.0–18 times smaller than those predicted by conventional transition state theory for the H transfer; for the D transfer, the ratio is 2.0–3.4; and for Mu it is 22–2.8×107. The large-curvature model predicts transmission coefficients as large as 41, 8, and 206 for the H, D, and Mu-transfer cases at 200 K, decreasing to 1.2, 1.1, and 1.4 at 2400 K. Despite the large effect of variationally optimizing the transition state location and the large size of the tunneling effect and the wide variation of both effects with temperature, improved canonical variational transition state theory with large-curvature ground-state transmission coefficients (ICVT/LCG) is accurate within a factor of 1.7 over a temperature range of a factor of 8, 300–2400 K, for all three reactions. At 200 K, the ICVT/LCG model underestimates the rate coefficients, by factors of 2.3, 1.9, and 1.5 for H, D, and Mu, respectively.