A Kinetic Study of the Gas-Phase Reaction of OH with Br₂

Abstract

An experimental, temperature-dependent kinetic study of the gas-phase reaction of the hydroxyl radical with molecular bromine (reaction 1) has been performed using a pulsed laser photolysis/pulsed-laser-induced fluorescence technique over a wide temperature range of 297 – 766 K, and at pressures between 6.68 and 40.29 kPa of helium. The experimental rate coefficients for reaction 1 demonstrate no correlation with pressure and exhibit a negative temperature dependence with a slight negative curvature in the Arrhenius plot. A non-linear least-squares fit with two floating parameters of the temperature dependent k₁(T) data set using an equation of the form k₁(T) = ATⁿ yields the recommended expression k₁(T) = 1.85×10⁻⁹T ^{− 0.66} cm³ molecule⁻¹ s⁻¹ for the temperature dependence of the reaction 1 rate coefficient. The potential energy surface (PES) of reaction 1 was investigated using quantum chemistry methods. The reaction proceeds through formation of a weakly bound OH···Br₂ complex and a PES saddle point with an energy below that of the reactants. Temperature dependence of the reaction rate coefficient was modeled using the RRKM method on the basis of the calculated PES.

I. Introduction

Brominated flame retardants are widely used chemicals, and over the years, more and more materials containing brominated organics are being subjected to thermal degradation in hazardous and municipal waste incinerators or accidental fires.¹ Brominated flame retardants are useful but also potentially damaging to the environment. They are frequently burned in the presence of chlorinated materials and upon combustion or thermal degradation can form various brominated/chlorinated by-products including polybrominated/chlorinated dibenzo-p-dioxins and dibenzofurans (PBCDD/F).^1–4 Their properties are similar to PCDD/Fs that are classified as carcinogenic and known to cause birth defects and chloroacne. This has stimulated the development of research directed at mechanistic and chemical kinetic modeling of combustion of bromo-chlopo-organics. Accurate chemical kinetic modeling is essential for understanding the complicated chemistry of these processes.

Along with the reactions of the hydroxyl radical with HCl, Cl₂, and HBr, the gas-phase reaction of the hydroxyl radical with molecular bromine

$$\text{OH}+{\text{Br}}_2\to \text{products}$$ (1)

probably plays a significant role in the combustion chemistry of bromo-chloro-organics. In the post-flame zone it should deplete OH and thus inhibits CO oxidation. Via this reaction, Br₂ molecules are converted to Br atoms that should have a significant effect on the concentration of brominating and chlorinating agents including BrCl that controls the composition of the final emissions of the polybromo-chloro-aromatic pollutants.^1–4 Although reaction 1 is potentially important in these processes, the rate coefficient of this reaction has not been studied at high temperatures.

To our knowledge, the kinetics of reaction 1 has been directly investigated in five studies^5–9 performed at low temperatures only. The importance of this reaction for atmospheric chemistry is described, e.g., in the earlier studies of Gilles et al.⁸ and Bedjanian et al.⁹ The current work represents the first experimental study of reaction 1 carried out at high temperatures in the range from 297 K (to compare with the earlier studies) to 766 K, which is relevant to combustion and other thermal processes.

II. Experimental Section

II. A. Experimental Technique

The experimental study of the temperature dependence of the rate coefficient for the reaction of the hydroxyl radical with molecular bromine was performed using a pulsed laser photolysis/pulsed-laser-induced fluorescence (PLP/PLIF) technique combined with a heatable, slow-flow reactor under pseudo first-order conditions with a large excess of molecular bromine. The experimental set-up has been described in detail in our previous article¹⁰ and is considered here only briefly.

