doi.org/10.26434/chemrxiv.10062161.v2

Modeling the OH-Initiated Oxidation of Mercury in the GlobalAtmosphere Without Violating Physical LawsTheodore Dibble, Hanna Tetu, yuge jiao, Colin Thackray, Daniel J. Jacob

Submitted date: 02/11/2019 • Posted date: 07/11/2019Licence: CC BY-NC-ND 4.0Citation information: Dibble, Theodore; Tetu, Hanna; jiao, yuge; Thackray, Colin; Jacob, Daniel J. (2019):Modeling the OH-Initiated Oxidation of Mercury in the Global Atmosphere Without Violating Physical Laws.ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.10062161.v2

We present a way for modelers to include the OH + Hg reaction while accounting quantitatively for thedissociation of HOHg•. We use high levels of quantum chemistry to establish the HO-Hg bond energy as 11.0kcal/mole, and calculate the equilibrium constant for OH + Hg = HOHg•. Using the measured rate constant forassociation of OH with Hg, we determine the rate constant for HOHg• dissociation. Theory is also used todemonstrate that HOHg• forms stable compounds, HOHgY, with atmospheric radicals (Y = NO2, HOO•,CH3OO•, and BrO). We then present rate constants for use in in modeling OH-initiated oxidation of Hg(0). Weuse this mechanism to model the global oxidation of Hg(0) in the period 2013-2015 using the GEOS-Chem 3Dmodel of atmospheric chemistry. Because of the rapid dissociation of HOHg•, OH accounts for <1% of theglobal oxidation of Hg(0) to Hg(II), while Br atoms account for 97%.

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

Theodore S. Dibblea*, Hanna L. Tetua, and Yuge Jiaoa, Colin P. Thackrayb, Daniel J. Jacobb, c

a) Department of Chemistry, State University of New York, College of Environmental Science and Forestry, 1 Forestry Drive, Syracuse, NY, 13210

b) Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

c) Department of Earth & Planetary Sciences, Harvard University, Cambridge, MA, USA

ABSTRACT

In 2005, Calvert and Lindberg 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 over-estimate 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/mole, and calculate the equilibrium constant for OH + Hg = HOHg•. Using the measured rate constant for 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 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%.

*Corresponding Author: tsdibble@esf.edu

 

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INTRODUCTION

The toxicity of mercury motivates research into its environmental chemistry and transport. It has long been realized that the atmosphere enables transport of mercury from emission sites to anywhere in the globe.1 Recently, the international community agreed to reduce emissions of mercury in order to reduce harm to humans and the environment. This agreement, the Minimata Convention, calls for modeling of mercury fate and transport in order to guide emissions reductions.2

Gaseous elemental mercury (Hg(0), aka GEM) dominates mercury emissions to the atmosphere.3 GEM is oxidized in the atmosphere to mercuric compounds (Hg(II)), which are soluble in water and, hence, efficiently removed by deposition.1 As a result, understanding the mechanism and kinetics of oxidation of Hg(0) is critically important for predicting when and where mercury enters ecosystems.4, 5 Yet the scientific community cannot agree on which species initiate the oxidation of GEM!6,7 This disagreement hinders the progress of research into the global cycling of mercury.

The hydroxyl radical (OH) is the most important oxidant for most organic and inorganic compounds in the atmosphere, so it is natural to suspect that it might play a major role in GEM oxidation. The reaction of OH with Hg is presumed to proceed via:

OH + Hg (+M) HOHg• (+M) (1)

where M is a third body. The three experimental studies of the kinetics of reaction (1) all agree well with each other; we summarize them here. Sommar et al. used a relative rate technique to obtain k1 = (8.7 ± 3) × 10-14 cm3 molecule-1 sec-1 at 295 K in 1 atm of air.8 Bauer et al reported an upper limit of 1.2 × 10-13 cm3 molecule-1 sec-1 at 298 K in 400 Torr of air using laser-induced fluorescence (LIF) detection of OH in the presence of excess Hg(0).9 Pal and Ariya used relative rate measurements to determine the rate constant as a function of temperature (283 K ≤ T ≤ 353 K) in 1 atm air.10 At 295 K, their Arrhenius expression corresponds to a value only 10% higher than that of Sommar et al.

Subsequently, in 2005, Goodsite et al.11 used computational chemistry to study the dissociation of HOHg•. They pointed out that the weak HO-Hg bond (they reported D0 = 9.4 kcal/mole) would lead to fast dissociation of HOHg•. On account of this fast dissociation, they largely discounted the importance of OH radical in Hg(0) oxidation in favor of oxidation by Br atoms.

Calvert and Lindberg12 tried to reconcile the fast dissociation of HOHg• with the results of the relative rate experiments. They pointed out that the high concentrations of radicals, •Y, in those experiments would enable HOHg• to react with radicals to make stable Hg(II) compounds via:

HOHg• + •Y (+M) HOHgY (+M) (2)

 

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in competition with HOHg• dissociation. They concluded that OH-initiated oxidation of GEM would be much less efficient in the atmosphere than implied by experiments, due to the much lower radical concentrations in the atmosphere. As of this writing, their paper has been cited approximately 200 times, and that of Goodsite et al. has been cited over 250 times, yet almost all models of Hg(0) oxidation that include OH-initiation assume that the OH + Hg reaction is irreversible. This assumption violates detailed balancing.

How do models of the OH-initiated oxidation of GEM reconcile their assumption that reaction (1) is irreversible with the results of Goodsite et al. and Calvert and Lindberg? Some models ignore the issue by using operational definitions of the products rather than specifying their identity.13,14 In other instances the assumed irreversibility of reaction (1) is rationalized8,10,15 by the rapid occurrence of:

HOHg• + O2 HgO + HOO (3)

However, we know now that reaction (3) cannot occur under atmospheric conditions, because it is endothermic by ~60 kcal/mole.16–20 This endothermicity largely arises from the very low bond energy of HgO (~4 kcal/mole). Furthermore, as a result of its weak bonding, the HgO molecule will fall apart extremely rapidly:

HgO Hg + O (4)

As a result of reaction (4), the occurrence of reaction (1) followed by reaction (3) cannot account for the loss of Hg(0) observed in the presence of OH without violating the law of mass conservation. While the last several years have seen extensive studies of the kinetics and mechanism of Br-initiated oxidation of Hg(0),18,21–28 similar work has not been carried out for OH-initiated oxidation.

The importance of OH in initiating Hg(0) oxidation depends, in large part, on the rate of HOHg• dissociation and the rate of oxidation of HOHg• to Hg(II) compounds. The rate of HOHg• dissociation has not been determined experimentally, and depends sensitively on the HO-Hg bond energy. We start by using quantum chemistry to determine the HO-Hg bond dissociation energy with high precision. We also show that the HHgO• isomer of HOHg• will not form from OH + Hg. Using standard methods of statistical mechanics we then obtain the equilibrium constant, K1(T), for HO-Hg formation in reaction (1). Together with the experimental measurements of k1(T), this enables determination of the rate constant, k-1(T), for HOHg• dissociation. Following this, we use quantum chemistry to demonstrate that HOHg•, like BrHg•,24,29 forms thermally stable molecules in addition reactions with NO2, HOO, CH3OO, and BrO:

HOHg• + NO2 HOHgONO (and isomers) (2a)

HOHg• + HOO• HOHgOOH (2b)

HOHg• + CH3OO• HOHgOOCH3 (2c)

HOHg• + BrO• HOHgOBr (2d)

 

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Also like BrHg•, HOHg• binds rather weakly to O2 and NO:

HOHg• + O2 HOHgOO• (2e)

HOHg• + NO HOHgNO (2f)

such that dissociation of HOHgOO• and HOHgNO occurs more rapidly than they could undergo other reactions. Next, we present arguments that HOHg• will not abstract hydrogen atoms from volatile organic compounds (VOCs) and will not add efficiently to alkenes. We then use the parallels between the HOHg-Y and BrHg-Y bond energies to suggest a set of rate constants for use in modeling the OH-initiated oxidation of Hg(0). Finally, we present results of modeling of the effect of OH-initiated oxidation of Hg(0) on global mercury concentrations.

