Structures, Vibrational Frequencies, and Bond Energies of the

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Structure, Vibrational Frequencies, and Bond Energies of the BrHgOX and BrHgXO Species Formed in Atmospheric Mercury Depletion Events Yuge Jiao, and Theodore Simon Dibble J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b06829 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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The Journal of Physical Chemistry

Structure, Vibrational Frequencies, and Bond Energies of the BrHgOX and BrHgXO Species Formed in Atmospheric Mercury Depletion Events Yuge Jiao and Theodore S. Dibble* Department of Chemistry, State University of New York, College of Environmental Science and Forestry, 1 Forestry Dr, Syracuse, NY, 13210

Abstract Photochemistry during the polar Spring leads to atmospheric mercury depletion events (AMDEs): Hg(0), which typically lives for months in the atmosphere, 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 that they will not dissociate before undergoing deposition, but BrHgClO is probably not that stable.

*Corresponding Author: [email protected]

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Introduction When light comes to polar regions in the spring, halogen chemistry drives dramatic reductions in the concentrations of ozone and mercury in the atmosphere.1,2 As shown in Figure 1, photochemistry in ice and snow releases photolabile halogen compounds. Oxidation of Hg(0) is mostly initiated by atomic bromine3: Br + Hg + M BrHg• + M

(1)

where M is an another molecule that quenches chemically activated BrHg•. Reaction 1 is followed by reaction of BrHg• with other radicals, •Y, to form BrHgY via barrierless association reactions. In polar regions, concentrations of halogen oxides are relatively high,3–6 so reaction (1) is assumed to be followed by1: BrHg• + XO• + M → BrHgOX + M

(2)

where M is a third body and X = Br, Cl, and I in decreasing order of importance. Gaseous bromine cycles rapidly between Br and BrO, and the resulting high concentrations of Br causes the concentration of Hg(0) to fall rapidly from background levels: sometimes by over 90% in 1 day.1 These rapid declines in [Hg(0)] are called atmospheric mercury depletion events (AMDEs), and are largely responsible for deposition of 300 metric tons of mercury to the Arctic each year.7

Figure 1. Schematic of some of the main processes believed to drive the destruction of ozone and mercury in atmospheric mercury depletion events (AMDEs).

Mercury is emitted to the atmosphere as Hg(0), mostly from coal-fired power plants and small-scale gold mining.8,9 Outside of AMDEs, atomic mercury can live for months in the atmosphere.10 This means that mercury emitted in one location can travel the globe before being transferred into ecosystems. Once in ecosystems, mercury bioaccumulates to dangerous levels. Transfer of mercury from the atmosphere to ecosystems is largely limited by the rate of oxidation of Hg(0).10,11 Atomic bromine is also the dominant species initiating the oxidation of Hg(0), globally.12,13 Outside of AMDEs, reaction (2) is part of the fate of BrHg•, although reaction with NO2 and HOO are probably more important14,15: BrHg• + NO2 + M → syn-BrHgONO + M 2 ACS Paragon Plus Environment

(3)

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BrHg• + HOO• + M → BrHgOOH + M

(4)

Thermodynamics limits the reactivity of BrHg• with organic compounds in the gaseous atmosphere,16 so reactions with radicals appear to dominate the fate of BrHg•. On account of the global effect of local mercury emissions, the international community signed a treaty, the Minimata Convention17, agreeing to reduce mercury emissions with a goal of lowering concentrations of environmental mercury to safe levels. Understanding how to achieve this goal is made extremely difficult by the fact that Hg(0) is re-emitted from ecosystems to the atmosphere.8 Scientists are carrying out extensive studies to understand the global biogeochemistry of mercury in order to help implement the Minimata Convention.18 Because populations of polar regions are particularly sensitive to mercury deposition,19 and because of the startling rapidity of Hg(0) oxidation in AMDEs, there is a large ongoing effort to understand AMDEs. Yet scientists attempting to understand this chemistry lack the most basic information on the kinetics and mechanisms of AMDEs. This lack of data seriously undermines efforts to synthesize field and modeling studies of both AMDEs and the global chemistry of mercury. Despite the importance of BrHgOX in AMDEs, there has been no experimental investigation of BrHgOBr, BrHgOCl, or BrHgOI, and only three computational studies.14,20,21 Furthermore, given the ability of halogen atoms to be polyvalent,22–24 and for some of these polyvalent compounds to be more stable than their singly valent isomers,23 reaction (2) may face competition from: BrHg• + XO• + M → BrHgXO + M