An excimer laser and an Nd:Yag pumped, frequency doubled, tunable pulsed dye laser were employed to generate the photolysis and probe laser pulses, respectively. Hydroxyl radicals were formed by the 193-nm pulsed laser photolysis of N₂O to O(¹D) and N₂, and the subsequent rapid reaction of O(¹D) with H₂O.^11,12

$${\text{N}}_2\text{O}+hv(193\text{nm})\to {\text{N}}_2+\text{O}({}^1\text{D})$$ (2)

$$\text{O}({}^1\text{D})+{\text{H}}_2\text{O}\to 2\text{OH}$$ (3)

OH was excited by the probe laser pulse at ~282 nm via the A²Σ⁺ – X²Π (1 – 0) transition followed by observation of fluorescence from the (1 – 1) and (0 – 0) bands at 308–316 nm (see, for example, references 13,14). The fluorescent radiation was monitored with a photomultiplier tube, using a UV band-pass filter (308 nm peak transmission) to minimize scattered light. The signal from the photomultiplier was amplified and then recorded by a 500-MHz digital oscilloscope to obtain the integrated voltage averaged for a desired number of laser pulses (typically 50 – 150) at single time delay. The value, S_t, received from the integration of the average voltage signal is a sum of two components: the integral from the average LIF signal of OH radicals, S_OH, (this term is proportional to the absolute concentration of OH) and the integral from the average scattered light signal, S_sc. The average integrated voltage for the scattered light was measured directly in the absence of OH radicals. For this measurement, the photolysis laser was not triggered during the accumulation of the scattered light signal. Kinetic information was obtained by varying the time delay between pulses of the photolysis and the probe lasers in the desired time interval using a digital delay generator.

We utilized four individually controlled flows of He (main carrier gas flow), H₂O/He, N₂O/He, and Br₂/Ar to prepare a reaction gas mixture. Three calibrated mass-flow controllers with appropriate flow ranges were employed to set the values of the three gas flows of He (main carrier gas flow), H₂O/He, N₂O/He and maintain their stability during the performance of the experiments. At selected times during the experiments, values of these three flows were controlled by measuring rates of pressure increases in the calibrated volumes located upstream from the gas inlet of the reactor. The fourth flow of Br₂/Ar was manually regulated by a metering valve. This flow was also determined by measuring the rate of the pressure increase in the calibrated volume before and after obtaining each OH temporal profile. A mean value of these two flow measurements was taken to calculate Br₂ concentration in the reaction zone. These pressure measurements were performed with capacitance manometers of 100.00 and 1000.0 Torr ranges (1 Torr = 133.322 Pa).

The independence of the measured flows on the surface-to-volume ratio of the calibrated volume was verified to ensure the absence of interference from heterogeneous absorption and desorption processes on the walls of the volume using three different calibrated Pyrex vessels (150.2, 724.5, and 6364 cm³). Bromine was accurately, manometrically diluted with argon using a Pyrex vacuum system and stored in ~ 22 L Pyrex bulb and ~ 9 L Pyrex cylindrical reservoir (~ 13.5 cm i.d. × ~ 68 cm length). These two reservoirs with different surface-to-volume ratios were used with the expressed purpose of verifying the absence of interference from Br₂ heterogeneous absorption and desorption processes on the walls of the containers. To minimize systematic error in the Br₂ concentration determination, we had prepared four Br₂/Ar mixtures with different concentrations of Br₂ ranged between 1.433 and 4.97%, and these were used without any correlation between Br₂ concentrations in those and established reaction temperatures.

All flows were premixed and directed though the pressure, temperature controlled, resistively heatable quartz reactor. The composite flow conditioned the reactor for several minutes prior to data collection, thereby minimizing any effects due to reactant adsorption on the delivery system and reactor walls, thus stabilizing the established experimental conditions. The total flow rate ranged between 8.7 and 25.5 STP cm³ s⁻¹. The total pressure in the reactor was measured with the capacitance manometers of 100.00 and 1000.0 Torr ranges. The gas temperature in the reaction zone was monitored with a retractable Chromel-Alumel thermocouple. The maximum total uncertainty in the measurements of the reaction temperatures, T, did not exceed 0.5% of T. (See reference ¹⁰ for details.)