METHODS

Calculations on HOHg-Y compounds used Gaussian0930 and Gaussian16.31 Spin-unrestricted methods were used for open-shell molecules except as noted. The standard Dunning’s (aug-)cc-pVXZ32 (X = D, T, Q, or 5) basis sets were used for O and H. To account for scalar relativistic effects, we used the Stuttgart/Cologne scalar pseudopotentials for the 60 innermost electrons of Hg (ECPMDF60).33–35 The corresponding (aug)-cc-pVXZ basis sets of Peterson and co-workers for electrons outside this ECP.33,35,36 Hereafter, we refer to this combination of pseudopotentials and basis sets as VXZ or AVXZ (when augmented with diffuse functions). Where not otherwise specified, post-Hartree-Fock methods correlated only the 5d and 6s electrons of Hg, the 4s and 4p electrons of Br, and the valence electrons of H, C, N, and O.

Calculations to determine HOHg-Y bond energies and the relative energy of HOHg• and its HHgO• isomer were carried out using geometries and unscaled harmonic vibrational frequencies (and zero-point energies) computed at PBE0/AVTZ. These calculations used a pruned grid of 99 radial shells with 590 angular points per shell. This level of theory has proven to do a good job for structure and vibrational frequencies of the analogous BrHgY species.24,29 Energies were recalculated at CCSD(T)/AVTZ.

The HO-Hg bond energy was determined by a composite method similar to the HEAT345-(Q) protocol.37,38 Coupled-cluster calculations used CFOUR Beta v2.039, except that UHF-CCSDT(Q) calculations were done by MRCC codes.40 RASSI/CASPT2 calculations were carried using Molcas 8.0.41 First, the geometries of OH and HOHg• were optimized at CCSD(T) with AVTZ and AVQZ basis sets using analytical gradients.42 Harmonic vibrational frequencies were calculated at CCSD(T)/AVTZ. Geometries were reoptimized using the analogous valence basis sets designed for correlating all electrons not included in the ECP.36,43 We denote this combination of basis sets and pseudopotentials as AwCVTZ. We determined core-valence effect on geometry, ΔCV, from the difference between geometric parameters computed at CCSD(T)/AVTZ versus CCSD(T,Full)/AwCVTZ.

 

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Absolute energies were refined at the CCSD(T)/AVQZ+ΔCV geometries. CCSD(T) energies with all electrons correlated were extrapolated to the complete basis set (CBS) limit using CCSD(T)/AwCVXZ energies for X=3 (T), 4 (Q), and 5 by fitting to the formula:44,45

(5)

These CCSD(T,Full)/CBS energies were used to obtain an initial value of the zero-point energy-exclusive bond energy at 0 K (De,CBS). As described below, correction terms to this value of De were added to account for the full triples excitations, a perturbative estimate of the quadruple excitations, and spin orbit coupling.

The effect, T, of the difference between the perturbative estimate of the triples excitation and its exact expresssion46,47 was determined by taking the difference between De computed at CCSDT/VTZ and CCSD(T)/VTZ:

T = De,CCSDT/VTZ - De,CCSD(T)/VTZ (6)

The corrections for the noniterative quadruple excitation48,49 ((Q)) were applied by comparing CCSDT(Q)/VDZ energies and CCSDT/VDZ energies as:

(Q) = De,CCSDT(Q)/VDZ - De,CCSDT/VDZ (7)

The correction for spin-orbit coupling (SOC) was computed using the restricted active space state interaction (RASSI) method50,51 with complete active space second-order perturbation theory (CASPT2)52,53 using the atomic mean field integral (AMFI)54 algorithm. The DK2 Hamiltonian was used in conjunction with relativistic RCC-ANO basis sets.55,56 The active space includes the 6s and 6p orbitals for Hg and the 2s and 2p orbitals for O. This approach yields a zero-field splitting for OH radical of 148 cm-1, which agrees well with the experimental value of 139.2 cm-1.57 Expanding the active space from (5e,6o) to (7e,7o) lowered this zero-field splitting by only 1.5 cm-1, suggesting that increasing the size of the active space would not significantly improve the accuracy of the calculation. Subtracting the reaction energy of the lowest spin-free (SF) state from that of the lowest spin-orbit (SO) state yields SOC:

SOC = De,SO-RASSI/ANO-RCC - De,SF-RASSI/ANO-CC (8)

Zero-point energies (ZPEs) of OH and HOHg• were computed at CCSD(T)/AVTZ. The final value of the bond energy, D0, was computed as:

D0 = De,CBS + T + (Q) + SOC + ZPE (9)

Results and Discussion

OH + Hg = HOHg•. Figure 1 displays the geometry of HOHg• and Table 1 compares the present results with previous theoretical results. The structure is rather sensitive to the method and basis set employed. Note that the CCSD(T)/AVQZ structure of Saiz-Lopez et al.26 is very close to that reported here (Hg-O distance shorter by 0.007 Å), but rather different from the geometry they

 

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reported using MRCISD+Q. The H-O bond distance is 0.0037 Å smaller in HOHg• than in the OH radical at the CCSD(T)/AVQZ + ΔCV level of theory. Table 2 lists the harmonic vibrational frequencies and band intensities of HOHg•, in which the frequency of the O-H stretch mode is only 31 cm-1 larger than in the OH radical. These small differences in structure and vibrational frequency between OH radical and the OH group of HOHg• do not reflect the large change in electronic structure upon addition of Hg to OH: both the Mulliken and Hirshfeld population analyses assign over half the spin density in HOHg• to the mercury atom.

Table 1. Structural parameters of HOHg• (2A’) reported in several studies (distances, R, in Ångstroms and angle, A, in degrees).

Method R(H-O) R(O-Hg) A(HOHg) Ref. B3LYP/CEP-121G 0.99 2.25 106.8 11 B3LYP/AVTZ a 0.9690 2.2079 103.6 58 B3LYP/ZORA-GI/NESC b -- 2.181 -- 20 M06-2X/AVTZ 0.964 2.100 106.2 59 MRCISD+Q/aug-cc-pVQZ 0.9433 2.1342 106.9 26 CCSD(T,Full)/AwCVTZ + ΔCV 0.9662 2.1031 103.88 this work a) using ECP60MWB b) using a triple- basis set

Figure 1. Geometry (bond distances in Å and bond angles in degrees) of HOHg• (2A’) at CCSD(T,Full)/AwCVTZ+ΔCV.

Table 2. Vibrational mode descriptions, harmonic frequencies (, cm-1), and integrated absorption intensities (S, km/mol) for HOHg• at CCSD(T)/AVTZ.

mode S

HgO stretch 401.4 10.2 HOHg bend 824.0 45.0 OH stretch 3749 42.0

 

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Table 3 lists the various contributions to the HO-Hg bond energy (D0). Note that the extrapolation of CCSD(T,Full) energies from AwCV5Z to the CBS limit changes the bond energy by only 0.18 kcal/mole. The other correction terms are modest, which encourages us to believe that the final result is very accurate. The T1 diagnostic60 for HOHg• is only 0.020, which is consistent with the modest effects we observe when extending the coupled cluster calculations past the perturbative estimate of the triples correction. As can be seen from Table 3, the sum of the T+ (Q) + SOC terms is quite small.

Table 3. Contributions to the HO-Hg bond energy (kcal/mol).

Term Value CCSD(T,Full)/CBS 12.45 ΔT 0.14 Δ(Q) 0.32 ΔSO -0.10 ΔZPE (harmonic) -1.80 Total 11.02

The HEAT345-(Q) method, which is similar to the approach used here, has an uncertainty of about 0.2 kcal/mol for bond energies of diatomic molecules in the first two rows of the periodic table.37,38,61 As discussed elsewhere, there are no benchmarks for HEAT345-(Q) for mercury compounds.62 HEAT345-(Q) includes a correction for the diagonal Born-Oppenheimer approximation. Because the bond being formed in reaction (1) is between two non-hydrogen atoms, we expect this correction to be negligible here. We estimate our value of D0 to have an uncertainty (2 s.d.) of about 0.4 kcal/mole; this assessment relies on the small size of the corrections to the CCSD(T,Full)/CBS energies seen in Table 3 and the high accuracy expected of the CCSD(T,Full)/AwCVTZ geometry and CCSD(T)/AVTZ harmonic frequencies.

