Atmospheric Chemistry of HOHg(II)O• Mimics That of a Hydroxyl Radical.

HOHg(II)O•, formed from HOHg(I)• + O3, is a key intermediate in the OH-initiated oxidation of Hg(0) in the atmosphere. As no experimental data are available for HOHg(II)O•, we use computational chemistry (CCSD(T)//M06-2X/AVTZ) to characterize its reactions with atmospheric trace gases (NO, NO2, CH4, C2H4, CH2O and CO). In summary, HOHg(II)O•, like the analogous BrHg(II)O• radical, largely mimics the reactivity of •OH in reactions with NOx, alkanes, alkenes, and aldehydes. The rate constant for its reaction with methane (HOHg(II)O• + CH4 → Hg(II)(OH)2 + •CH3) is about four times higher than that of •OH at 298 K. All of these reactions maintain mercury as Hg(II), except for HOHg(II)O• + CO → HOHg(I)• + CO2. Considering only the six reactions studied here, we find that reduction by CO dominates the fate of HOHg(II)O• (79-93%) in many air masses (in the stratosphere and at ground level in rural, marine, and polluted urban regions) with only modest competition from HOHg(II)O• + CH4 (<15%). We expect that this work will help global modeling of atmospheric mercury chemistry.

Together, Not Separately, OH and O3 Oxidize Hg(0) to Hg(II) in the Atmosphere.

Mercury, a highly toxic metal, is emitted to the atmosphere mostly as gaseous Hg(0). Atmospheric Hg(0) enters ecosystems largely through uptake by vegetation, while Hg(II) largely enters ecosystems in oceans and in rainfall. Consequently, the redox chemistry of atmospheric mercury strongly influences its fate and its global biogeochemical cycling. Here we report on the oxidation and reduction of Hg(I) (BrHg and HOHg radicals) in reactions with ozone and how the electronic structure of these Hg(I) species affects the kinetics of these reactions. The oxidation reactions lead to YHgO· + O2 (Y = Br and OH), while the reduction reactions produce Hg(0), OY, and O2. According to our calculations with CCSD(T), NEVPT2, and CAM-B3LYP-D3BJ, the kinetics of both oxidation reactions are very similar and much faster than their reduction counterparts. Past modeling of field data has supported the idea that OH and/or O3 (rather than Br) dominates Hg(II) production in the continental boundary layer. Almost all models invoking OH- and ozone-initiated oxidation of Hg(0) assume that these reactions produce Hg(II) in one step, despite the lack of plausible mechanisms. The two-step mechanism of formation of HOHg followed by its reaction with ozone helps reconcile modeling results with mechanistic insights.

Combined Experimental and Computational Kinetics Studies for the Atmospherically Important BrHg Radical Reacting with NO and O2.

We report on the first experimental determination of the absolute rate constant of the reaction of BrHg + NO in N2 bath gas using a laser photolysis-laser-induced fluorescence (LP-LIF) system. The rate constant of the reaction of BrHg + NO is determined to be 7.0-0.9+1.3 × 10-12 cm3 molecule-1 s-1 over 50-700 Torr and 315-353 K. The absence of a pressure or temperature dependence suggests that this reaction leads mainly to mercury reduction (Hg + BrNO) rather than mercury oxidation (BrHgNO). Our theoretical calculations using NEVPT2 energies on density functional theory (DFT) geometries are consistent with a barrierless reaction to form Hg + BrNO. The equilibrium constants and the rate constants of the reaction BrHg + O2 ⇌ BrHgOO are computed theoretically because they are too low to be measured in the LP-LIF system. Molecular oxygen quenches the LIF signal of BrHg with a large rate constant of (1.7 ± 0.1) × 10-10 cm3 molecule-1 s-1. Thus, different techniques that capture the absolute [BrHg(X̃)] would be advantageous for kinetics studies of BrHg reactions in the presence of O2. The computed equilibrium constant suggests a non-negligible upper limit of the fraction of BrHg stored as BrHgOO (up to 0.5) at low-temperature conditions, e.g., in the upper troposphere and in polar winters at ground level. Preliminary results indicate that BrHgOO behaves like HOO or organic peroxy radicals in reactions with atmospheric radicals.

Improved Mechanistic Model of the Atmospheric Redox Chemistry of Mercury.