The molecular concentration of each reagent in the reaction zone was derived from its partial concentration, measurements of the flow rates, the reaction temperature and total pressure under the ideal gas assumption. Typical reaction mixtures used in these experiments consisted of the following molecular concentrations ranged: N₂O, 2.02×10¹³ – 7.11×10¹³; H₂O, 1.0×10¹⁵ – 2.0×10¹⁵; He, 1.51×10¹⁸ – 3.81×10¹⁸; Ar, 0.0 – 1.08×10¹⁶; Br₂, 0.0 – 2.64×10¹⁴ in units of molecule cm⁻³.

The chemicals utilized in this study had the following stated minimum purities (and were supplied by): He, 99.999% (The BOC Group, Inc.); Ar, 99.999% (The BOC Group, Inc.); Br₂, 99.99% (Aldrich); N₂O, 9.98% mixture of 99.99% purity in 99.999% He (The BOC Group, Inc.); H₂O, A.C.S. reagent grade (Sigma-Aldrich). Analysis of Br₂ sample showed only very small levels of impurities, and these very small concentrations had a negligible effect on the observed OH decay rates.

II. B. Reaction Rate Measurements and Results

All kinetics runs were performed under pseudo first-order conditions in a large excess of molecular bromine with respect to the initial concentration of the hydroxyl radical, [OH]₀, which ranged approximately from 1.0×10¹⁰ to 1.9×10¹¹ molecule cm⁻³. The initial concentrations of OH radicals were estimated by a procedure similar to that described in reference ¹⁰. An uncertainty in the ratio between any two values of [OH]₀ taken at the same temperature is about 10%. Exact knowledge of the initial OH concentrations is not critical for determination of rate coefficients because the experiments were carried out under pseudo first-order conditions with a large excess of bromine. The evaluated detection sensitivity limit for OH radicals, defined by unity signal-to-noise ratio, was around 1×10⁸ molecule cm⁻³.

A typical set of OH temporal profiles (a set of experiments) are presented in Figure 1 as a plot of ln(S_OH) = ln(S_t – S_sc) versus time delays, t. The initial detection time, t₀, for each set of experiments was established depending on experimental conditions, so that this time delay followed the photolysis of the reaction mixture and was sufficient for the completion of the reaction O(¹D) with H₂O and for rotational and vibrational equilibration of OH radicals to the Boltzmann distribution.^12,15 The initial detection time value, t₀, in all OH temporal decay profiles was not less than 0.2 ms (vide infra).

Figure 1.

Examples of relative OH concentration temporal profiles obtained under the following conditions: helium buffer gas, temperature T = 766 K, total pressure P = 40.29 kPa (302.2 Torr), [N₂O] = 3.17×10¹³ molecule cm⁻³, [H₂O] = 1.8×10¹⁵ molecule cm⁻³; [Br₂] = 0, 3.07×10¹³, 5.79×10¹³, 8.11×10¹³, 1.22×10¹⁴, 1.52×10¹⁴, 1.76×10¹⁴, 2.28×10¹⁴, 2.64×10¹⁴ molecule cm⁻³ for profiles 1 – 9, respectively.

OH radical temporal profiles were analyzed assuming the pseudo first-order kinetic behavior of the OH signal:

$$ln(S_{\text{OH}})=ln(S_{\text{t}}-S_{\text{sc}})=\text{constant}-k^{\prime }t$$ (I)

where the effective first-order rate coefficient, k′, is given by:

$$k^{\prime }=k_1[{\text{Br}}_2]+k_0$$ (II)

k₁ is the bimolecular rate coefficient for reaction 1; [Br₂] is the molecular bromine concentration; k₀ is the effective first order rate coefficient of OH decay due to possible OH reactions with background impurities in the buffer gas, N₂O, H₂O, and OH diffusion/flow out of the detection zone (OH background loss). The effective first-order rate coefficient values, k′, were obtained from linear least-squares-fits of the experimental values ln(S_OH) to equation I. (These least-squares fits and all next least-squares fits were performed with no weighting of the data points.)