Goodsite et al.11 and Ezarfi et al.58 obtained somewhat lower values of D0 that we did (9.0 and 9.5 kcal/mole, respectively). They both used a low level of theory (B3LYP), so the discrepancy between their values and ours is understandable. Cremer et al. used explicitly relativistic calculations with a basis set that was triple-zeta quality; they computed CCSD(T) energies at a B3LYP geometry.20 Their bond enthalpy of 12.4 kcal/mole at 298 K corresponds to D0 of 11.4 kcal/mole, which agrees very well with our result. Tossell63 reported D0 of only 5.5 kcal/mole ay CCSD(T)//CCD/SBK. Guzman and Bozzelli59 reported a bond enthalpy of 14.1 kcal/mole at 298 K, corresponding to D0 of 13.1 kcal/mole. Although their bond enthalpy was based on CCSD(T)/CBS energies, it relied on experimental values of the enthalpies of formation of mercury halides–values that possess uncertainties of at least 2 kcal/mole.64 Note that one theoretical study reported the unphysical result that HOHg• was unstable by 21 kcal/mole with respect to OH + Hg.65

Recall that the product of OH + Hg has not been determined experimentally. Conceivably, this reaction could produce HHgO•. Because HHgO• is an Hg(II) compound, formation of

 

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HHgO• from OH + Hg would tend to invalidate the arguments of Calvert and Lindberg regarding the efficiency of OH-initiated oxidation of Hg(0). Note that, based on literature thermodynamics,66,21 one can estimate that BrHgO• and ClHgO• are more stable than the corresponding BrO-Hg and ClO-Hg complexes by almost 20 kcal/mole. So we were somewhat surprised to find that HHgO• lies 37.7 (36.0) kcal/mol above HOHg• at the CCSD(T)//PBE0/AVTZ (PBE0/AVTZ) level of theory. Given these results, we can conclude that HHgO• cannot be formed from OH + Hg.

Using the value of D0 obtained here, together with literature data on Hg and OH (listed in the Supporting Information), we computed the equilibrium constant, Kc(T), for reaction (1) at several temperatures over the range 200-320 K. These values can be fit with less than 2% error by the expression: Kc = 2.74 × 10-24 e+5770T cm3 molecule-1 (10)

We now use Kc(T) and k1(T) to determine the rate constant, k-1(T), for dissociation of HOHg. Pal and Ariya10 reported the bimolecular rate constant, k1, (T, 1 atm), for HOHg• formation as 3.55 × 10-14 e+294/T cm3 molecule-1 sec-1 at 1 atm of pressure. The rate constant will depend on the pressure. Given that the analogous reactions forming ClHg• and BrHg• appear to be in the low-pressure limit at pressures up to 600 Torr,67,68 and given that the HO-Hg bond is significantly weaker than the bonds in ClHg and BrHg,20 we assume that reaction (1) is also in the low-pressure limit. This implies that k1(T, 1 atm) = k1,0(T)[M]1atm, where k1,0(T) is the rate constant in the low-pressure limit and [M]1atm is the total number density of gas phase species at one atmosphere total pressure at the corresponding temperature. With this assumption, we can express the rate of reaction (1) as:

Rate = k1,0(T)[OH][Hg][M] (11)

We find k1,0(T), the termolecular association rate constant, to be:

k1(T) = 3.34 × 10-33 e+43/T cm6 molecule-2 sec-1 (12)

with error of less than 1.5% due to the fitting expression. The resulting bimolecular rate constant for dissociation of HOHg• is fit to within 4% by the expression:

k-1,0(T) = 1.22 × 10-9 e-5720/T cm3 molecule-1 sec-1 (13)

where the rate of dissociation equals k-1,0(T)[HOHg•][M]. At 298 K and 1 atm, k-1,0 equals 140 sec-1, corresponding to a lifetime of only 7 ms. This lifetime is significantly longer than the 0.3 ms computed by Goodsite et al.,11 on account of our finding a stronger bond energy.

Bimolecular Reactions of HOHg• Figure 2 depicts the structures of the stable Hg(II) species that can be formed in reactions of HOHg• with various atmospherically abundant radicals (•Y). HOHg-Y distances are very similar to those computed for BrHg-Y at the same level of theory.24 Paralleling our results for BrHg• + NO2, interaction of HOHg• with NO2 yields three isomers/conformers: HOHgNO2, anti-HOHgONO, and syn-HOHgONO. Figure 3 depicts the potential energy profile for the HOHg• + NO2 system, including transition states for

 

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isomerization of HOHgNO2 to anti-HOHgONO to syn-HOHgONO. Note that the HOHgO• + NO (not shown in Figure 3) lies 7 kcal/mole above HOHg• + NO2 at CCSD(T)//PBE0/AVTZ, so HOHgO• + NO will not form from HOHg + NO2.

Figure 2. Structures of HOHgY compounds. Bond lengths (in Å) and angles (in degrees) at PBE0/AVTZ.

Figure 3: Potential Energy Profile for HOHg• + NO2 at CCSD(T)//PBE0/AVTZ. The two conformers of syn-HOHgONO are treated as one species here.

 

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At 298 K, 99.98% of the products of HOHg• + NO2 will exist as syn-HOHgONO. RRKM/Master Equation calculations in MultiWell69–71 and MESMER72 indicate that at conditions typical of the tropopause (220 K and 0.1 atm), more than 90% of HOHgNO2 will promptly (~20 ps) isomerize to the HOHgONO conformers, and the anti conformer is transformed to the syn conformer in less than 1 s. However, under these conditions, the lifetime for transforming the small remaining fraction of thermalized HOHgNO2 to syn-HOHgONO is about 1000 sec. By contrast, at 1 atm and 298 K, the system only takes about 1 second to reach equilibrium. For modeling purposes, it seems reasonable to treat syn-HOHgONO as the sole product of addition of NO2 to HOHg•.

HOHg-Y bond energies (D0) are listed in Table 4. Note that Guzman and Bozzelli59 obtained 56.2 kcal/mole (at 298 K) for the HOHg-OBr bond enthalpy, which is in good agreement with our value of D0 = 56.7 kcal/mole. Figure 4 shows that values of D0 for each HOHg-Y compound nearly match those for the corresponding BrHg-Y.21 Regression analysis shows them to correlate as:

D0(HOHg-Y) = 1.008 × D0(HOHg-Y) + 1.2 kcal/mole (14)

with R2 = 0.996. Note two methodological differences between these two studies: structures were obtained with PBE0 for HOHgY and B3LYP for BrHgY; also, the BrHg-Y calculations correlated more orbitals than is proper for the AVTZ basis set. For higher level studies of the structures and energetics of BrHgY compounds, see references 24 and 62.

Y PBE0 CCSD(T)//PBE0 -OBr 51.9 56.7 -ONO (syn-cis) 39.0 45.3 -ONO (syn-trans) 38.8 45.2 -ONO (anti) 33.0 40.0 -NO2 35.3 38.0 -OOH 38.6 44.1 -OOCH3 38.1 44.1 -NO 11.2 11.0 -O2 8.6 9.3

Table 4: HOHg-Y bond energies (kcal/mole at 0 K) at PBE0/AVTZ and CCSD(T)//PBE0/AVTZ.

Although we previously discussed the possibility that BrHg• would react with organic peroxy radicals (ROO•) to form BrHgOOR,22 no studies of this reaction have been published. Here we find that the HOHg-OOCH3 bond energy to be the same as that for HOHg-OOH. This tends to support our speculations on the stability of BrHgOOR.

 

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Figure 4: HOHg-Y bond energies (kcal/mole at CCSD(T)//PBE0/AVTZ) from this work vs. BrHg-Y bond energies (CCSD(T)//B3LYP/AVTZ) from Ref 21. The diagonal line corresponds to equal bond energies in the two classes of molecules.