We present a new chemical mechanism for Hg0/HgI/HgII atmospheric cycling, including recent laboratory and computational data, and implement it in the GEOS-Chem global atmospheric chemistry model for comparison to observations. Our mechanism includes the oxidation of Hg0 by Br and OH, subsequent oxidation of HgI by ozone and radicals, respeciation of HgII in aerosols and cloud droplets, and speciated HgII photolysis in the gas and aqueous phases. The tropospheric Hg lifetime against deposition in the model is 5.5 months, consistent with observational constraints. The model reproduces the observed global surface Hg0 concentrations and HgII wet deposition fluxes. Br and OH make comparable contributions to global net oxidation of Hg0 to HgII. Ozone is the principal HgI oxidant, enabling the efficient oxidation of Hg0 to HgII by OH. BrHgIIOH and HgII(OH)2, the initial HgII products of Hg0 oxidation, respeciate in aerosols and clouds to organic and inorganic complexes, and volatilize to photostable forms. Reduction of HgII to Hg0 takes place largely through photolysis of aqueous HgII-organic complexes. 71% of model HgII deposition is to the oceans. Major uncertainties for atmospheric Hg chemistry modeling include Br concentrations, stability and reactions of HgI, and speciation and photoreduction of HgII in aerosols and clouds.

Theoretical Study of the Monohydration of Mercury Compounds of Atmospheric Interest.

The structures, vibrational frequencies, and model IR spectra of the monohydrates of oxygenated mercury compounds (BrHgO, BrHgOH, BrHgOOH, BrHgNO2, BrHgONO, and HgOH) have been theoretically studied using the ωB97X-D/aug-cc-pVTZ level of theory. The ground state potential energy surface exhibits several stable structures of these monohydrates. The thermodynamic properties of the hydration reactions have been calculated at different levels of theory including DFT and coupled-cluster calculations DK-CCSD(T) with the ANO-RCC-Large basis sets. Standard enthalpies and Gibbs free energies of hydration were computed. The temperature dependence of ΔrG°(T) was evaluated for the most stable complexes over the temperature range 200-400 K. Thermodynamic data revealed that the highest fraction hydrated at 298 K and 100% relative humidity will be BrHgNO2-H2O at ∼5%.

Modeling the OH-Initiated Oxidation of Mercury in the Global Atmosphere without Violating Physical Laws.

In 2005, Calvert and Lindberg (Calvert, J. G.; Lindberg, S. E. Atmos. Environ. 2005, 39, 3355-3367) wrote that the use of laboratory-derived rate constants for OH + Hg(0) "...to determine the extent of Hg removal by OH in the troposphere will greatly overestimate the importance of Hg removal by this reaction." The HOHg• intermediate formed from OH + Hg will mostly fall apart in the atmosphere before it can react. By contrast, in laboratory experiments, Calvert and Lindberg expected HOHg• to react with radicals (whose concentrations are much higher than in the atmosphere). Yet, almost all models of oxidation of Hg(0) ignore the argument of Calvert and Lindberg. We present a way for modelers to include the OH + Hg reaction while accounting quantitatively for the dissociation of HOHg•. We use high levels of quantum chemistry to establish the HO-Hg bond energy as 11.0 kcal/mol and calculate the equilibrium constant for OH + Hg = HOHg•. Using the measured rate constant for the association of OH with Hg, we determine the rate constant for HOHg• dissociation. Theory is also used to demonstrate that HOHg• forms stable compounds, HOHgY, with atmospheric radicals (Y = NO2, HOO•, CH3OO•, and BrO). We then present rate constants for use in modeling OH-initiated oxidation of Hg(0). We use this mechanism to model the global oxidation of Hg(0) in the period 2013-2015 using the GEOS-Chem 3D model of atmospheric chemistry. Because of the rapid dissociation of HOHg•, OH accounts for <1% of the global oxidation of Hg(0) to Hg(II), while Br atoms account for 97%.

BrHgO• + C2H4 and BrHgO• + HCHO in Atmospheric Oxidation of Mercury: Determining Rate Constants of Reactions with Prereactive Complexes and Bifurcation.