Examples of measured k′ versus bromine concentration dependences are presented in Figure 2. We determined the bimolecular rate coefficient, k₁, from the slope of the least-squares straight line through the k′ versus [Br₂] data points including the (0, k₀) point, where k₀ was derived from the OH temporal profile directly measured at zero concentration of Br₂. For each set of experiments, the difference between the value of k₀ directly measured in the absence of bromine and k₀ found from the zero-abscissa intercept of the least-squares straight line in the ([Br₂], k′) coordinates was within the experimental uncertainties (2σ level of statistical uncertainties obtained from the linear least-squares-fits). We analyzed the possible effect of a minor deviation from the first-order kinetic behavior of the OH background loss on the measurement of k₁ values using data processing with the background-loss correction described in references 10,16–19. Under all the experimental conditions in our study, it was found that this effect was very small (less than 0.8% of k₁ value) such that no background-loss correction was necessary.

Figure 2.

Examples of experimentally obtained k′ vs [Br₂] dependencies.

The kinetic study of the reaction OH with molecular bromine was performed over the temperature range 297 – 766 K and at pressures between 6.68 and 40.29 kPa of helium. The experimental conditions and bimolecular rate coefficients measured for reaction 1 are summarized in Table 1. Over the entire experimental temperature range, the initial concentration of the hydroxyl radicals was varied by changing the photolysis laser intensity and the concentration of N₂O from set to set of experiments.

TABLE 1.

Conditions and Results of Experiments to Measure Rate Coefficients of the Reaction of Hydroxyl Radicals with Molecular Bromine

no.a	T / K	P / kPa	[Br2] range / 1012 molecule cm−3	Ib / mJ pulse−1 cm−2	[OH]0 / 1010 molecule cm−3	k1c / 10−11 molecule−1 cm3s−1
1	297	13.41	8.89 – 95.4	13	12	4.30±0.17
2	321	6.68	14.1 – 108	7.2	5.1	4.226±0.059
3	321	6.68	14.4 – 109	1.4	1.0	4.143±0.072
4	349	13.41	7.32 – 88.9	16	7.1	3.75±0.16
5	349	13.41	7.33 – 89.2	4.5	2.0	3.81±0.17
6	389	13.41	16.6 – 114	13	4.8	3.546±0.073
7	389	13.41	16.8 – 115	12	4.4	3.50±0.18
8	477	13.41	10.27 – 128	12	19	3.167±0.060
9	477	13.41	10.34 – 128	2.8	4.4	3.190±0.097
10	541	26.88	5.50 – 156	6.0	3.7	2.927±0.090
11	541	26.88	5.81 – 157	8.6	5.3	2.974±0.094
12	605	13.40	14.1 – 201	11	18	2.734±0.039
13	605	13.40	14.2 – 197	1.6	2.6	2.721±0.049
14	686	26.88	10.1 – 170	11	2.7	2.45±0.11
15	686	26.88	10.3 – 163	11	15	2.50±0.14
16	765	13.40	9.36 – 246	16	18	2.283±0.054
17	765	13.40	10.0 – 248	2.8	3.2	2.34±0.12
18	766	40.29	30.7 – 264	12	19	2.245±0.060

^aExperiment number.

^bPhotolysis laser intensity.

^cError limits represent 2σ statistical uncertainties only. Maximum estimated systematic uncertainty is 5% of the rate coefficient value (see text).

The measured rate coefficients demonstrate no correlation with pressure or initial concentration of hydroxyl radicals within the experimental ranges. The independence of the rate coefficient values on the initial OH radical concentration indicates the absence of any effect of possible secondary reaction on the behavior of the kinetics of OH radical decay, that should be due to the low values of [OH]₀ ≈ (1.0 – 19)×10¹⁰ molecule cm⁻³. Similarly, the observed absence of any correlation between the measured rate coefficients and the photolysis laser intensity shows that the potential effects of reactions of OH with the products of the photolysis of molecular bromine are negligible. At the highest reaction temperatures established in this study, the absence of any potential effects from thermal decomposition of molecular bromine was verified by measuring rate coefficients at different pressures and bulk flow velocities varied by factors of approximately 3 and 2, respectively.