In a previous paper24 we argued that BrHgNO thermally dissociates faster than it could undergo other reactions. Given that HOHgNO and BrHgNO possess essentially the same Hg-N bond energy, we conclude that the main fate of HOHgNO is dissociation. The same argument holds for individual molecules of BrHgOO• and HOHgOO•. However, the abundance of O2 means that, at any given time, small fractions of BrHg• and HOHg• will exist as BrHgOO• and HOHgOO•, respectively. Calculations at higher levels of theory are needed to obtain reliable values of Hg-O2 bond energies in these radicals and to investigate the reactions of these compounds in the atmosphere.

Having dealt with the reactions of HOHg• with abundant radicals, let us consider how HOHg• might react with VOCs: by abstraction of hydrogen atoms or addition to sp2-hybridized carbon atoms. We previously reported that BrHg• will not abstract hydrogen atoms from volatile organic compounds (VOCs). These reactions are thermodynamically disfavored due to the weakness of the BrHg-H bond (D0 = 73 ± 3 kcal/mole).73 Here we report that the isodesmic reaction:

HOHgH + BrHg• HOHg• + BrHgH (15)

possesses an enthalpy of reaction (at 0 K) of +3.5 kcal/mole at CCSD(T)//PBE0/AVTZ. This means that the HOHg-H bond energy amounts to only 76 ± 3 kcal/mole, which is much weaker than C-H and O-H bonds in VOCs. Consequently, we do not expect HOHg• to abstract hydrogen atoms from VOCs.

 

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Our study73 of the BrHg• + CH2=CH2 reaction showed that, like OH + CH2=CH2, this reaction proceeds by a barrierless formation of a van der Waals complex, which then passes over a transition state to form BrHgCH2CH2•. Figure 5 depicts the potential energy profile for the analogous HOHg• + ethylene system at PBE0/AVTZ. Like the analogous BrHg + ethylene reaction, this reaction is roughly thermoneutral. At the PBE0/AVTZ level of theory, we find that, as compared to the BrHg• + CH2=CH2 reaction, the transition state and reaction products in the HOHg• + CH2=CH2 system are both slightly higher in energy relative to reactants (by 1.4 and 3.2 kcal/mole). As we showed, the weakness of the BrHg-CH2CH2• bond means that this radical will dissociate before undergoing any bimolecular collisions.73 Given the higher barrier and lesser stability of the products in the HOHg• + CH2=CH2 reaction, we suggests that HOHg• addition to alkenes will be very inefficient.

Figure 5. Potential energy profile for HOHg + CH2=CH2 at PBE0/AVTZ.

Proposed Mechanism and Rate Constants for the OH-Initiated oxidation of Hg(0). Based on the similarity of the BrHg-Y and HOHg-Y bond energies, their formation reactions will likely possess similar pressure- and temperature-dependent rate constants, k([M],T). For purposes of modeling, we suggest assuming that the values are identical. We fit the rate constants reported by Jiao and Dibble22 for BrHg• + NO2 and BrHg• + HOO to the Troe expression:74

k([M],T) = (16)

where Fc is assumed to be 0.6, k0 is the rate constant in the low-pressure limit, k∞ is the rate constant in the high-pressure limit, and is defined by:

(17)

The resulting values of k0(T) and k∞(T) are listed in Table 5. Consistent with Horowitz et al.,23 we assume the rate constant for HOHg• + •Y takes on one value for Y = •NO2 and another value for all other •Y.

It has been shown that BrHg-OX bond energies vary rather little between X=Cl, Br, and I;62,59 Guzman and Bozzelli showed this for HOHg-OX 59 Consequently, we include HOHg• reaction with ClO and IO in the mechanism in Table 5. In a previous paper, we demonstrated the

 

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existence of BrHgXO compounds (X=Cl, Br, I) that were 26-28 kcal/mole less stable than the corresponding BrHgOX species.62 So we confidently predict that the corresponding HOHgXO compounds exist and are similarly less stable than their HOHgOX counterparts.

Table 5. Mechanism and rate constants for the OH-initiated oxidation of Hg(0). The reaction OH + Hg + M HOHg• + M is assumed to be in the low-pressure limit.

Reaction Rate Constanta, b OH + Hg + M HOHg• + M 3.34 × 10-33 e+43/T HOHg• + M OH + Hg + M 1.22 × 10-9 e-5720/T

HOHg• + NO2 M syn-HOHgONO

k0(T) = 7.1 × 10-29 (T/300)-4.5 k∞(T) = 1.2 × 10-10 (T/300)-1.9

HOHg• + •Y M HOHgY

•Y = (HOO, CH3OO, ClO, BrO, etc.) k0(T) = 2.3 × 10-29 (T/300)-4.4 k∞(T) = 6.9 × 10-11 (T/300)-2.4

a) k1 and both values of k0 are in units of cm6 molecule-2 sec-1. k-1 and k∞ are in units of cm3 molecule-1 sec-1. b) k0(T) and k∞(T) are used in the Troe expression (Eqns. 16 and 17 in the text) to get k([M],T)

Calvert and Lindberg12 buttressed their analysis of the experiment of Pal and Ariya10 with kinetic modeling. We carried out simulations based on their model, after updating the mercury chemistry and adding OH reaction with isopropylnitrite and multiple generations of reactions of the products. We find that the fate of HOHg• under the experimental conditions of Pal and Ariya is almost entirely reaction with NO2 rather than dissociation. Analysis of the extent of formation of NO2 in the experiments of Sommar et al.8 reaches the same conclusion. Details of both analyses may be found in the Supporting Information.

Global Modeling of Oxidation of Gaseous Elemental Mercury We added the above mechanism of OH-initiated oxidation of elemental mercury to the GEOS-Chem global chemistry and transport model75 to quantify its atmospheric efficiency and calculate its impact on global atmospheric Hg. We simulated both OH- and Br-initiated oxidation of elemental mercury using GEOS-Chem version 12.3.1.76 The GEOS-Chem model simulates concentrations of the relevant oxidant radical species (OH, Br, Cl, NO2, HO2, BrO, ClO, etc.), and we added mercury redox chemistry to this model’s standard simulation. Organic peroxy radicals were not included as reactants with BrHg• or HOHg•. We simulated Hg concentrations for the years 2013-2015 with 4x5 horizontal resolution and 47 vertical levels, using emissions and land surface flux boundary conditions taken from Horowitz et al.23 As in that work, we coupled our atmospheric simulation to the MITgcm ocean Hg simulation.77 Horowitz et al. considered Hg(0) oxidation by Br and Cl atoms in the gas phase and by OH(aq), O3(aq), and HOCl(aq) in cloudwater. They found that gas-phase oxidation by Br atoms accounted for 97% of the global formation of Hg(II).

Gas-phase OH-initiated Hg oxidation was added as defined in Table 5. Other oxidation pathways were as in Horowitz et al. but the pressure and temperature dependence of the second stage of Br-initiated oxidation was changed to reflect the corresponding Troe expressions above. Following Saiz-Lopez et al.,27 we used the photolysis cross sections of BrHgY species to

 

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calculate photolysis rate constants using the Fast-JX code implemented in GEOS-Chem.78,79 Photolysis of BrHgY is assumed to produce BrHg• + •Y with the exception of BrHgONO, which leads to BrHgOH via BrHgO•.25 We assume that, for each BrHgY species, the analogous HOHgY species has the same photolysis properties. While the substitution of OH for Br should cause shifts in the absorption spectra and corresponding differences in photolysis lifetimes, this effect would have to be large to affect our overall conclusions. By treating the photo-reduction of BrHgY and HOHgY identically, our simulations isolate the impact of the OH-initiated oxidation as described in this work.

Figure 6 shows the annually averaged fraction of HOHg• (top) and BrHg• (bottom) that goes on to form Hg(II) species. OH-initiated oxidation is highly inefficient at ground level. At all surface locations in the simulation, less than 15% of HOHg• goes on to form Hg(II) instead of decomposing to Hg(0). For most of the globe, this fraction is less than 5%, but the Eastern United States, Europe, and Eastern China show elevated fractions due to the presence of higher quantities of second-stage oxidants such as NO2. In contrast to oxidation via OH, Br-initiated oxidation is more than 70% efficient at ground level for most of the Northern Hemisphere. Since thermal decomposition of HOHg• competes with the second stage of oxidation, the efficiency of converting HOHg• to Hg(II) increases with increasing altitude.