Models suggest BrHgONO to be the major Hg(II) species formed in the global oxidation of Hg(0), and BrHgONO undergoes rapid photolysis to produce the thermally stable radical BrHgO•. We previously used quantum chemistry to demonstrate that BrHgO• can, like •OH radicals, readily abstract hydrogen atoms from sp3-hybridized carbon atoms as well as add to NO and NO2. In the present work, we reveal that BrHgO• can also add to C2H4 to form BrHgOCH2CH2•, although this addition appears to proceed with a lower rate constant than the analogous addition of •OH to C2H4. Additionally, BrHgO• can readily react with HCHO in two different ways: either by addition to carbon or by abstraction of a hydrogen atom. The minimum energy path for the BrHgO• + HCHO reaction bifurcates, forming two prereactive complexes, each of which passes over a separate transition state to form different products. Rate constants computed using Master Equation simulations indicate that hydrogen abstraction dominates over addition at atmospheric temperatures (200 K ≤ T ≤ 333 K) and pressures (0.01 atm ≤ P ≤ 1 atm). Subsequently, we compute the atmospheric fate of BrHgO• in a variety of air masses and find that BrHgOH formation via hydrogen abstraction will be the predominant fate (∼70-99%), with major competition (∼20%) coming from addition to NO and NO2 in polluted urban regions and stratospheric air. Given the absence of either field data on the identity of Hg(II) compounds or experimental data on the kinetics of BrHgO• reactions, the present manuscript should provide guidance to a range of scientists studying atmospheric mercury.

Computational Study on the Photolysis of BrHgONO and the Reactions of BrHgO• with CH4, C2H6, NO, and NO2: Implications for Formation of Hg(II) Compounds in the Atmosphere.

Global models suggest BrHgONO to be the major Hg(II) species initially formed in atmospheric oxidation of Hg(0) in most of the atmosphere, but its atmospheric fate has not been previously investigated. In the present work, we use quantum chemistry to predict that BrHgONO photolysis produces the thermally stable radical BrHgO•. Subsequently, BrHgO• may react with NO2 to form thermally stable BrHgONO2, or with NO to re-form BrHgONO. Additionally, BrHgO• abstracts hydrogen atoms from CH4 and C2H6 with higher rate constants than does •OH, producing a stable BrHgOH molecule. Because BrHgO• can abstract hydrogen atoms from sp3-hybridized carbons on many organic compounds, we expect production of BrHgOH to dominate globally, although formation of BrHgONO and BrHgONO2 may compete in urban regions. In the absence of experimental data on the kinetics and fate of BrHgONO and BrHgO•, we aim to guide modelers and other scientists in their search for Hg(II) compounds in the atmosphere.

Correction: Comment on "Isomerization of the methoxy radical revisited: the impact of water dimers" by B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2016, 18, 27728 and "Isomerization of methoxy radical in the troposphere: competition between acidic, neutral and basic catalysts" by P. Kumar, B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2017, 19, 278.

Correction for 'Comment on "Isomerization of the methoxy radical revisited: the impact of water dimers" by B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2016, 18, 27728 and "Isomerization of methoxy radical in the troposphere: competition between acidic, neutral and basic catalysts" by P. Kumar, B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2017, 19, 278' by Theodore S. Dibble et al., Phys. Chem. Chem. Phys., 2018, 20, 11481-11482.

Comment on "Isomerization of the methoxy radical revisited: the impact of water dimers" by B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2016, 18, 27728 and "Isomerization of methoxy radical in the troposphere: competition between acidic, neutral and basic catalysts" by P. Kumar, B. Bandyopadhyay et al., Phys. Chem. Chem. Phys., 2017, 19, 278.

In two recent papers Bandyopadhyay and co-workers studied how atmospheric trace gases catalyze the isomerization of methoxy radical (CH3O˙) to hydroxymethyl radical (˙CH2OH). Their second paper extensively discussed the altitude dependence of this catalyzed isomerization. Unfortunately, they did not compare their computed isomerization rates with the abundant kinetic data on the long-established fate of CH3O˙: reaction with O2. This Comment shows that the fastest rate they compute for catalyzed isomerization is over one million times slower than the O2 reaction at all altitudes considered in those papers. Furthermore, we argue that, even if the reaction CH3O˙ → ˙CH2OH were to occur, it would not have any atmospheric consequence. This is because the near-exclusive atmospheric fate of both ˙CH2OH and CH3O˙ is reaction with O2 to produce CH2[double bond, length as m-dash]O + HOO.

