Experimental and theoretical studies of the reaction of the phenyl radical with methane

The kinetics of the metathetical reaction of phenyl radical with methane has been studied theoretically and experimentally. The rate constants determined by two complementary methods, pyrolysis/Fourier transform infrared spectrometry and pulsed laser photolysis/mass spectrometry in the temperature range 600-980 K, give the Arrhenius equation: K₁ = 10^{12.78 ± 0.13} exp[(-6201 ± 225)/T] cm³/(mol s). At the best theoretical level employed (G2M(CC,MP2)), the barrier for the reaction at 0 K is E₁ ⁰ = 9.3 kcal/mol. The rate constant k₁ calculated from theoretical molecular parameters fits experimental data if the barrier height is increased to 10.5 kcal/mol. The fitted barrier is well within the 2-3 kcal/mol accuracy of the G2M method for the present open-shell, seven-heavy-atom system. Because of the relatively high reaction barrier and the predicted high imaginary frequency (1551 cm^-1), tunneling corrections resulted in a significant enhancement in the calculated rate constant, 150% at 500 K and 7% at 2000 K. The theoretical result also correlates well with recently reported shock-tube data measured in the temperature range 1050-1450 K by UV absorption spectrometry. Kinetic analysis of the toluene formation data obtained from the photolysis of acetophenone without and with added H₂ and CR₄ gave the rate constant for the recombination of CH₃ and C₆H₅, k₂ = (1.38 ± 0.08) x 10¹³ exp[-(23 ± 36)/T] cm³/(mol s) for the temperature range 300-980 K.