Estimation of the rate constants of second order reactions using mean centering of ratio spectra

A new application of the mean centering of ratio spectra method is proposed for estimation of the rate constants of second order reactions, using kinetic-spectrophotometric data. The method is based on the mean centering of the ratio spectra to obtain a kinetic profile of the product. Using computational fitting, the rate constant can be obtained without any ambiguity. An interesting feature of second-order reactions is that the number of steps in the reaction is less than the number of absorbing species, resulting in a rank-deficient response matrix. Through using row mean centering of ratio spectra, the pure response of the product of the reaction could be obtained, and thus an accurate estimation of rate constant would be possible. The applicability of the method was evaluated by using several model data. The reaction of 1,2-naphthoquinone-4-sulfonate sodium (NQS) and 3-nitroaniline (TNA) in ethanol as a real system was also studied applying the proposed method.     

A priori rate constants for kinetic modeling

The advent of computer-aided methods for constructing detailed kinetic models of multicomponent reacting systems provides fresh motivation for the development of efficient and accurate methods for estimating rate constants. There is now the real likelihood that a priori rate estimates, formerly of primarily academic interest, could directly impact major public policy and business decisions. This opportunity brings many challenges. The process of building a computer model for a real-world system can require hundreds of thousands of rate estimates, making most existing rate calculation techniques impractical. Also, the demands for tight error bars on model predictions used to make major decisions often imply levels of accuracy unachievable with existing rate calculation techniques. Past and recent progress towards developing fast and accurate rate estimates is selectively reviewed, and our methodology is outlined. New rate estimates for several types of reactions involving O and HO₂ are presented. Several technical issues requiring further work by the theoretical chemistry community are highlighted. Electronic supplementary material to this paper can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00214-002-0368-4. Received: 6 February 2002 / Accepted: 2 June 2002 / Published online: 2 October 2002 Acknowledgements. This work was partially supported by the National Computational Science Alliance under Grant CTS010006 N and utilized the Origin 2000 High-performance Computing and UniTree Mass Storage systems. We are grateful for financial support from the EPA Center for Airborne Organics, the NSF CAREER program, Alstom Power, Dow Chemical, and the Office of Basic Energy Science, U.S. Department of Energy through grant DE-FG02-98ER14914. The authors acknowledge the contribution of Hans-Heinrich Carstensen in the initial stages of this work. Correspondence to: W.H. Green Jr. e-mail: whgreen@mit.edu Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00214-002-0368-4     

The ratio of the rate constants for H atom abstraction and β-cleavage for bis-oxyisopropylidene biradical

The relative reactivity of bis-oxyisopropylidene biradical ‘OCMe₂O’ generated upon homolysis of the O−O bond of dimethyldioxirane was characterized by the ratio of the rate constants for H atom abstraction and β-cleavage:k ₃ /k ₂ =0.23±0.06 L mol⁻¹ (314 K). Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1321–1323, July, 1998.     

A desk computer program for the calculation of rate constants

A desk computer program has been written in BASIC programming language to optimize the values of rate constants determined from kinetic measurements of time and concentration data. The program is capable of the simultaneous refinement of a maximum of 5 rate constants. A FORTRAN version using the Gear method is also available.

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Determination of the elementary reaction rate constants on the basis of the summary values of the rate constants

Conclusions The rate constants of reactions of atomic oxygen with methane, ethane, ethylene, and propylene along different pathways were determined on the basis of the ratios between the concentrations of the products formed and the summary rate constants measured earlier.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2693–2699, December, 1971.     