In all experiments water was added to the reaction mixtures and its concentration was varied from 1.0×10¹⁵ to 2.0×10¹⁵ molecule cm⁻³ from set to set of experiments to ensure that the reaction of O(¹D) with H₂O, and rotational and vibrational equilibration of OH radicals to the Boltzmann distribution proceeded sufficiently fast and had negligible effect on the measured rate coefficients (see references 12,15, respectively). Furthermore, over the entire experimental temperature range, we selectively obtained temporal profiles of the formation of OH (ν = 0) under typical experimental conditions in the absence of molecular bromine. We observed a prompt OH (ν = 0) formation, which was always much faster than t₀, indicating that the reaction of O(¹D) with H₂O, and rotational and vibrational equilibration of OH radicals to the Boltzmann distribution proceeded fast enough to be neglected at the time delays t ≥ t₀. Otherwise, a non-prompt OH (ν = 0) formation would be observed due to the lack of completion of these processes.

Figure 3 displays an Arrhenius plot of our k₁(T) data along with those from previous studies. (Plotted error bars for our data and the data from reference ⁸ were calculated by taking the square root of the sum of the squares of the statistical and systematic errors.) The experimental variation of the reaction 1 rate coefficients with temperature obtained in the current study exhibits a negative temperature dependence with a slight negative curvature in the Arrhenius coordinates. A non-linear least-squares fit with two floating parameters for the k₁(T) data set using an equation of the form k₁(T) = ATⁿ yields the recommended expression

Figure 3.

Temperature dependence of the rate coefficient for the reaction of OH with Br₂ displayed in Arrhenius coordinates. Open green hexagon, blue triangle up, red diamonds, black circles, squares, and filled black circles represent experimental data from references 5–9 and current experimental data, respectively. The black solid line represents the least-squares fit of equation III (see text). The dotted and the dashed red lines represent the results of computational modeling of reaction 1 performed in the current study. Dotted red line – model based on CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVDZ calculations; dashed red line – model with the PES saddle point energy decreased by 2.0 kJ mol⁻¹.

$$k_1(T)=1.85\times {10}^{-9}{T}^{-0.66}{\text{cm}}^3{\text{molecule}}^{-1}{\text{s}}^{-1}(297-766\text{K})$$ (III)

for the rate coefficient temperature dependence of the reaction OH with Br₂. (Numbers in parentheses indicate the temperature range.) 2σ error limits of the parameters A and n in expression III are 3.2×10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ and 0.03, respectively. The maximum and the average square deviations of our experimental rate coefficients are only 3.4% and 1.8% of the calculated values; thus expression III reproduces our experimental data set of the measured rate coefficients very well.

To determine the limits of uncertainties of the measured k₁ values we subdivided sources of error in the measured experimental physical parameters into statistical and systematic categories according to their physical nature or behavior observed during the performance of the calibrations and experiments.¹⁰ The evaluation of potential systematic errors was mainly based on the finite accuracies stated by the manufacturers for the devices used in our experiments. The uncertainties in the measured experimental parameters were propagated to the final values of the uncertainties in the measured rate coefficients, using different mathematical procedures for propagating systematic and statistical uncertainties.²⁰ The error limits of the experimentally determined rate coefficients listed in Table 1 represent the 2σ level of statistical (random) uncertainty only. The evaluated maximum of the systematic uncertainty in the experimental rate coefficients is 5% of the value. (See reference ¹⁰ for details.)

III. Potential Energy Surface and Transition State Theory Model of the OH + Br₂ Reaction

The potential energy surface (PES) of reaction 1 was studied using quantum chemistry. Two methods were used for optimization of molecular structures and calculation of vibrational frequencies: density functional BH&HLYP^21,22 and CCSD,^23,24 both with the aug-cc-pVDZ basis set.²⁵ The Gaussian 03 program²⁶ was used in all potential energy surface (PES) calculations. The version of the BH&HLYP functional implemented in Gaussian 03²⁶ was used which, as described in the Gaussian manual, is different from that of reference ²¹. In addition, high-level single-point energy calculations were carried out for the PES stationary points using the CCSD(T)^23,24 method with two basis sets, aug-cc-pVDZ and aug-cc-pVTZ.²⁵ All CCSD(T) results lead to the same qualitative conclusions regarding the mechanism of reaction 1; energy values quoted in the text henceforth are those obtained in the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVDZ calculations and include vibrational zero point energies unless stated otherwise. The results of the PES study are summarized in Table 2 and the detailed information is given in the Supporting Information (Table 1S, Figure 1S).