Figure 6. Annually averaged percent of HOHg• (top) and BrHg• (bottom) going on to form Hg(II) compounds. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude.

 

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Because of the inefficiency of OH-initiated oxidation, adding OH-initiated oxidation to a model that already includes Br-initiated oxidation has a small effect on concentrations of total gaseous mercury (TGM, the sum of gas-phase Hg(0) and Hg(II)). In highly polluted areas (North America, Europe and East Asia) concentrations of reactive gaseous mercury (Hg(II) (g), aka RGM) increase by up to 5%. Outside of these areas, OH-initiated oxidation has effectively no in-situ effect on RGM or TGM concentrations. However, the addition of OH-initiated oxidation near sources of Hg emissions decreases the atmospheric lifetime of these emissions, and decreases global TGM mass by 2%. Figure 7 shows the fraction of total Hg(II) formation originating from Hg + OH. In the most polluted regions, it can reach up to 83%, but is less than 1% for the majority of the globe at ground level. Globally, Hg + OH contributes 0.5% of Hg(II) formation.

Figure 7. Annually averaged percent of total oxidation initiated by OH. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude.

Recently, Saiz-Lopez et al.26 suggested that photolysis of HOHg• and BrHg• could be an important atmospheric reduction process, and that photolysis occurs somewhat more rapidly for BrHg• than HOHg•. Inclusion of this effect would not make OH important for global oxidation of GEM.

CONCLUSIONS AND FURTHER WORK

We have presented a mechanism and rate constants for the two-step oxidation of Hg(0) initiated by OH radical in the gaseous atmosphere. We implemented these results into the GEOS-Chem global atmospheric Hg model. The resulting simulations predict that the main pathway for Hg(0) oxidation to Hg(II) occurs through the initial Hg + Br reaction. We find that the Hg + OH pathway contributes <1% of the conversion of Hg(0) to Hg(II), globally, but up to 83% in polluted regions.

Experimental investigation of k1([M],T) using direct monitoring of OH radical by LIF only led to an upper limit to k1(298).9 Under those experimental conditions, the lifetime for loss of OH

 

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by processes other than reaction with Hg(0) was about 5 ms. Our results indicate that HOHg• possesses a lifetime of 7 ms at 298 K and 1 atm of air. Consequently, we suggest that the fast regeneration of OH from dissociation of HOHg• does not present an insuperable obstacle to use of LIF to measure k1.

Experimental measurements of k-1([M],T) would improve the reliability of our model of HOHg• formation and dissociation. Note that Saiz-Lopez et al.26 reported that HOHg• will be photolyzed with a global lifetime of ~100 seconds, but experiments are needed to verify their computed photo-absorption cross-sections. Experimentally determining either k-1([M],T) or these photo-absorption cross-section will be a challenge, since, to date, HOHg• has only been detected in a single laboratory study, and only in aqueous solution.80

Except for the value of the bimolecular rate constant, k1(T, 1 atm), over the range 283 K ≤ T ≤ 353 K, our entire mechanism is based on computational chemistry and chemical insight. In particular, the rate constants for BrHg• reaction with NO2 and HOO• used for the HOHg• + •Y reactions are, themselves, the result of calculations that have yet to be verified by experiment. Validation or improvement of the HOHg• + •Y rate constants is a high-priority item for improving the reliability of our mechanism.

Previously, Saiz-Lopez et al. reported relativistic CASPT2 calculations indicating that photolysis of BrHgY compounds occurs very rapidly in the atmosphere,27 and Lam et al. affirmed this for BrHgONO using non-relativistic EOM-CCSD calculations.25 No laboratory experimental data has been reported for any BrHgY or HOHgY compound, and the spectra of HOHgY compounds has not been computed. These compounds are important targets for future studies, since atmospheric modelers need to know their spectra, photolysis quantum yields, and whether their photolysis leads to photo-reduction.

■ ASSOCIATED CONTENT

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: ___. Absolute energies of all species at all levels of theory along with zero-point energies, structural data, rotational constants, and vibrational frequencies; values of the T1 diagnostic; thermochemical data; kinetic analyses of previous experiments; Figures showing additional model results (PDF); kinetic model for analysis of experiment (Excel).

ACKNOWLEDGEMENTS

The work at SUNY-ESF was partially supported by the National Science Foundation under award 1609848. Some computations were carried out using resources of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number ACI-1053575; specifically, we used Bridges at the Pittsburgh Supercomputing Center (PSC) and Comet at the San Diego Supercomputer Center (SDSC). We

 

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also thank Huiting Mao for helpful discussions and Khoa T. Lam for advice on calculations. The work at Harvard was supported by the US National Science Foundation Atmospheric Chemistry Program under award AGS-1643217.

TOC Graphic

 

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download fileview on ChemRxivHO-initated GEM oxidation 2019.10.30.pdf (1.08 MiB)

S‐1  

Supporting Information for

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

Theodore S. Dibblea*, Hanna L. Tetua, and Yuge Jiaoa, Colin P. Thackrayb, Daniel J. Jacobb, c

a) Department of Chemistry, State University of New York, College of Environmental Science and Forestry, 1 Forestry Drive, Syracuse, NY, 13210

b) Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

c) Department of Earth & Planetary Sciences, Harvard University, Cambridge, MA, USA

Contents

Table S1. Cartesian coordinates (Å), harmonic vibrational frequencies (cm-1) and rotational constants (GHz) for OH and HOHg using coupled-clusters.

Table S2. Absolute energies (Hartree) and zero-point vibrational energies (kcal/mole) for computing HO-Hg bond energy.

Input File 1: Input file for program thermo for computing equilibrium constant for OH + Hg = HOHg•. Table S3: Literature thermodynamics and resulting thermodynamics properties for HOHg•.. Table S4: Cartesian coordinates (Å), harmonic vibrational frequencies (cm-1) and rotational constants (GHz) for all species at PBE0/AVTZ. Table S5. Absolute energies (Hartree), zero-point vibrational energies (kcal/mole), and rotational constants (GHz) at CCSD(T)//PBE0/AVTZ for computing HOHg-Y bond energies and isomerization kinetics of HOHgNO2. Analysis of the experiment of Sommar et al on the kinetics of OH + Hg Figure S1. Structures of transition states connecting isomers and conformers of the products of HOHg• + NO2. Figure S1S2. Annually averaged [Br]:[OH] ratio. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude. Figure S2S3. Annually averaged fraction of Hg(I) as HgOH. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude.

S‐2  

Table S1. Bond lengths (R, in Å) and angles (A, in degrees), rotational constants (cm-1) for OH and HOHg using couple clusters with various basis sets and correlating all (Full) electrons or with a frozen core (FC).

Species Parameter AVTZ AVQZ AwCVTZ(FC) AwCVTZ(Full) CV AVQZ+CVOH R(OH) -- 0.9706 0.9729 0.9721 -0.0007 0.9699

HOHg R(HgO) 2.1129 2.1060 2.1116 2.1087 -0.0029 2.1031 R(OH) 0.9694 0.9669 0.9691 0.9684 -0.0006 0.9662 A(HgOH) 103.86 103.99 103.86 103.75 -0.11 103.88

Species Rotational Constants (cm-1) OH 18.9016 HOHg 20.5065 0.2395 0.2367

Table S2. Absolute Energies (Hartree) and zero-point energy (ZPE, kcal/mol) of OH, Hg and HOHg at CCSD(T)/AVQZ+ΔCV geometries.