SACM/CT Study of the dissociation/recombination dynamics of hydrogen peroxide on an ab initio potential energy surface. Part II. Specific rate constants k(E,J), thermal rate constants k infinity(T), and lifetime distributions

Statistical adiabatic channel model/classical trajectory (SACM/CT) calculations of the dissociation/recombination dynamics of hydrogen peroxide, H(2)O(2) <--> 2HO, have been performed on an ab initio potential energy surface by Kuhn, Rizzo, Luckhaus, Quack, and Suhm (J. Chem. Phys. 1999, 111, 2565). Specific rate constants k(E,J), thermal rate constants k(infinity)(T), and lifetime distributions are determined. After averaging over J, the derived k(E,J) are in quantitative agreement with non-exponential time-profiles of HO formation recorded after overtone excitation of H(2)O(2) near the dissociation threshold by Scherer and Zewail (J. Chem. Phys. 1987, 87, 97). The thermal high pressure rate constants for HO recombination agree with experimental data as well and can be represented by k(rec,infinity)/10(-10) cm(3) molecule(-1) s(-1) approximately [0.376 (298 K/T)(0.47) + 0.013 (T/298 K)(0.74)] over the range 60-1500 K. Non-statistical lifetime distributions are suggested not to have been of major relevance for the available experiment.     

A time-dependent method for computing thermal rate constants

Presented is an efficient numerical method for computing thermal rate constants for quantum systems with few, localized degrees of freedom. The starting point is the work of Miller, Schwartz and Tromp in which the rate constant is expressed in terms of an equilibrium flux-flux correlation function. The correlation function can be calculated very efficiently by using a combination of discrete momentum and coordinate representation. This saves time by replacing the matrix multiplications normally involved in evaluating propagators with fast Fourier transforms.     

On reaction rate constants and rate kernels

A simple model for a reversible isomerization reaction A ? B is used to show how rate constants and their time-dependent generalizations can be related to microscopic reactive steps and nonreactive internal dynamics (e.g., vibrational relaxation).     

Analyzing the uniqueness of the rate constants calculated from complex kinetic systems: A study of the hydrolysis of ciclohexanecarbonitriles

In this article, a novel methodology for the study of complex reaction mechanisms is explored, and applied to the kinetic analysis of the hydrolysis reactions of ciclohexanecarbonitriles. The kinetic data were first analyzed with the help of classic linear techniques. Subsequently, the determination of the rate constants by a non‐linear, least‐squares (LS) fitting method, followed by a novel eigenvalue‐eigenvector analysis of the sensitivity coefficients, permitted us to obtain the maximum possible information from the kinetic data. The non‐linear, LS‐fitting method, carried out by means of a new version of OPKINE program, allowed the calculation of all the rate constants of the mechanism; in addition, the sensitivity analysis permitted us to establish the uniqueness and reliability of calculated rate coefficients. Finally, the results of the sensitivity analysis were tested by means of a simulation procedure, and the results compared to those obtained from classic linear methods. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 611–626, 1999.     

Thermal dissociation and recombination of alkyl and haloalkyl peroxynitrates: An SACM modelling study

Recent experimental results on the thermal decomposition and the reverse recombination of alkyl and haloalkyl peroxynitrates are modelled with an SACM formalism. The molecules RO₂NO₂ with R = CH₃, CF₃, CF₂Cl, CFCl₂, CCl₃, and C₂H₅ are considered. Detailed and simplified reduced falloff expressions are compared. Limiting low (??_o) and high pressure (??_x) rate constants, such as derived from a fit of these falloff expressions to the experiments, are compared with absolute predictions, based on general knowledge about energy transfer (〈ΔE〉 in ??_o) and on a recently proposed simple SACM estimate for ??_x. The analysis also allows for a derivation of the bond energies of the mentioned molecules.     

Calculations of the rate constants of elementary reactions

Russian Chemical Bulletin -     

A novel method for calculating rate constants of diffusion-influenced reactions

In the present work we suggest a method for calculating rate constants of chemical processes affected by mobility of reactants. The method is based on the encounter theory. Unlike the widely accepted model of collision complexes it provides a general formal solution for practically arbitrary reaction scheme.     