TABLE 2.

Energies of Reactants, Products, and Stationary Points on the PES mf the OH + Br₂ Reaction Obtained in Quantum Chemical Calculations.^a

Method	Species b
	OH···Br2	TSb	HOBr + Br
BH&HLYP/aug-cc-pVDZ optimization
BH&HLYP/aug-cc-pVDZ	−7.41	9.78	−7.55
CCSD(T)/aug-cc-pVDZ	−10.08	−12.57	−36.70
CCSD(T)/aug-cc-pVTZ	−8.94	−10.32	−22.83
CCSD/aug-cc-pVDZ optimization
CCSD/aug-cc-pVDZ	−8.91	4.36	−33.18
CCSD(T)/aug-cc-pVDZ	−10.29	−5.48	−37.47
CCSD(T)/aug-cc-pVTZ	−9.25	−4.86	−23.61
Experimental c	-	-	−13.3 ± 8.8

^aEnergy values are given in kJ mol⁻¹ relative to OH + Br₂ and include zero-point vibrational energy (ZPE) and spin-orbit corrections for OH (−0.000317 h) and Br (inus;0.005597 h).

^bPES saddle point between the OH···Br₂ complex and the HOBr + Br products.

^cThermochemical data from references 27–33.

The reaction path leading from the OH + Br₂ reactants to the HOBr + Br products has a shallow van der Waals minimum (weakly bound OH···Br₂ complex, −9.2 kJ mol⁻¹ relative to the reactants) on the reactants side, followed by a small energy barrier (PES saddle point, −4.9 kJ mol⁻¹ relative to the reactants). In this respect, the mechanism of reaction 1 is qualitatively similar to that of the reaction between OH and Cl₂.¹⁰ However, the top of the energy barrier is below the energy of the reactants, unlike in the case of the OH + Cl₂ reaction, where the barrier is located ~10 kJ mol⁻¹ above the reactants.

In an attempt to provide means for an extrapolation of the experimental k₁(T) dependence to temperatures outside the experimental range, an RRKM model of reaction 1 was created in the current work. Molecular structure and vibrational frequencies of the saddle point obtained in the CCSD/aug-cc-pVDZ-level calculations were used, together with the experimental properties of the reactants and products.^27–33

Modeling was performed under the assumption that most of the trajectories sampling the coordinate space of the OH···Br₂ complex and having energies above that of the reactants proceed back to OH + Br₂ and only a small fraction passes through the PES saddle point and leads to the HOBr + Br products. Thus, the saddle point was assumed to represent the dynamic bottleneck of the reaction. This is a reasonable assumption given the fact that the decomposition of the OH···Br₂ complex back to the reactants is expected to have a transition state that is significantly “looser” and thus has larger density of states than that of the OH···Br₂ → HOBr + Br route.

Rate coefficient values were calculated using the equation

$$k(T)=\frac{Q_{\mathit{trans}}^{‡}(T)Q_{\mathit{inact}}^{‡}(T)}{{hQ}_{OH}(T)Q_{{Br}_2}(T)}\underset{E_0}{\overset{\infty }{\int }}{W}^{‡}(E-E_1)exp\left(-\frac{E-E_0}{k_{B}T}\right)dE$$ (IV)