Structures, Vibrational Frequencies, and Bond Energies of the BrHgOX and BrHgXO Species Formed in Atmospheric Mercury Depletion Events.

Photochemistry during the polar spring leads to atmospheric mercury depletion events (AMDEs): Hg(0), which typically lives for months in the atmosphere, and can experience losses of more than 90% in less than a day. These dramatic losses are known to be initiated largely by Br + Hg + M → BrHg• + M, but the fate of BrHg• is a matter of guesswork. It is believed that BrHg• largely reacts with halogen oxides XO (X = Cl, Br, and I) to form BrHgOX compounds, but these species have never been studied experimentally. Here, we use quantum chemistry to characterize the structures, vibrational frequencies, and thermodynamics of these BrHgOX species and their BrHgXO isomers. The BrHgXO isomers have never previously been studied in experiments or computations. We find the BrHgOX species are 24-28 kcal/mol more stable than their BrHgXO isomers. When formed during polar AMDEs, BrHgBrO and BrHgIO appear sufficiently stable in that they will not dissociate before undergoing deposition, but BrHgClO is probably not that stable.

First kinetic study of the atmospherically important reactions BrHg˙ + NO2 and BrHg˙ + HOO.

We use computational chemistry to determine the rate constants and product yields for the reactions of BrHg˙ with the atmospherically abundant radicals NO2 and HOO. The reactants, products, and well-defined transition states are characterized using CCSD(T) with large basis sets. The potential energy profiles for the barrierless addition of HOO and NO2 to BrHg˙ are characterized using CASPT2 and RHF-CCSDT, and the rate constants are computed as a function of temperature and pressure using variational transition state theory and master equation simulations. The calculated rate constant for the addition of NO2 to BrHg˙ is larger than that for the addition of HOO by a factor of up to two under atmospheric conditions. For the reaction of HOO with BrHg˙ the addition reaction entirely dominates competing HOO + BrHg˙ reaction channels. The addition of NO2 to BrHg˙ initially produces both BrHgNO2 and BrHgONO, but after a few seconds under atmospheric conditions the sole product is syn-BrHgONO. A previously unsuspected reaction channel for BrHg˙ + NO2 competes with the addition to yield Hg + BrNO2. This reaction reduces the mercury oxidation state in BrHg˙ from Hg(i) to Hg(0) and slows the atmospheric oxidation of Hg(0). While the rate constant for this reduction channel is not well-constrained by the present calculations, it may be as much as 18% as large as the oxidation channel under some atmospheric conditions. As no experimental kinetic or product yield data are available for the reactions studied here, this work will provide guidance for atmospheric modelers and experimental kineticists.

Quality Structures, Vibrational Frequencies, and Thermochemistry of the Products of Reaction of BrHg(•) with NO2, HO2, ClO, BrO, and IO.

Quantum chemical calculations have been carried out to investigate the structures, vibrational frequencies, and thermochemistry of the products of BrHg(•) reactions with atmospherically abundant radicals Y(•) (Y = NO2, HO2, ClO, BrO, or IO). The coupled cluster method with single and double excitations (CCSD), combined with relativistic effective core potentials, is used to determine the equilibrium geometries and harmonic vibrational frequencies of BrHgY species. The BrHg-Y bond energies are refined using CCSD with a noniterative estimate of the triple excitations (CCSD(T)) combined with core-valence correlation consistent basis sets. We also assess the performances of various DFT methods for calculating molecular structures and vibrational frequencies of BrHgY species. We attempted to estimate spin-orbit coupling effects on bond energies computed by comparing results from standard and two-component spin-orbit density functional theory (DFT) but obtained unphysical results. The results of the present work will provide guidance for future studies of the halogen-initiated chemistry of mercury.

Quantum Chemical Study of Autoignition of Methyl Butanoate.