Level of theory/Basis Set HgOH Hg OH CCSD(T,full)/AcwVTZ -229.0311101 -153.3103858 -75.7028212 CCSD(T,full)/AcwVQZ -229.1220877 -153.3776988 -75.7253279 CCSD(T,full)/AcwV5Z -229.1583990 -153.4066457 -75.7322037 CCSD(T,full)/CBSa -229.1795636 -153.4235391 -75.7361871 CCSD(T)/VTZ -228.6195091 -152.9666018 -75.6377222 CCSDT/VTZ -228.6185704 -152.9651402 -75.6380173 CCSDT/VDZ -228.4423767 -152.8719825 -75.5594626 CCSDT(Q)/VDZ -228.4439567 -152.8728023 -75.5597117 ZPE CCSD(T)/AVTZ (kcal/mol) 7.11 0 5.31

SF-RASSI/CASPT2 -19679.99314 -19604.27270 -75.69673 SO-RASSI/CASPT2 -19679.99333 -19604.27271 -75.69707

a) see Equation (5) in the text of the paper

 

S‐3  

Input File 1: Input file for program thermo for computing Kc for OH + Hg = HOHg•.  KCAL MCC 9 200. 220. 240. 260. 280. 298.15 300. 320. 340. 3 reac Hg 15.42 Hg 1 1 1 0.0 1 0 'HAR' 'CM-1' reac OH 8.90 OH 1 1 2 0.0 2 139.7 2 2 'HAR' 'CM-1' 1 vib 3718. -75.40 1 2 qro 18.9016 1.0 2 prod HOHg_10.5 13.30 HOHg 1 1 1 0.0 2 4 'HAR' 'CM-1' 1 vib 401. -5.91 1 2 vib 824. -3.47 1 3 vib 3749. -78.33 1 4 top 0.2381 20.50651 1 ! SQRT(0.2395×0.2367) 20.5065    

Table S3: Literature enthalpies (kcal mole-1) for OH and Hg, calculated enthalpies for HOHg•, and calculated entropies (cal mole-1 K-1) and free energies (kcal mole-1) for all three species from the program thermo. Entropies in parentheses are from JPL Data Evaluation #18.a Standard state is 1 bar partial pressure. Species fH° (0 K) fH° (298.15 K) S° (298.15 K) fG° (298.15 K) OHb 8.90 8.96 43.86 (43.91) 7.93 Hga 15.42 14.67 41.82 (41.81) 7.62 HOHg 13.30 11.64 64.52 9.78

a) J. B. Burkholder, S. P. Sander, J. Abbatt, J. R. Barker, R. E. Huie, C. E. Kolb, M. J. Kurylo, V. L. Orkin, D. M.

Wilmouth, and P. H. Wine "Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation No. 18," JPL Publication 15-10, Jet Propulsion Laboratory, Pasadena, 2015 http://jpldataeval.jpl.nasa.gov.

b) Active Thermochemical Tables version 1.22e. https://atct.anl.gov.

S‐4  

Table S4. Cartesian coordinates (Å), unscaled harmonic vibrational frequencies (cm-1) and rotational constants (GHz) for all species at PBE0/AVTZ.

CH3OO• C 1.08387500 -0.17975500 0.00002000 H 1.13923100 -0.79795000 -0.89521900 H 1.86351300 0.57900300 -0.00163700 H 1.14115300 -0.79618200 0.89630700 O -0.15795900 0.53737200 0.00005700 O -1.17293400 -0.27566400 -0.00000300

Frequencies: 135.19, 499.83, 953.36, 1129.88, 1184.91, 1253.47, 1440.09, 1467.09, 1478.31, 3063.10, 3158.63, 3173.04

 

HOHg• O 0.01050700 1.90746000 0.00000000 H -0.92465100 2.14652800 0.00000000 Hg 0.01050700 -0.21757800 0.00000000

Frequencies: 366.40, 812.34, 3813.72

 

HOHgCH2CH2• Hg -0.20991000 -0.07257600 -0.00001800 C 1.85215200 -0.52123000 -0.00172800 H 2.01172300 -1.13133000 0.88726500 H 2.01120800 -1.12566200 -0.89468900 C 2.59894700 0.72236800 0.00196400 H 2.82179800 1.24007900 -0.92150100 H 2.82234100 1.23423500 0.92855200 O -2.10869100 0.56984000 -0.00344900 H -2.71135000 -0.17680000 0.02796900

Frequencies: 37.77, 93.61, 140.12, 227.56, 322.55, 466.58, 557.76, 612.20, 721.96, 853.78, 950.10, 1054.68, 1122.01, 1244.22, 1445.89, 1484.60, 3076.42, 3137.64, 3162.98, 3263.13

 

TS for HOH•g + CH2=CH2 Hg -0.26950400 -0.14869400 -0.00000100 C 2.34486700 -0.39014500 0.00000700 H 2.30742000 -0.96201700 0.91967100 H 2.30742700 -0.96203400 -0.91964700 C 2.73534000 0.90167200 -0.00000300 H 2.87573200 1.44976400 -0.92345700 H 2.87572400 1.44978100 0.92344200 O -2.06432100 0.94480700 0.00000500 H -2.77268100 0.29241000 -0.00001100

Frequencies: 133.90i, 32.00, 44.86, 153.52, 194.56, 341.53, 410.02, 811.23, 814.34, 899.20, 935.37, 1017.22, 1233.18, 1313.42, 1460.59, 1591.45, 3149.51, 3160.67, 3229.54, 3257.21, 3841.98

 

HOHgNO O 2.15154700 -0.35930400 -0.00005300 H 2.64857100 0.46357600 0.00093100 Hg 0.18414500 0.04060500 -0.00001200 N -1.93867800 0.44733700 -0.00005000 O -2.62772200 -0.49611300 0.00009800

Frequencies: 102.53, 108.87, 116.87, 247.95, 518.94, 573.92, 860.93, 1730.87, 3861.73

 

HOHgNO2 O -0.11231300 2.29827400 0.00000000 H 0.77341300 2.67239400 0.00000000 Hg 0.00000000 0.34390500 0.00000000 N 0.00483200 -1.72660100 0.00000000

Frequencies: 104.96, 109.10, 155.74, 272.36, 294.20, 539.10, 608.50, 856.73, 945.96, 1424.91, 1627.40, 3861.00

S‐5  

O 1.08102500 -2.27876200 0.00000000 O -1.06961600 -2.28183300 0.00000000

 

HOHgONO_anti O 2.33037900 -0.36030700 0.12108500 H 2.65654100 -0.62237100 -0.74434700 Hg 0.42929700 0.04956000 -0.00296500 O -1.48539200 0.58291400 -0.01296500 N -2.31675900 -0.51296700 0.00875600 O -3.44286100 -0.19156900 0.00690700

Frequencies: 92.77, 112.61, 126.43, 193.41, 222.32, 407.90, 627.06, 790.40, 950.81, 968.07, 1745.97, 3864.42

 

HOHgONO syn-cis O -2.22911000 -0.41144200 -0.00058200 H -2.29566300 -1.37067800 0.00117200 Hg -0.33002400 0.08486200 0.00007800 O 1.56176300 0.89534100 -0.00014200 N 2.47732500 -0.01600900 -0.00020700 O 2.08688900 -1.14717300 -0.00001700

Frequencies: 95.79, 127.07, 145.29, 159.91, 388.67, 401.89, 616.55, 901.14, 958.09, 1095.91, 1599.67, 3861.88

12.7058231 1.6792417 1.4832153 GHz  

HOHgONO syn-trans 8 -2.160242 0.617805 -0.00000 1 -2.781737 -0.115509 -0.0000 80 -0.328923 -0.086716 -0.0000 8 1.563315 -0.899394 0.0000 7 2.472319 0.019228 0.0000 8 2.070590 1.146367 0.0000

Frequencies: 94.0251, 119.9597, 140.4335, 158.2994, 388.7822, 406.4456, 612.4727, 901.6904, 950.6004, 1093.3436, 1601.9141, 3864.6126 12.1627080 1.7010833 1.4923608 GHz

HOHgOO• O 2.11318800 0.30541100 -0.11959200 H 2.43569600 0.58765300 0.74123800 Hg 0.18934100 -0.05340600 0.00317400 O -1.79370300 -0.45949100 0.01236100 O -2.51735900 0.61468400 -0.01716200

Frequencies: 9.85, 124.12, 154.80, 272.56, 529.63, 623.08, 948.39, 1210.90, 3856.72

 

