New empirical rate expression for reactions without a barrier: Analysis of the reaction of CN with O2

Abstract

The rate coefficients of reactions that occur on potential energy surfaces without a barrier often exhibit a negative temperature dependence at low temperatures. Generally, this behavior is modeled with either the Harcourt–Essen equation, k(T)=AT−m, or a “negative” activation energy, k(T)=ATm exp{ΔE/kBT}. Neither of these expressions is consistent with the Wigner threshold law. The general expression k(T)=(1+T/TW)−m∑l=0∞Al(1+T/TW)−l(T/TW)l is proposed where the relative angular momentum of the reacting species is l, TW and m are independent parameters to be extracted from the data, and the amplitude of each partial wave is Al. This expression may be approximated by k(T)=A0(1+T/TW)−m exp[(T/TW)/(1+T/TW)]. For CN+O2→ NCO+O and CO+NO the above expression reproduces the rate data, the branching ratio to the CO+NO channel, and the reactive cross section for the NCO+O channel. The rate coefficient for the NCO+O channel is given by k(cm3 s−1)=1.79×10−10(+T/21.7)−1.38{exp[(T/21.7)/(1+T/21.7)]−1}+4.62×10−12 exp[(T/21.7)/(1+T/21.7)] while for CO+NO we obtain k(cm3 s−1)=1.79×10−10(1+T/21.7)−1.38. An analytic form of the C–O bonding potential and the electric dipole–quadrupole interaction is used to show that the quantum threshold region extends up to 7 K. These results demonstrate the need of a complete quantum treatment for reactions that proceed on potential surfaces without a barrier.