Statistical Rate Theory in Combustion: An Operational Approach

  • Matthias OlzmannEmail author
Part of the Green Energy and Technology book series (GREEN)


Statistical rate theory is a valuable tool to rationalize the microscopic mechanisms of elementary chemical steps in the gas phase, to analyze results of kinetic experiments, and to adequately parameterize the temperature and pressure dependence of rate coefficients. We briefly describe the essential elements of statistical rate theory that are relevant for the kinetic characterization of reactions under combustion conditions, emphasizing application aspects. The calculation of rate coefficients for reactions over potential energy barriers and potential energy wells is elucidated. In the former case conventional transition state theory is used, in the latter case the temperature and pressure dependence is described by means of master equations with specific rate coefficients from RRKM theory and the simplified statistical adiabatic channel model. Examples for the different types of reaction are given, and crucial quantities are discussed. The article primarily aims at readers on an intermediate level between graduate students and junior scientists, who are interested in performing practical calculations, and who are looking for a compact presentation of the topic as a guide to the extensive literature.


Master Equation Rate Coefficient Transition State Theory Collisional Energy Transfer RRKM Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Important Symbols and Abbreviations


Average of quantity X


Vector/matrix containing elements a(E i )/a(E i , E j )


Rotational constant


Rotational constant for centrifugal motion in SACM


Morse parameter


ith eigenvector of the matrix J


Energy transfer parameter of the stepladder model


Average energy transferred per collision (all, up and down)


Average energy transferred per down collision


Average energy transferred per up collision


Zero-point energy correction in SACM


Threshold energy of reaction i


Initial distribution of the intermediate in a complex-forming bimolecular reaction


Angular momentum coupling factor in SACM


Density of states correction factor


Planck′s constant


Harmonic oscillator


Total angular momentum quantum number


Matrix of the master equation, for definition see Eq. 21.3


Rate coefficient of reaction i


High-pressure limiting value of the rate coefficient for reaction i


Boltzmann′s constant


Reaction path degeneracy for reaction i


Distribution of a reacting species


Steady-state distribution of a reacting species


Normalized steady-state distribution of a reacting species




Collisional transition probability (density) for a collision EE


Phase space theory


Reaction coordinate/interfragment distance


Equilibrium distance


Partition function for hindered internal rotor (local coordinate)


Partition function for harmonic oscillator (normal coordinate)


Partition function for harmonic oscillator (local coordinate)


Partition function


Gas constant


Rate of reaction of a complex-forming bimolecular reaction


Rice, Ramsperger, Kassel, Marcus


Statistical adiabatic channel model




Transition state theory




Classical interfragment potential


Cumulative reaction probability/sum of states for reaction/transition state i


Interpolation parameter of simplified SACM or energy transfer parameter of the exponential down model


Morse parameter


Collision efficiency in a chemically activated reaction


Vibrational or rotational quantum in SACM


ith eigenvalue of the matrix J


Density of states


Symmetry number


Collision frequency (unit: s−1)



Financial support by the Deutsche Forschungsgemeinschaft (SFB 606 “Non-Stationary Combustion: Transport Phenomena, Chemical Reactions, Technical Systems”) and by the European Cooperation in Science and Technology (COST, Action CM0901 “Detailed Chemical Kinetic Models for Cleaner Combustion”) is gratefully acknowledged.


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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Institut für Physikalische ChemieKarlsruher Institut für Technologie (KIT)KarlsruheGermany

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