HOHgOOH O 2.10997400 -0.39531200 -0.11045200 H 2.47761500 -0.44437600 0.77579400 Hg 0.21140500 0.06014100 0.00308600 O -1.69785700 0.56823400 -0.01468600 H -2.96205000 -0.59823000 0.73051600 O -2.46561700 -0.64400300 -0.09401500

Frequencies: 117.28, 141.60, 166.04, 247.73, 275.30, 563.26, 636.41, 953.90, 969.87, 1374.20, 3814.37

HOHgOBr O -1.210006 0.222304 2.448117 H -1.118086 -0.065304 3.360519 Hg 0 0.498846 0.002806 1.532879 O 2.154774 -0.271331 0.489574 Br 3.261446 1.177288 0.517167

Frequencies: 82.3287, 100.4642, 173.1336, 176.7552, 513.2004, 625.5346, 722.0277, 966.1473, 3865.2590 17.26172 0.72400 0.69635 GHz

HOO• O 0.05511600 -0.60142000 0.00000000 H -0.88185800 -0.86402100 0.00000000 O 0.05511600 0.70942300 0.00000000

Frequencies: 1217.99, 1458.48, 3647.41

S‐6  

NO N 0.00000000 0.00000000 -0.60818500 O 0.00000000 0.00000000 0.53216200 

Frequency: 2022.61

NO2 N 0.00000000 0.00000000 0.31610400 O 0.00000000 1.09253500 -0.13829600 O 0.00000000 -1.09253500 -0.13829600

Frequencies: 780.43, 1435.84, 1776.38

O2 O 0.00000000 0.00000000 0.59693600 O 0.00000000 0.00000000 -0.59693600

Frequency: 1704.60

CH2=CH2 C 0.00000000 0.00000000 0.66173400 H 0.00000000 0.92272200 1.23063300 H 0.00000000 -0.92272200 1.23063300 C 0.00000000 0.00000000 -0.66173400 H 0.00000000 -0.92272200 -1.23063300 H 0.00000000 0.92272200 -1.23063300

Frequencies: 824.37, 979.62, 985.82, 1063.67 1237.78, 1378.90, 1466.22, 1700.22, 3141.96, 3158.10, 3218.10

TS [HOHgNO2 anti-HOHgONO] Hg 0.36291000 0.00830000 0.00000000 O -1.64885500 1.03472200 -0.0000000 N -1.87194200 -0.23726900 0.00000000 O -2.98689000 -0.63402500 -0.0000000 O 2.30061100 -0.33983100 -0.0000000 H 2.75185200 0.50992500 0.0000000

Frequencies: 307.58i, 110.97, 120.42, 162.12, 232.50, 312.84, 598.90, 784.90, 979.37, 1230.64, 1679.45, 3852.48 19.0988135 1.4294076 1.3298760 GHz

TS [anti-HOHgONO-->syn-HOHgONO] Hg 0.39934400 -0.06230000 -0.01543500 O -1.45080100 -0.74460800 -0.17316900 N -2.45937700 -0.03154300 0.48118500 O -2.96406700 0.77566500 -0.19444000 O 2.23751200 0.58948000 0.00362300 H 2.68697800 0.24053800 0.77843000

Frequencies: 224.05i, 98.88, 116.57, 155.43, 186.48, 516.74, 631.49, 720.91, 858.29, 971.00, 1739.44, 3862.65 16.9404489, 1.3206041, 1.2553045 GHz

TS [cis-trans] syn-HOHgONO   8 2.191253 0.533108 -0.111050 1 2.578641 0.532119 0.768719 80 0.332563 -0.086265 0.001208 8 -1.555719 -0.892553 -0.003517 7 -2.484694 0.011572 0.001360 8 -2.109386 1.145457 0.005203

Frequencies: 89.6158i, 120.8916, 136.6857, 164.1415, 380.6952, 412.8314, 612.5693, 900.2156, 947.3333, 1073.6658, 1612.7089, 3864.1433 

12.3995991 1.6707267 1.4790194 GHz

HOHgOOCH3 H 2.764289 0.256176 0.706042 Hg 0.451305 -0.072863 -0.026777 O -1.365741 -0.837678 -0.191041 O -2.238793 -0.066395 0.639194 C -3.032927 0.710621 -0.216165 H -3.601223 0.083227 -0.90789

Frequencies: 44.8170, 113.8309, 129.3393, 166.0633, 217.9223, 275.7847, 442.9395, 585.8291, 644.6935, 907.5841, 953.2643, 1079.3058, 1174.1647, 1214.2159, 1440.9058, 1454.3649, 1499.6806, 3001.5221, 3078.7218, 3124.9196, 3867.7840

S‐7  

H -3.717848 1.252909 0.438834 H -2.427556 1.427759 -0.784712 HOHgH H -0.000018734 0.00000 0.0000 Hg 0.000063362 0.00000 0.0000 O -0.000032451 0.00000 0.0000 H -0.000012177 0.00000 0.0000

Frequencies: 598.47, 605.80, 620.13, 875.29 2189.33 3888.08 684.0818399 7.6429827 7.5585341 GHz

 

Table S5. Absolute energies (in Hartree), zero-point vibrational energies (ZPE, in kcal/mole), and value of the T1 diagnostic at PBE0/AVTZ geometries for HOHg• chemistry. Species PBE0/AVTZ ZPE CCSD(T)/AVTZ T1 HOHg• -229.2097675 7.14 -228.6431202 0.0222 NO2 -204.9465629 5.71 -204.8164244 0.0239 HOO -150.8139351 9.04 -150.72615 0.0290 CH3OO (conformer?) -190.0847754 27.07 -189.96061 0.0281 NO -129.8023078 2.89 -129.72574 0.0231 O2 -150.2301511 2.43 -150.14049 0.0172 BrO -491.891995 1.09 -490.71793 0.0324 HHgO -229.1499778 5.64 -228.580582 0.0255 CH2=CH2 -78.5120167 32.02 -- -- HOHgH -229.8363131 12.54 -- -- syn-HOHgONO -434.2214999 14.79 -433.53477 0.0239 anti-HOHgONO -434.2114166 14.44 -433.52589 0.0222 HOHgNO2 -434.2166795 15.39 -433.524166 0.0234 HOHgOOH -380.0893637 18.76 -379.44362 0.0203 HOHgOOCH3 -419.3585639 36.31 -418.6774353 0.0198 HOHgNO -359.0325453 11.6 -358.38887 0.0292 HOHgOO -379.4560835 11.10 -378.80090 0.0294 HOHgOBr -721.1878517 10.32 -719.45479 HOHgO• -304.3302811 9.18 -303.72133 0.0215 HOHgCH2CH2• -307.7322529 39.89 -- 0.0292 TS (HOHg + CH2=CH2

HOHgCH2CH2•) -307.7218942 39.85 -- --

HOHg-- CH2=CH2 (van der Waals complex)

-307.724828 39.94 -- --

TS (HOHgNO2 anti-HOHgONO)

-434.1849917 14.38 -433.49771 0.0214

TS (anti syn HOHgONO) -434.1986904 14.09 -433.51397 0.0215 TS syn-HOHgONO (cis trans)

-434.2208763 14.61 -433.53424 0.0237

   

S‐8  

Analysis of the Experiment of Sommar et al on the kinetics of OH + Hg.

The idea is to estimate the competition between HOHg dissociation and reaction with NO2 under the conditions of the experiment of Sommar et al (Sommar, J.; Gårdfeldt, K.; Strömberg, D.; Feng, X. A Kinetic Study of the Gas-Phase Reaction between the Hydroxyl Radical and Atomic Mercury. Atmos. Environ. 2001, 35 (17), 3049–3054).

We will estimate the total (gross) concentration of NO2 produced at the time of the first data collection (5 minutes).

1. NO2 produced by ROO + NO RO + NO2 (RH)

We start by using the mechanism (see Scheme below) from J. Phys. Chem. A 2000, 104, 5072-5079 to identify all reactions that convert NO to NO2 in the OH-initiated oxidation of cyclohexane (identified in the text, below, as CH).

