Non-Boltzmann Chemical Kinetics



Malte Döntgen

Group Leader Computational Chemistry


+49 241 80 26907



Gas phase chemistry is often governed by complex reaction mechanisms. In these mechanisms, sequences and competitions of multiple reactions can fundamentally affect the global reactivity in the gas phase. Classically, single reactions of a reaction sequence are treated separately. In reality, however, these reactions are strongly linked to each other through the excess energy steming from each individual reaction [1]. This excess energy chemically activates intermediates of reaction sequences and can initiate so-called prompt reactions [2, 3], also referred to as hot reactions [4].

A prominent example is the prompt dissociation of radicals formed through abstraction of a hydrogen atom, i.e. hot β-scission [4]. The animation shows how a hot β-scission reaction evolves on a prototypical potential energy surface. When emerging from the initial transition state (TSH), the produced radical is in a chemically activated state and either “falls” down into the potential energy well (thermalization) or it promptly dissociates towards the products on the right hand side of the illustrated reaction scheme. The branching between the prompt and the thermal pathway strongly depends on the shape of the potential energy surface. The figure shows three prototypical potential energy surfaces of hot β-scission reactions in the upper limit, the transition regime, and the lower limit. For the upper limit, the chemically activated radical has so much excess energy that it promptly dissociates completely. In the lower limit, it is the other way around and the radical is always stabilized into the potential energy well. In the transition regime, the chemically activated radical is partially stabilized and partially dissociates promptly. The effect of the so-called non-Boltzmann energy distribution (cf. red energy distribution) on predictions of flame speeds [2, 3] and ignition delay times [5] cannot be neglected when modeling macroscopic processes.

*** NB Animation ***
Reaction scheme of a hot β-scision reaction
  Potential cases of hot beta-scission reactions Copyright: © 2017, American Chemical Society Potential cases of hot β-scission reactions. Reprinted with permission from Copyright 2017, American Chemical Society


  1. [1] M. Döntgen, K. Leonhard, "Discussion of the Sepration of Chemical and Relaxational Kinetics of Chemically Activated Intermediates in Master Equation Simulations", J. Phys. Chem. A 121 (2017), 1563-1570
  2. [2] N.J. Labbé, R. Sivaramakrishnan, C.F. Goldsmith, Y. Georgievskii, J.A. Miller, S.J. Klippenstein, "Weakly Bound Free Radicals in Combustion: "Prompt" Dissociation of Formyl Radicals and Its Effect on Laminar Flame Speeds", J. Phys. Chem. Lett. 7 (2016), 85-89
  3. [3] N.J. Labbé, R. Sivaramakrishnan, C.F. Goldsmith, Y. Georgievskii, J.A. Miller, S.J. Klippenstein, "Ramifications of including non-equilibrium effects for HCO in flame chemistry", Proc. Combust. Inst. 36 (2017), 525-532
  4. [4] M. Döntgen, L.C. Kröger, K. Leonhard, "Hot β-scission of radicals formed via hydrogen abstraction", Proc. Combust. Inst. 36 (2017), 135-142
  5. [5] A. Wildenberg, M. Döntgen, I.S. Roy, C. Huang, B. Lefort, L. Le Moyne, A. Kéromnès, K. Leonhard, K.A. Heufer, "Solveing the riddle of the high-temperature chemistry of 1,3-dioxolane", Proc. Combust. Inst. 39 (2022), In Press
  6. [6] H. Minwegen, M. Döntgen, C. Hemken, R.D. Büttgen, K. Leonhard, K.A. Heufer, "Experimental and theoretical investigation of methyl formate oxidation including hot β-scission", Proc. Combust. Inst. 37 (2019), 307-314
  7. [7] W.A. Kopp, U. Burke, M. Döntgen, L.C. Kröger, H. Minwegen, K.A. Heufer, K. Leonhard, "Ab initio kinetics predictions for H-atom abstraction from 2-butanone by H and CH3 and the subsequent unimolecular reactions", Proc. Comust. Inst. 36 (2017), 203-210
  8. [8] W.A. Kopp, L.C. Kröger, M. Döntgen, S. Jacobs, U. Burke, H.J. Curran, K.A. Heufer, K. Leonhard, "Detailed kinetic modeling of dimethoxymethane. Part I: Ab initio thermochemistry and kinetics predictions for key reactions", Combust. Flame 189 (2018), 433-442
  9. [9] L.C. Kröger, M. Döntgen, D. Firaha, W.A. Kopp, K. Leonhard, "Ab initio kinetics predictions for H-atom abstraction from diethoxymethane by hydrogen, methyl, and ethyl radicals and the subsequent unimolecular reactions", Proc. Combust. Inst. 37 (2019), 275-282