(5)

The resulting compounds BrHgClO, BrHgBrO, and BrHgIO have never been studied by experiment or computation. The lack of information on the chemical identity of Hg(II) compounds formed in the atmospheric oxidation of Hg(0) limits scientists’ abilities to carry out reliable field and modeling studies of mercury oxidation processes. This paper is part of an ongoing effort to provide molecular-level insights into the processes controlling Hg(0) oxidation. The goal of this paper is to provide highly reliable molecular structures, vibrational frequencies, vibrational intensities, and thermodynamics for BrHgXO and BrHgOX species. The information on molecular structure and vibrations will be invaluable for experimental detection of these compounds. The thermodynamic data will be important for determining which of these pairs of isomers is thermodynamically favored, as well as for benchmarking quantum chemistry methods for studying the competition among various products of the reaction of BrHg• with XO•. The paper is structured as follows: the Methods section describes the variety of approaches used to obtain highly accurate geometries: a) using quadruple-ζ basis sets together with coupled clusters with single and double excitations and a perturbative estimate of triple excitations (CCSD(T)); b) accounting for the effects of spin-orbit coupling (SOC); and c) accounting for core-valence (CV) corrections. The Methods sections continues to discuss extrapolation of the CCSD(T) energies to the basis set limit, correcting the CCSD(T) energies for higher excitations, and SOC and CV effects on energies. The Results section starts by presenting molecular structures of BrHgXO and BrHgOX, periodic trends in those structures, and differences between BrHgOX and BrHgXO isomers. Vibrational frequencies and intensities are presented next. We then address the many terms influencing the BrHg-OX and BrHg-XO bond energies before discussing periodic trends and the differences between isomers. This is followed 3 ACS Paragon Plus Environment


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by a discussion of the uncertainties in computed bond energies and the thermodynamic stability of BrHgOX and BrHgXO species. We conclude by discussing the value of this work, particularly for using the bond energies to benchmark future studies of the competing product channels of BrHg• + XO• reactions.

Method Energy-consistent Stuttgart/Cologne scalar relativistic pseudopotentials for Hg (ECP60), Br (ECP10), and I (ECP28) were used throughout this work.25–27 The valence electrons for Hg, Br, and I were treated with (aug)-cc-pVXZ (X = D, T, Q, or 5) basis sets of Peterson and co-workers.25,27,28 O and Cl are treated by the corresponding Dunning’s (aug)-cc-pVXZ29 and (aug)-cc-pV(X+d)Z30 basis sets, respectively. For simplicity, we refer to this combination of pseudopotentials/basis sets as VXZ (X = D, T, Q, or 5) or AVXZ (when augmented with diffuse functions). The frozen core (FC) approximation was employed except where otherwise specified. The frozen core approximation correlates the following electrons: 2s2p of O, 3s3p of Cl, 4s4p of Br, 5s5p of I, and 5d6s of Hg. Spin-unrestricted methods were used for open-shell molecules except as noted. Geometries of BrHgOX and BrHgXO were optimized with the CCSD(T) method in conjunction with the VTZ, AVTZ, and AVQZ basis sets using the algorithm recently developed by Cheng and Gauss31 for CCSD(T) analytical gradients. A pre-calculated force constant at a lower level of theory was provided to accelerate the geometry optimization. Harmonic vibrational frequencies were calculated at CCSD(T)/AVTZ with the frozen core approximation. Effects of core-valence correlation and spin-orbit coupling on geometries were evaluated. For the effects of core-valence correlation, geometries were reoptimized using the weighted core-valence correlation-consistent basis sets with the corresponding pseudopotentials (cc-pwCVTZ-PP) for Hg,28 Br,27 and I,27 and cc-pwCVTZ basis sets for O and Cl.32 The valence and sub-valence electrons were correlated, except for the 1s electrons of Cl. This combination of basis sets and pseudopotentials is labeled wCVTZ. The core-valence effect on geometry, ΔCV, was evaluated by comparing CCSD(T)/VTZ geometries with CCSD(T,Full)/wCVTZ geometries. For the effects of spin-orbit coupling (SOC) on geometries, we employed the analytical gradient of the two-component CCSD(T) theory including SOC (2c-SOC-CCSD(T)) of Wang and Gauss.33 Stuttgart/Cologne two-component spin-orbit pseudopotentials were used for Hg,26 Br,25 and I,25 while no spin-orbit pseudopotentials were used for O or Cl. The SOC effect on the geometries, ΔSOC, were computed from the differences between CCSD(T)/VTZ geometries and 2c-SOC-CCSD(T)/VTZ geometries. For the diatomic radicals, the SOC effect on geometries was obtained from the literature27,34 at the MRCI level. The final geometries are, therefore, at the CCSD(T)/AVQZ+ΔCV+ΔSOC level of theory. Single point energies were computed at the CCSD(T)/AVQZ+ΔCV+ΔSOC geometries using strategies similar to the Feller-Peterson-Dixon35–37 or the HEAT345-(Q) composite methods.38,39 CCSD(T) frozen core energies were extrapolated to the complete basis set (CBS) limit using a three-point exponential formula40,41 with CCSD(T)/AVTZ, CCSD(T)/AVQZ, and CCSD(T)/AV5Z energies as