S‐9  

NOTES

a) The “O2, NO” over an arrow represents two reactions: First, O2 adds to a carbon centered radical to form a peroxy radical (ROO); second, the peroxy radical reacts with NO to make an alkoxy radical (RO) + NO2.

b) “isom.” stands for isomerization, that is, a 1,5 H-shift reaction

c) “decomp.” stands for C-C scission to form a C-centered radical and an aldehyde or ketone.

ASSUME branching ratio for RONO2 formation is 0.15, so ROO + NO makes 85% RO + NO2. So the product of each reaction arrow with “O2, NO” over it is only formed in 85% yield.

ASSUME we can neglect ROO + NO2 ROONO2 as a loss process for ROO (because the ROONO2 will dissociate in ~1 sec).

Branching Fractions:

Note: cyclohexoxy makes cyclohexanone (via reaction R6 of the mechanism paper) in competition with scission (R5). Scission occurs to a significant extent as a chemically activated reaction when RO is produced from ROO + NO. As a result, the ratio of O2 reaction to scission at high [NO] (as in Sommar et al and this cyclohexane mechanism paper) is ~0.7. This means that the fraction of cyclohexoxy reacting with O2 is 0.4 and the fraction undergoing scission (propagating the organic radical chemistry) is 0.6.

Note that the 4th generation carbon-centered radical reacts with O2 mostly makes an aldehyde (90%) versus making RC(O•)OH (10%).

Let f equal the ratio of molecules of NO2 produced per molecule of cyclohexane (CH) reacted. f decreases as we proceed from the first to the second, etc. generation of ROO•.

For the 1st generation, f=0.85

For the 2nd generation, f = 0.85 × 0.6 × 0.85 = 0.43

For the 3rd generation, f = 0.85 × 0.6 × 0.85 × 0.85 = 0.37

For the 4th generation, f = 0.85 × 0.6 × 0.85 × 0.85 × 0.1 = 0.04

Approximate f for each of the next two as 0.04, also. So f = 1.8 and

So the [NO2] produced from ROO + NO (not including R=H) =1.8 × [CH]reacted

At t=5 minutes (300 sec), we can see from Figure 2 of Sommar et al. that ln([CH]0/[CH]t) = 0.44. This means [CH]t/[CH]0 = 0.64, meaning [CH]reacted = 0.36 × (5.2 × 1014) = 1.9 × 1014 molecule cm-3.

So the [NO2] produced from ROO + NO (not including R=H) is (from 2.a.) 1.8 times [CH]reacted

[NO2] produced from ROO + NO = 3.3 × 1014 molecule cm-3

2. NO2 produced in HOO + NO OH + NO2

S‐10  

Consider, next, that HOO is produced in cyclohexane oxidation, and this HOO is source of NO2, via the reaction HOO + NO → OH + NO2.

We will get at the extent of this NO2 production by considering the OH produced in the same reaction. Every OH produced corresponds to a molecule of NO2 produced. All of the OH produced in the first 5 minutes has reacted, mostly with cyclohexane or CH3ONO (for the moment, we neglect OH + NO2 HONO2). ASSUME a negligible fraction of OH has reacted with Hg due to its low concentration and the low OH + Hg rate constant. ASSUME that the fraction of loss of OH with oxidation products of cyclohexane is low at 5 minutes (not a good assumption at longer times).

Then the extent of OH reacted with CH equals [CH]reacted = 1.9 × 1014 molecule cm-3. But we also need to compute the extent of the reaction OH + CH3ONO, which is trickier:

Consider OH + CH3ONO CH2ONO* HCHO + NO2. If the pseudo-first order rate constant, k’, for loss of OH via reaction with CH3ONO and CH were the same, then OH reacted with CH3ONO would equal [CH]reacted. However, this is not the case:

a) k for OH + CH3ONO is 2.6 × 10-13 cm3 molecule-1 sec-1 (NIST) but k for OH + CH is 7.2 × 10-12 cm3 molecule-1 sec-1

b) The initial [CH3ONO] is much greater than the initial [CH]. I am going to ASSUME that the concentration ratio [CH3ONO]/[CH] stays constant (at 5.8).

The ratio of OH lost in reaction with CH3ONO to that lost in reaction with CH is k’loss via

CH3ONO /k’loss via CH. Using the information in (a) and (b), one gets:

[OH] reacted with CH3ONO = 5.8 (2.6 × 10-13)/( 7.2 × 10-12) [CH]reacted

= 0.4 × 1014 molecule cm-3

[OH]produced = [OH]reacted = (1.9 +0.4) × 1014 molecule cm-3 = 2.3 × 1014 molecule cm-3. Recall that these mechanistic and kinetic gymnastics were carried out with the goal of computing the NO2 produced in HOO + NO OH + NO2. The NO2 produced in this reaction equals the OH produced in this reaction, which equals the OH lost in all reaction (what we just calculated, above).

So the [NO2] produced in HOO + NO = 2.3 × 1014 molecule cm-3

The TOTAL [NO2] produced (from HOO + NO AND ROO + NO)=

3.4 × 1014 molecule cm-3 + 2.3 × 1014 molecule cm-3 = 5.7 × 1014 molecule cm-3

3. Competition between HOHg dissociation and reaction with NO2

Above, we determined that the gross (total) production of NO2 amounted to 5.7 × 1014 molecule cm-3. Of course, NO2 will also be lost by various processes, so the [NO2] above does not correspond to the actual value of [NO2] at t= 5 minutes. Here I assume that only ~40% of this

S‐11  

NO2 is available for reaction with HOHg when I estimate k’ for loss of HOHg by reaction with NO2: [NO2] ≈ 2.0 × 1014 molecule cm-3

ASSUME: kHOHg + NO2 ≈ kBrHg + NO2

≈ 7 × 10-11 cm3 molecule-1 sec-1 at 1 atm and 295 K from Jiao, Y.; Dibble, T. S. First Kinetic Study of the Atmospherically Important Reactions BrHg + NO2 and BrHg + HOO. Phys. Chem. Chem. Phys. 2017, 19 (3).

The pseudo-first order rate constant, k’HOHg + NO2, or loss of HOHg by reaction with NO2 equals:

k’HOHg + NO2 = kHOHg + NO2[NO2]

= 7 × 10-11 cm3 molecule-1 sec-1 [2.0 × 1014 molecule cm-3]

= 1.4 × 104 sec-1

By contrast, the rate constant for HOHg dissociation, kdissoc, as listed in Eqn 13 of the paper, is k-1,0(T) = 1.22 × 10-9 e-5720/T cm3 molecule-1 sec-1, where the rate of dissociation equals

k-1,0(T)[HOHg•][M]

so the pseudo-first rate constant for HOHg dissociation, k’dissoc:

k’dissoc = k-1,0(T)[M]

= 4.6 × 10-18 cm3 molecule-1 sec-1 [2.5 × 1019 molecule cm-3]

= 110 sec-1

Because k’dissoc is ~100× smaller than k’HOHg + NO2, it is reasonable to equate the observed (net) rate of loss of Hg(0) with the rate of reaction of Hg(0) with OH radical.

 

 

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Figure S1. Structures of transition states connecting isomers and conformers of the products of HOHg• + NO2.

Substitution of OH for Br adds a degree of conformational freedom, but only one of these isomers possesses more than one conformer (See Figure 2 in the text). In HOHgNO2, all atoms lie in the same plane; a structure with the hydrogen atom perp to the NO2 group corresponds to a transition state connecting two indistinguishable planar HOHgNO2 structures. For anti-HOHgONO, only one conformer was found; in this structure of C1 symmetry, the hydrogen atom sticks out of the roughly planar arrangement of the other atoms. Syn-HOHgONO possesses two conformers of Cs symmetry; one in which the hydrogen atom is cis to the -ON=O group and one trans. The cis structure is more stable by 0.07 kcal/mole. These two are connected by a transition state in which the hydrogen atom is perp to the -ON=O group. This transition state lies only 0.15 kcal/mole above the cis conformer.

S‐13  

Figure S2. Annually averaged [Br]:[OH] ratio. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude.

Figure S3. Annually averaged fraction of Hg(I) as HgOH. (Left) spatial variation at ground level for the entire globe. (Right) variation with altitude and latitude averaged over longitude.

 

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