On the propagation rate constants of cationic polymerizations

The concepts employed to explain polymerizations by ionizing radiations are used for a critical examination of the concepts involved in interpreting the kinetics of chemically initiated cationic polymerizations. It is explained how the interactions of the propagating carbenium ions with the solvent, monomer, and anion can result in the formation of up to six distinct unpaired species and several kinds of ion pairs; therefore, the consumption of the monomer can be governed simultaneously by many rate constants. Only one of these can have any general theoretical use, and suggestions are made for how it can be measured. For the first time, it is shown that the ion‐pairing process must involve a ligand displacement and so resembles the amination of the Ag⁺ ion, for example, in an aqueous solution by NH₃, rather than an association of inert ions of unchanging identity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2537–2544, 2002     

Evaluation of the rate constants in chemical reactions

This article is concerned with the application of a new method to recover the rate constants in chemical reactions. The method is based on treating the unknown parameters as time dependent. With appropriate experimental data the unknown rate constants are guided from an arbitrary initial condition to their true value at a final time. An explicit equation describing the time evolution of the parameters is obtained by minimizing the error along the trajectory. The method leads to an iterative algorithm which is described in detail. Numerical results with the method indicate that accurate estimates of the rate constants can be obtained directly from experimental data. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 151–159, 1998.     

Theoretical calculations of the unimolecular canonical rate constants

Microcanonical rate constants k(E) and canonical rate constants k(T) for unimolecular reactions have been obtained through the calculations of cumulative reaction probabilities N(E) with the unsymmetrical Eckart potential tunneling correction. By way of example, the reactions HCN→CNH (I) and FNC→NCF (II) have been employed. For reaction (I), the calculated rate constants are in agreement with the experimental data; for reaction (II), the results are in accordance with the rate constants kCVT/MEPSAG(T) calculated by the common program POLYRATE.     

Third-order rate constants of atmospheric importance

Input data and results are presented for the calculation of a number of third-order rate constants of atmospheric interest using Troe′s approximate method. A comparison with experimental data indicates that this approach provides a reliable method for predicting unknown rate constants and estimating temperature dependences. These calculations form the basis of the recommendations of the NASA review panel for third-order rate constants to be used in atmospheric modeling.     

The load dependence of rate constants

As experimental techniques in biophysics have progressed at the single molecule level, there has been considerable interest in understanding how external mechanical influences (such as load) affect chemical reactions. The majority of biophysical studies investigating load-dependent kinetics use an equation where the rate constant exponentially depends on force, which is sometimes called Bell's equation. This equation requires the determination of two parameters that describe the potential energy-strain function: k(0), which is the reaction rate in the absence of load, and x(c), which is the difference in strain between the reactant and transition states. However, there have been theoretical studies based on Kramers' theory suggesting that the rate constant should have load-dependent pre-exponential terms and nonlinear load-dependent terms in the exponential. Kramers' theory requires an exact knowledge of the potential energy-strain function, which is in general not known for an experimental system. Here, we derive a general approximation of Kramers' theory where the potential energy-strain function is described by five parameters, which can, for small loads, be reduced to four-, three-, and finally to two parameters (Bell's equation). We then use an idealized physical system to validate our approximations to Kramers' theory and show how they can predict parameters of interest (such as k(0) and x(c)) better than Bell's equation. Finally, we show previously published experimental data that are not well fitted by Bell's equation but are adequately fitted by these more exact equations.     

Temperature dependence of the rate constants of cryochemical reactions

The temperature dependence of the reaction rate constant for tunneling transfer of an atomic particle in solid near absolute zero was studied. Different mechanisms describing the temperature dependence were considered: reorganization of the medium, modulation of parameters of the potential barrier, and under-barrier friction. It was established that for the rate constant (K) at low temperatures the equation InK=InK ₀+C ₄ T ⁴+C ₅ T ⁵+C ₆ T ⁶+C ₈ T ⁸ is valid. Experimental data were compared with the theory. A good agreement is achieved when the quantum nature of the hydrogen crystal is applied under the assumption of a predominant role of reorganization of the medium. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1906–1914, October, 1999.