An experimental and theoretical investigation of the gas-phase benzene–OH radical adduct + O₂reaction

Abstract

The reaction of the hydroxycyclohexadienyl radical (HO-C 6 H 6 ) (the adduct from the benzene + OH reaction) with O 2 has been investigated using laser flash photolysis with UV-absorption spectroscopic detection, and DFT and ab initio quantum mechanical calculations. An absolute absorption spectrum was measured for the benzene-OH adduct, and its reaction with O 2 , giving a peroxy radical species, was seen to be equilibrated around room-temperature. An equilibrium constant of 1.15 AE 0.6 Â 10 À19 cm 3 molecule À1 was determined at 295 K from an analysis of transient absorption signals using a detailed reaction mechanism. Equilibrium constants were obtained in this way at six different temperatures between 265 and 345 K. The temperaturedependence of these data indicates that the DH 0 298 and DS 0 298 for the title reaction are À10.5 AE 1.3 kcal mol À1 and À33.9 AE 1.4 cal K À1 mol À1 respectively (second-law analysis of the data, 2s errors). A third-law analysis of the data (using a value for DS 0 298 of À38.3 cal K À1 mol À1 , derived from DFT and ab initio calculations) yields a value for DH 0 298 of À11.7 AE 0.2 kcal mol À1 , which compares with an ab initio calculated value of À12.2 kcal mol À1 . Absorption signals at 260-275 nm, in the presence of high concentrations of O 2 , were observed that are consistent with the presence of the benzene-OH peroxy radical, and with stable products of its chemistry. Equilibrium constants obtained from these data agree well with our other determinations. The effective lifetime of the equilibrium system-adduct + O 2 Ð adduct À O 2 -is dictated either by an additional, irreversible reaction of the benzene-OH adduct with O 2 or by a unimolecular transformation of the peroxy species. Assuming the former case, a bimolecular rate constant of around 5.5 AE 3.0 Â 10 À16 cm 3 molecule À1 s À1 was estimated from a kinetic simulation of our decay signals. This rate constant does not appear to vary significantly between 265 and 320 K, but it must be emphasised that it was estimated with a fairly high uncertainty.

Modified variable phase method for the solution of coupled radial Schrödinger equations

“…The method of the hyperspherical harmonics is very convenient for the description of the three-body structure of two-neutron halos that appear in Borromean nuclei 6 He, 11 Li, etc., at the very edge of the nuclear stability (see recent works [21,22], and references therein, for a more detailed discussion of the successes and challenges of this approach). The relative motion of three clusters is described in the space of 064308-6 hyperspherical coordinates (ρ, 5 ), and the nuclear wave function J π is decomposed on a basis of hyperspherical harmonics ϒ Kν ( 5 ) [20], J π = Kν ψ J π Kν (ρ)ϒ Kν ( 5 ).…”

“…As an example, we consider the calculation of the 0 + continuum wave function of the 6 He nucleus at excitation energy 2 MeV. All possible hyperharmonics up to the value of K = 20 are included in the wave function expansion, giving a system of Schrödinger equations with ∼70 coupled channels.…”

“…The method is powerful for both bound and continuum states. We have demonstrated its usefulness by computing a low-lying monopole continuum state of the Borromean halo nucleus 6 He in a three-body cluster model using a hyperspherical harmonic expansion. ACKNOWLEDGMENTS S.N.E.…”

“…Usually these transformations are rather awkward and tedious. Another approach to overcome the difficulty is to use a so-called invariant imbedding method, in which the propagated quantity is not a wave function matrix = {ψ in (r)}, but rather its logarithmic derivative −1 [6][7][8] or its inverse matrix R = −1 [9][10][11]. These methods have found broad application, especially for large coupled-channel calculations.…”

Optimization of generalized multichannel quantum defect reference functions for Feshbach resonance characterization

“…Assuming a strong interaction between the open and closed channels pictured in Figure 1a, we determine the reference functions f adia and g adia associated to the individual adiabatic channels of Figure 1b with the Milne phase-amplitude method [45]. In order to avoid the tricky numerical evaluation of the non-Born-Oppenheimer coupling between the adiabatic channels, the set of coupled equations of eq.3) in the diabatic representation is solved by propagating the related diabatic logarithmic derivative matrix L dia of the wave function Ψ using the renormalized Numerov method implemented by Johnson [48]. If M(R) is the eigenvectors matrix of H so , it can be shown that the corresponding adiabatic logarithmic derivative matrix L adia is given by:…”