On the errors of Arrhenius parameters and estimated rate constant values

Héberger, Károly; Kemény, Sándor; Vidóczy, Tamás

doi:10.1002/kin.550190302

Cited by 70 publications

(49 citation statements)

References 8 publications

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“…First, if the relative weights (ratios) are statistical or instrumental, the magnitudes of the deviations should reflect the experimental errors. When this is true, the value of the reduced chi-squared, 2 divided by the number of degrees of freedom, will be near unity. In this situation, the deviations are said to be internally consistent and they may be used without modification.…”

Section: Chi-squared Minimizationmentioning

confidence: 95%

“…After experiments have been performed, the best-fit values of the independent parameters are generally determined by minimizing the chi-squared merit function, 2 (a), defined by…”

Section: Chi-squared Minimizationmentioning

confidence: 99%

“…Early work in this area culminated in the excellent article by Cvetanović, Singleton, and Paraskevopoulos [1]. Later, the need to include correlations and confidence intervals was pointed out by Héberger, Kemény, and Vidóczy [2]. Data reduction techniques are now considered a routine part of the analysis of kinetic data [3].…”

Section: Introductionmentioning

confidence: 99%

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The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Hessler

1997

Int. J. Chem. Kinet.

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Experimental kineticists are always faced with the problem of reducing kinetic data to extract physically meaningful information. A particularly vexing problem arises when different models reproduce the data but yield different values for the physical parameters. For over forty-five years Monte Carlo simulation techniques have been used to study the statistical behavior of parameters extracted from data. Not only do these simulations provide realistic uncertainties, correlation coefficients, and confidence envelopes, but they also provide insight into the nature of the model. These insights may be obtained by viewing two-dimensional scatter plots of the fractional changes of the parameters and one-dimensional histograms of the distributions of the changes in the parameters. Monte Carlo simulations are illustrated with examples from and the high-pressure rate coefficient for OH ϩ CH : CH ϩ H O 4 3 2 methyl-methyl association. A more complex problem involves models for pressure-dependent rate coefficients in the falloff region. We have modeled methyl-methyl association with five of the most current analytic approximations for behavior in the falloff region. All of these reproduce the data to within their uncertainties. However, when Monte Carlo techniques are applied the correlations between the parameters and the nonlinear nature of their behavior become evident. We postulate that the statistical behavior of the parameters of a model may be used to distinguish one model from another and, thereby, identify those analytic approximations that hold promise for further investigation and utilization. Finally, the recent advent of highspeed workstations implies that Monte Carlo simulations should become a routine part of the analysis of kinetic data.

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Section: Chi-squared Minimizationmentioning

confidence: 95%

“…After experiments have been performed, the best-fit values of the independent parameters are generally determined by minimizing the chi-squared merit function, 2 (a), defined by…”

Section: Chi-squared Minimizationmentioning

confidence: 99%

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The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Hessler

1997

Int. J. Chem. Kinet.

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“…It is well established but rarely acknowledged that uncertainties on paired Arrhenius parameters are highly correlated (Héberger and Kemény, 1987;Nagy and Turányi, 2011). Since such correlations have direct bearing on the application of carbonate ∆47 reordering models (e.g., Lloyd et al, 2017), it is worth considering how the families of dolomite ∆47 reordering parameters covary here.…”

Section: The Transient Defect/equilibrium Defect Modelmentioning

confidence: 99%

Experimental calibration of clumped isotope reordering in dolomite

Lloyd

Ryb

Eiler

2018

Geochimica et Cosmochimica Acta

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“…The uncertainties of Arrhenius parameters have also been investigated by Héberger et al [4]. They concluded that the Arrhenius coefficients determined in most experiments are highly correlated and that this correlation should be characterized by a covariance matrix.…”

Section: Introductionmentioning

confidence: 97%

Uncertainty of Arrhenius parameters

Nagy

Turányi

2011

Int J of Chemical Kinetics

107

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Chemical kinetics databases for many elementary gas-phase reactions provide the recommended values of the Arrhenius parameters, the temperature range of their validity, and the temperature dependence of the uncertainty of the rate coefficient k. An analytical expression is derived that describes the temperature dependence of the uncertainty of k as a function of the elements of the covariance matrix of the Arrhenius parameters. Based on this analytical expression, the various descriptions of the temperature dependence of the uncertainty of k used in the combustion, and in the IUPAC and JPL atmospheric chemical databases are analyzed in detail. Recommendations are given for an improved representation of the uncertainty information in future chemical kinetics databases using the covariance matrix of the Arrhenius parameters. Utilization of the joint uncertainty of the Arrhenius parameters is needed for a correct uncertainty analysis in varying temperature chemical kinetic systems. A method is suggested for the determination of the covariance matrix and the joint probability density function of the Arrhenius parameters from the present uncertainty information given in the kinetics databases. The method is demonstrated on seven gas kinetic reactions exhibiting different types of uncertainty representation. C

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On the errors of Arrhenius parameters and estimated rate constant values

Abstract: A detailed statistical study is presented, based on simulated experimental data, on the estimation of activation parameters using the Arrhenius equation: k = A exp!B/T).

Cited by 70 publications

References 8 publications

The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Experimental calibration of clumped isotope reordering in dolomite

Uncertainty of Arrhenius parameters

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