where $Q_{\mathit{trans}}^{‡}(T)$ and $Q_{\mathit{inact}}^{‡}(T)$ are the partition functions of the translational and the overall 2-dimensional (inactive) rotational degrees of freedom of the transition state, Q_OH (T) and Q_Br2 (T) are the partition functions of the OH and Br₂ reactants, W ^‡(E – E₁) is the sum-of-states function of the active^34–36 degrees of freedom of the transition state, E₀ and E₁ are the energies of the reactants and the transition state, respectively (E₀ > E₁), and k_B and h are the Boltzmann and the Planck constants. Equation IV was obtained by simplification of a formula derived by Mozurkewich and Benson³⁷ (equation 12 of reference ³⁷) for reactions proceeding over shallow potential energy wells. The simplification resulted from the above mentioned assumption of predominant dissociation of the OH···Br₂ complexes to OH + Br₂ and from an approximate treatment of the effects of angular momentum (J) conservation where the rate coefficient value obtained for J = 0 is multiplied by the ratio of the partition functions of the two-dimensional rotational (inactive) degrees of freedom of the transition state and the active molecule. The latter ratio (1.2) is close to unity, which justifies the use of the approximation.

The reaction transition state has one torsional degree of freedom. The PES of this torsion, obtained using a BH&HLYP relaxed scan of the H-O-Br-Br dihedral angle has two unequal maxima (5 and 30 kJ mol⁻¹). The partition function of this torsional degree of freedom was calculated by summing over the energy levels evaluated via a numerical solution of the Schrödinger equation. The FGH1D program³⁸ of Johnson was used in the energy level calculations. For the calculation of the sum-of-states function (W ^‡(E – E₁)), this degree of freedom was replaced with a sinusoidal internal hindered rotor with the rotational constant B = 29.5 cm⁻¹ and the hindering barrier height of 10.1 kJ mol⁻¹. These parameters were selected so that the temperature dependence of the resultant partition function matched that obtained using the exact energy levels with the accuracy of 3% or better in the 200 – 3000 K range of temperatures. Existence of the low-lying excited electronic state²⁷ of OH (139.7 cm⁻¹) was taken into account in the rate coefficient calculations.

The rate coefficients calculated using the saddle point (transition state) energy of −4.9 kJ mol⁻¹ relative to the reactants obtained in the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVDZ calculations are presented in Figure 3 (red dotted line). The calculated rate coefficients are, on average, 40% lower that the experimental values. Adjustment of the saddle point energy by −2 kJ mol⁻¹ (to −6.9 kJ mol⁻¹) results in a better average agreement with experiment (red dashed line). However, despite the general agreement with the experimental temperature dependence of the rate coefficient of reaction 1, the calculated k₁(T) line displays a markedly different trend in its curvature on an Arrhenius plot. While our experimental data set has a slight negative curvature, the results of modeling exhibit a slight positive curvature.

IV. Comparison with Previous Studies and Discussion

To our knowledge, all previous direct kinetic studies^5–9 of the reaction of OH + Br₂ have been performed at low temperatures. Data reported in references 5 and 6 were measured at room temperature only. The rate coefficient value obtained by Poulet et al⁵ is in excellent agreement with that given by expression III at room temperature. The result of k₁ value reported by Loewenstein et al⁶ is 23% higher than that given by expression III at room temperature. Nevertheless, it agrees with our room temperature measurement within combined experimental uncertainties of both studies.

Experimental temperature-dependent kinetic investigations of the reaction of the hydroxyl radical with molecular bromine were carried out in three studies.^7–9 Boodaghians et al⁷ measured k₁ at four temperatures only over the temperature range of 262 – 303 K. As can be seen from Figure 3 these k₁ data are systematically lower than ours and those from references 5–9 in the common temperature intervals, but they are in agreement with them near room temperature within the experimental uncertainties. Their data show a slight positive temperature dependence (see Figure 3). However, Boodaghians et al⁷ preferred to regard the reaction of OH with Br₂ as being temperature-independent within experimental uncertainty over the temperature range studied.

