(425d) Detailed Modeling of Low-Temperature Alkane Oxidation: High-Pressure Rate Rules for Alkyl+O2 Reactions

In recent years the CBS-QB3 method has emerged as a reliable tool for kinetic studies. Specifically for alkyl+O₂ systems, earlier studies on ethyl+O₂ and propyl+O₂ employing this composite method to compute the PES were able to reproduce experimental results with high accuracy without any barrier adjustments. In addition, detailed analyses on ethyl+O₂ andpropyl+O₂ as well as an on-going one on butyl+O₂ identify the dominance of only three important reaction pathways: (1) re-dissociation of alkyl-peroxy to alkyl+O₂, (2) concerted HO₂ elimination from alkyl-peroxy yielding the corresponding olefin, and (3) isomerization via the 1,5 H-shift to form g-hydroperoxy-alkyl. Therefore, the objective of the current work is to apply the same CBS-QB3 method to systematically derive high-pressure rate rules for the first three important reactions found in alkyl+O₂ systems using a comprehensive set of different types of representative reactions.

Calculations. The electronic structure calculations were carried out using the Gaussian 03 suite of programs. The CBS-QB3 method was used to calculate geometries and frequencies. All reported results for stable molecules as well as transition states (TS) were obtained for the lowest energy conformer of a given species. Thermodynamic properties (e.g., entropies and heat capacities) were calculated using standard statistical mechanics methods. Some low-frequency vibrational modes, which resemble internal rotations around single bonds, were replaced in the thermodynamics calculations by an explicit treatment of hindered rotations (HR). High-pressure rate constant calculations were computed using canonical transition state theory (TST) with tunneling corrections based on asymmetric Eckart potentials. Individual TST rate coefficients for reactions in the training set of a given class are generalized by fixing the temperature exponent of the modified Arrhenius expression (k(T)=A×Tⁿ×exp(-E/RT) and averaging the pre-exponential factors and barriers. This procedure yields averaged rate expressions to which we refer to as rate estimation rules.

Re-dissociation of alkyl-peroxy. The rate constant for ROO¥ = R¥+O₂ can be determined from the equilibrium constant and the rate constant for the R+O₂ association step. Since the association reactions proceed with no barrier, one would preferentially obtain those rate constants from experiments. Therefore, in our calculations we focus on systematic trends in the bond dissociation energies (BDE) of the RO₂ radicals. Fig. 1 presents the BDEs for a series of ROO¥ radicals, containing linear and branched alkyl groups with peroxy groups bound to primary, secondary and tertiary carbons. It is evident that the calculated bond strengths depend on the nature of the alkyl carbon radical site to which the O₂ binds: tertiary > secondary > primary > methyl peroxy radical. Our results are consistent with other published studies.

Rate rules for the 1,5-H shift reaction. Fig. 2 shows the trends for rate constants (per hydrogen) for all intramolecular 1,5 H-shift reactions at different types of C-H group: tertiary > secondary > primary. While the rate expressions do group together, we observe some spread among those belonging to the same group. This may be due to different conformations of the ring TS. Therefore at this point we consider these data as preliminary. The rate estimation rules based on the results shown in Fig. 2. are:

k_prim.(T) = (2.1×10⁶ s^-1)×T^1.50×exp[-21.2 kcal/mol/(RT)]                    (Eq.1)

k_sec.(T) = (6.4×10⁶ s^-1)×T^1.33×exp[-18.2 kcal/mol/(RT)]                   (Eq.2)

k_tert.(T) = (8.1×10⁶ s^-1)×T^1.31×exp[-15.9 kcal/mol/(RT)]       (Eq.3)

Rate rules for the concerted elimination of HO_2. There are 9 different reaction classes for ROO¥→alkene+HO_2, based on the nature of the peroxy group (primary, secondary or tertiary) and the C-H bond that is broken. Fig. 3 presents results for reactions involving primary RO₂ radicals. With the exception of HO₂ elimination from ethyl peroxy, the rate coefficients do not reflect a big impact of reacting C-H bond type (secondary or tertiary) on the rate constant; thus these can be approximated by a single generic rate coefficient. For secondary and tertiary RO₂ radicals we observe a wider spread in the rate constants, which could still be represented by a single rate rule for each set. However, given the importance of this reaction type, we are currently analyzing whether subdividing those sets into smaller part would lead to improvements in accuracy that warrants the use of more detailed rate estimation rules.

Conclusions. The successful derivation of high-pressure rate rules at CBS-QB3 level for important reaction classes found in alkyl+O₂ suggests this is a promising approach to correctly characterize the complex kinetics of real alkyl+O₂ systems which are not applicable to detailed analysis using accurate electronic structure calculations. When used as input for a QRRK/MSC analysis, this approach makes it possible to treat these reactions as pressure-dependent systems and thus provides a framework to develop realistic kinetic models applicable for engine conditions.

References

(1)       Huynh, L. K.; Carstensen, H.-H.; Dean, A. M. J Phys. Chem. A (submitted) 2010.

(2)       Petway, S. V.; Ismail, H.; Green, W. H.; Estupin, E. G.; Jusinski, L. E.; Taatjes, C. A. J. Phys. Chem. A 2007, 111, 3891.