Methyl butanoate is a widely studied surrogate for fatty acid esters used in biodiesel fuel. Here we report a detailed analysis of the thermodynamics and kinetics of the autoignition chemistry of methyl butanoate. We employ composite CBS-QB3 calculations to construct the potential energy profiles of radicals derived from methyl butanoate. We compare our results with recently published G3MP2B3 results for reactions of peroxy (ROO(•)) and hydroperoxy alkyl ((•)QOOH) radicals and comment on differences in barrier heights and reaction enthalpies. Our emphasis, however, is on hydroperoxy alkylperoxy ((•)OOQOOH) radicals that are critical for autoignition of diesel fuel. We examined four classes of reactions: peroxy radical interconversion of (•)OOQOOH ((•)OOQOOH→ HOOQOO(•)), H-migration reactions (from carbon to oxygen), HO2 elimination, and cyclic ether formation with elimination of OH radical. We evaluate the significance of reaction pathways by comparing rate coefficients in the high-pressure limit. Unexpectedly, we find a low activation barriers for 1,8 H-migration of RC(═O)OCH2OO(•). We also find peroxy radical interconversion of (•)OOQOOH radicals from methyl butanoate commonly possess the lowest barriers of any unimolecular reaction of these radicals, despite that they proceed via 8-, 10- and 11-member ring transition states. At temperatures relevant to autoignition, these peroxy radical interconversions are dominant or significant reaction pathways. This means that some (•)OOQOOH radicals that were expected to be produced in negligible yields are, instead, major products in the autoignition of methylbutanoate (MB). These reactions have not previously been considered for MB, and will require revision of models of autoignition of methyl butanoate and other esters.

Quantum chemistry guide to PTRMS studies of as-yet undetected products of the bromine-atom initiated oxidation of gaseous elemental mercury.

A series of BrHgY compounds (Y = NO2, ClO, BrO, HOO, etc.) are expected to be formed in the Br-initiated oxidation of Hg(0) to Hg(II) in the atmosphere. These BrHgY compounds have not yet been reported in any experiment. This article investigates the potential to use proton-transfer reaction mass spectrometry (PTRMS) to detect these atmospherically important species. We show that reaction of the standard PTRMS reagent (H3O(+)) with BrHgY leads to stable parent (M + 1) ions, BrHgYH(+), for most of these radicals, Y. Rate constants for the proton transfer reaction H3O(+) + BrHgY are computed using average dipole orientation theory. Calculations are also carried out on the commercially available compounds HgCl2, HgBr2, and HgI2 to enable tests of the present work.

Rate constants and kinetic isotope effects for methoxy radical reacting with NO2 and O2.

Relative rate studies were carried out to determine the temperature dependent rate constant ratio k1/k2a: CH3O· + O2 → HCHO + HO2· and CH3O· + NO2 (+M) → CH3ONO2 (+M) over the temperature range 250­333 K in an environmental chamber at 700 Torr using Fourier transform infrared detection. Absolute rate constants k2 were determined using laser flash photolysis/laser-induced fluorescence under the same conditions. The analogous experiments were carried out for the reactions of the perdeuterated methoxy radical (CD3O·). Absolute rate constants k2 were in excellent agreement with the recommendations of the JPL Data Evaluation panel. The combined data (i.e., k1/k2 and k2) allow the determination of k1 as 1.3(­0.5)(+0.9) × 10(­14) exp[−(663 ± 144)/T] cm(3) s(­1), corresponding to 1.4 × 10(­15) cm(3) s(­1) at 298 K. The rate constant at 298 K is in excellent agreement with previous work, but the observed temperature dependence is less than was previously reported. The deuterium isotope effect, kH/kD, can be expressed in the Arrhenius form as k1/k3 = (1.7(­0.4)(+0.5)) exp((306 ± 70)/T). The deuterium isotope effect does not appear to be greatly influenced by tunneling, which is consistent with a previous theoretical work by Hu and Dibble. (Hu, H.; Dibble, T. S., J. Phys. Chem. A 2013, 117, 14230­14242.)

Quantum chemistry, reaction kinetics, and tunneling effects in the reaction of methoxy radicals with O(2).