= + +

(6)

where B and C are fitting parameters, and n = 3 for AVTZ, n = 4 for AVQZ, and n = 5 for AV5Z.


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The effects of electron correlation from the sub-valence shells (5s5p for Hg, 4s4p4d for I, 3s3p3d for Br, 2s2p for Cl, and 1s for O) were determined as core-valence corrections on energies (δECV). A two-point extrapolation formula42 was used with the AwCVTZ and AwCVQZ basis sets to obtain the CCSD(T) energy with correlation of all electrons outside the pseudopotentials (except Cl 1s)

= + +

(7)

where D is a fitting parameter. Then δECV is computed as δ = ,//

− ,//

(8)

The 4f electrons of Hg are replaced by the pseudopotentials used here, but their energies lie above those of the Hg 5s electrons in all-electron calculations. The core-valence correlation from 4f electrons (δECV-4f) was accounted by CCSD(T) calculations with all-electron basis sets aug-cc-pwCVTZ-DK28,43 (denoted as AwCVTZ-DK) using the second-order Douglas–Kroll–Hess (DK2) Hamiltonian.44,45 Additional tight 2f2g1h functions were added for Hg.46 The 4f orbitals of Hg were rotated as needed. Note that restricted open shell methods were used for radicals in DK2-CCSD(T)/AwCVTZ-DK calculations. The corresponding energy correction, δECV-4f , is determined as " # = $ ,# &'(()*+),/

$

− $ ,# '+ &'(()*+),/

$

(9)

The energy corrections for full triples excitation47,48 (δET) were applied by taking the difference between CCSDT/VTZ energies and CCSD(T)/VTZ energies as " = / − /

(10)

The corrections for the noniterative quadruples excitation49,50 (δE(Q)) were applied by comparing CCSDT(Q)/VDZ energies and CCSDT/VDZ energies as " = / − /

(11)

Most of the scalar relativistic effect has been accounted in the scalar relativistic ECP. The scalar relativistic effect (δESR) from O and Cl were determined by the third-order Douglas-Kroll-Hess Hamiltonians51 with all-electron AVTZ-DK basis sets (AV(T+d)V-DK for Cl) at the CCSD(T) level. For purposes of comparison, we also computed δESR using the second-order Douglas–Kroll–Hess Hamiltonians44,45 with AVTZ-DK basis sets as well as mass-velocity plus 2-electron Darwin term (MVD2e)52 calculation with uncontracted AVTZ basis sets. The result of these comparisons is presented in the Supporting Information. The final (but very important) correction to the energies was for spin-orbit coupling (δESOC). This was accounted for a posteriori using the restricted active space state interaction (RASSI) method53,54 with complete active space second-order perturbation theory (CASPT2)55,56. The atomic mean field integral (AMFI)57 approach was used to reduce the computational cost. The all-electron relativistic RCC-ANO basis sets58,59 were employed with the DK2 Hamiltonian in these calculations. 5d electrons for I were correlated in addition to normal valence electrons. We followed the same methodology that has been used to investigate the SOC effect of iodine-containing compounds.60,61 The active space for BrHgOX and BrHgXO species include the valence p orbitals for the halogens, the 6s6p orbitals for Hg, and the 2p orbitals for O. We tested this methodology by comparing zero-field splitting of halogen oxides with 5 ACS Paragon Plus Environment


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calculated and experimental results from the literature. The calculated zero-field splitting values are in error with respect to experiments by -0.09 kcal/mol, -0.29 kcal/mol, and -0.65 kcal/mol, for OCl (2Π),62 OBr (2Π),63 and OI (2Π),64 respectively (see Table S8 in the Supporting Information). Further improvement would presumably require a larger active space, as suggested by the results for IO by Sulkova et al.60 and Khanniche et al61. However, the active space for halogen oxide moiety (9,6) in the current study, when combined with the active space for BrHg• (7,7), is approaching the limit of our computational resources. δESOC was computed as the difference of reaction energies at the lowest spin-orbit state RASSI/CASPT2 and the lowest spin-free (SF) state RASSI/CASPT2 "- = - .//0- . − .//0- .