Measurements performed in references 8 and 9 showed a distinct, albeit weak, negative temperature dependences k₁(T) = (1.98 ± 0.51) × 10⁻¹¹exp[(238 ± 70 K/T)] and k₁(T) = (1.8 ± 0.3) × 10⁻¹¹exp[(235 ± 50 K/T)] cm³molecule⁻¹s⁻¹, respectively, which are in agreement with each other. As can be seen from Figure 3 the plot of equation III lies between the data obtained by Gilles et al⁸ and Bedjanian et al.⁹ These data are in agreement with equation III within the reported experimental uncertainties and can be combined with the current experimental k₁(T) data set. Indeed, if our k₁(T) data set is combined with the k₁(T) data sets from references 8, 9, then the least-squares fit of the resultant combined set of data to the equation of the form k₁(T) = AT ⁿ yields the expression

$$k_1(T)=1.96\times {10}^{-9}{T}^{-0.67}{\text{cm}}^3{\text{molecule}}^{-1}{\text{s}}^{-1}(230-766\text{K})$$ (V)

The maximum and average square deviations of experimental rate coefficient values of the resultant combined set of data from those calculated using two-parameter expression V are 15% and 6% of the calculated value, respectively. The maximum deviation between values given by equations III and V is 0.9 % in the temperature range 230 – 766 K. Thus, either expression III or that V can be recommended for the temperature dependence of the reaction of the hydroxyl radical with molecular bromine in the temperature range from 230 to 766 K, because these two expressions give practically the same values of k₁(T).

HOBr and Br are expected to be the products of reaction 1. This product channel is exothermic (ΔH⁰₂₉₈ = −15.7 ± 8.8 kJ mol^{−1 27–29}). The only other product channel that can be suggested, that producing HBr + BrO, is endothermic (ΔH⁰₂₉₈ = 14.8 ± 6.4 kJ mol^{−1 27,28,30}). 100% yield of the atomic Br product was observed in reaction 1 experimentally.^5,6 The conclusion of the dominance of the HOBr + Br product channel is also supported by an analogy with the OH + Cl₂ reaction where a 100% yield of Cl was observed experimentally⁶ and a PES study performed in reference ¹⁰ demonstrated that the reaction proceeds to form only HOCl + Cl products, with the alternative (HCl + ClO) channel requiring overcoming a large potential energy barrier.

The rate coefficients calculated using the model of reaction 1 created in the current study on the basis of CCSD(T)/aug-cc-pVTZ //CCSD/aug-cc-pVDZ PES calculations are, generally, in good agreement with the experimental values. Without any model adjustment, the calculated rate coefficient values are only ~ 40% lower than the experimental ones. This deviation is quite reasonable for a model completely based on ab initio PES. Adjustment of the energy of the PES saddle point by only −2 kJ mol⁻¹ brings the calculated values into a much better agreement with experiment. Comparison of the experimental and the calculated 0 K enthalpies of reaction 1 (Table 2) is not very conclusive regarding the adequacy of the computational methods used because of the large uncertainty of the experimental value resulting, primarily, from that in the H_f⁰₂₉₈(HOBr) (± 8.4 kJ mol⁻¹);²⁹ the 0 K reaction enthalpy values calculated at the CCSD(T)/aug-cc-pVTZ level are only 0.7 – 1.4 kJ mol⁻¹ outside of the estimated envelope of uncertainty of the experimental value. The deviation depends on the size of the basis set used in single-point energy calculations: it becomes significantly larger (~15 kJ mol⁻¹) if the smaller aug-cc-pVDZ basis set is used.

Despite the generally good agreement between the calculated and the experimental values of the rate coefficients, the failure of the computational model to reproduce the experimental negative curvature of the Arrhenius plot of the rate coefficient is disconcerting. The model thus is not suitable for extrapolation of the experimental data to temperatures outside the experimental range. Instead, use of equations III or V are recommended. It may be possible that a more involved version of the rate theory (e.g., microcanonical variational approach to the selection of the position of the dynamic bottleneck of the reaction and explicit accounting for the finite ratio of the rates of dissociation of the OH···Br₂ complex to reactants and products) can improve the agreement between computations and experiment. However, application of more complicated versions of rate theory will be meaningful only if a larger degree of certainty is achieved in the properties of the reaction PES.