The reaction of the methoxy radical with O2 is the prototype for the reaction of a range of larger alkoxy radicals with O2 in the lower atmosphere. This reaction presents major challenges to quantum chemistry, with CCSD(T) overpredicting the barrier height by about 7 kcal/mol in the complete basis set limit. CCSD(T) calculations also indicate that the CH3OOO(•) analog of the HOOO(•) radical is energetically unstable with respect to CH3O(•) + O2, a finding that seems unlikely. The previous successful prediction of the barrier height using CCSD(T)/cc-pVTZ energies at CASSCF/6-311G(d,p) geometries is shown to rely on the use of a metastable Hartree-Fock reference wave function. The performance of several density functionals is explored and B3LYP is selected to examine the role of tunneling, including the competition between small curvature tunneling (SCT) and large curvature tunneling (LCT). SCT is found to be sufficient to describe tunneling, in contrast to the typical findings for bimolecular hydrogen-abstraction reactions. The previously proposed mechanism of a cyclic transition state yields rate constants for CH3O(•) + O2 that faithfully reproduces the experimentally derived Arrhenius pre-exponential term. Predictions of the branching ratios for the competing reactions CH2DO(•) + O2 → CHDO + HO2 (1a) and CH2DO(•) + O2→ CH2O + DO2 (1b) are also in good agreement with experiment.

Cis-trans isomerization of chemically activated 1-methylallyl radical and fate of the resulting 2-buten-1-peroxy radical.

The cis-trans isomerization of chemically activated 1-methylallyl is investigated using RRKM/Master Equation methods for a range of pressures and temperatures. This system is a prototype for a large range of allylic radicals formed from highly exothermic (∼35 kcal/mol) OH + alkene reactions. Energies, vibrational frequencies, anharmonic constants, and the torsional potential of the methyl group are computed with density functional theory for both isomers and the transition state connecting them. Chemically activated radicals are found to undergo rapid cis-trans isomerization leading to stabilization of significant amounts of both isomers. In addition, the thermal rate constant for trans → cis isomerization of 1-methylallyl is computed to be high enough to dominate reaction with O(2) in 10 atm of air at 700 K, so models of the chemistry of the (more abundant and more commonly studied) trans-alkenes may need to be modified to include the cis isomers of the corresponding allylic radicals. Addition of molecular oxygen to 1-methylallyl radical can form 2-butene-1-peroxy radical (CH(3)CH═CHCH(2)OO(•)), and quantum chemistry is used to thoroughly explore the possible unimolecular reactions of the cis and trans isomers of this radical. The cis isomer of the 2-butene-1-peroxy radical has the lowest barrier (via 1,6 H-shift) to further reaction, but this barrier appears to be too high to compete with loss of O(2).

Temperature-dependent branching ratios of deuterated methoxy radicals (CH2DO•) reacting with O2.

The methoxy radical is an intermediate in the atmospheric oxidation of methane, and the branching ratio (k(1a)/k(1b)) (CH(2)DO• + O(2) → CHDO + HO(2) (1a) and CH(2)DO• + O(2) → CH(2)O + DO(2) (1b)) strongly influences the HD/H(2) ratio in the atmosphere, which is widely used to investigate the global cycling of molecular hydrogen. By using the FT-IR smog chamber technique, we measured the yields of CH(2)O and CHDO from the reaction at 250-333 K. Kinetic modeling was used to confirm the suppression of secondary chemistry. The resulting branching ratios are well fit by an Arrhenius expression: ln(k(1a)/k(1b)) = (416 ± 152)/T + (0.52 ± 0.53), which agrees with the room-temperature results reported in the only previous study. The present results will be used to test our theoretical understanding of the role of tunneling in the methoxy + O(2) reaction, which is the prototype for the entire class of alkoxy + O(2) reactions.

Impact of tunneling on hydrogen-migration of the n-propylperoxy radical.

The kinetics of three unimolecular reactions of the n-propylperoxy radical were studied by canonical variational transition state theory and multidimensional small curvature tunneling (SCT). The reactions studied were 1,5 and 1,4 H-migration, and HO(2) elimination. Benchmark calculations were carried out at the CCSD(T) level in order to determine which density functional to use for SCT calculations for each reaction. For 1,5 and 1,4 H-migration, and HO(2) elimination, the M05-2X, B3LYP and B1B95 functionals, respectively, performed closest to the benchmark when coupled to the 6-311+G(2df,2p) basis set. The SCT tunneling corrections, κ(T), computed here were much larger than those calculated from the Wigner or zero-curvature tunneling treatments at low temperatures, but the asymmetric Eckart method works surprisingly well in these three reactions. Comparison of energy-dependent transmission coefficients, Γ(E), indicates that not only the magnitude, but also the sign, of the error in the Eckart approximation is a function of energy; therefore, the error introduced by using the Eckart approach depends strongly on the steady state energy distribution. These results may provide guidance for future studies of tunneling effects in reactions of other peroxy radicals.