(12)

Bond energies were computed as 1 = ∆ + ∆ + ∆ + ∆ + ∆# + ∆. + ∆- + ∆

34

(13)

where ∆Ei is an incremental difference in bond energies (sums and differences in δEi) due to effect i. Most calculations were carried out using CFOUR Beta v2.0 codes, including the vibrational frequencies and intensities.65 The DK-CCSD(T) calculations were performed on NWChem 6.6 program.66 The RASSI/CASPT2 calculations were carried using Molcas 8.0.67 UHF-CCSDT(Q) calculations were done by MRCC codes.68,69

Results and Discussion Figure 2 displays the geometries of the BrHgOX and BrHgXO species. Bond distances and valence angles are listed at CCSD(T)/AVQZ along with the corrections for spin-orbit coupling and core-valence correlation, ending with the final CCSD(T)/AVQZ+ΔCV+ΔSOC geometries. All six species are planar and, therefore, possess Cs symmetry; the ground electronic states are all of A’ symmetry. At CCSD(T)/AVQZ+ΔCV+ΔSOC, XO bond distances are 0.12-0.14 Å smaller in BrHgXO and XO than in BrHgOX, presumably reflecting some double-bond character in the X-O bonds of BrHgX-O and the halogen oxides. X-O bond distances increase from Cl to Br and from Br to I by 0.11-0.16 Å; similar periodic trends in X-O bond lengths have been noted in the literature.23,70 By contrast, the lengths of the Br-HgOX and Br-HgXO bonds increase only by only 0.0026 Å and 0.019 Å, respectively, over the series from X = Cl to X = I. By comparison to the BrHg• radical (see Table S2), the BrHg bond distance is much shorter (by 0.11-0.14 Å) in BrHgOX and BrHgXO. HgX bond distances in BrHgXO also increase from Cl to Br to I. Bond angles show no clear periodic trends. Curiously, the BrHgOX dihedral angle is 180 degrees, while the BrHgXO dihedral angle is 0 degrees. CCSD(T)/AVQZ geometries for BrHgOBr and BrHgOCl computed here are nearly identical (to 0.001 Å and 0.1 degrees) to those computed in the dissertation of Shepler21 with a very similar approach. Both ΔCV and ΔSOC are negative for bond lengths, except that ΔSOC is positive (albeit only slightly) for BrHgO-X distances. ΔCV always has a larger effect on bond lengths than ΔSOC. The magnitude of ΔCV is consistently on the order of 0.01-0.02 Å. For similar compounds, K. A. Peterson and co-workers46,70 had previously shown that the effects of spin-orbit coupling and core-valence correlation cannot be neglected if one wants to compute accurate geometries. 6 ACS Paragon Plus Environment

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Figure 2. Geometries (bond distances, r, in Å and bond angles, A, in degrees) of BrHgOX and BrHgXO at CCSD(T)/AVQZ level (normal font), spin-orbit coupling correction (in italic), core-valence correlation correction (in red), and at CCSD(T)/AVQZ+ΔCV+ΔSOC level (in bold). Note that the Br-Hg-O-X dihedral angle is 180 degrees, while the Br-Hg-X-O dihedral angle is 0 degrees.



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Table 1. Vibrational mode symmetries and descriptions, harmonic frequencies (ν, cm-1), and integrated absorption intensities (S, km/mol) for BrHgOX at CCSD(T)/AVTZ. symmetry

mode

A' A'' A' A' A' A'

BrHgO bend Out-of-plane bend HgOX bend BrHg stretch HgO stretch XO stretch

BrHgOCl

BrHgOBr

S 1.22 6.04 2.34 8.54 34.8 43.0

ν 60.2 116 167 263 523 735

ν 49.8 116 126 262 491 675

S 0.521 6.36 1.73 8.35 20.8 79.4

BrHgOI ν 44.0 116 108 260. 461 666

S 0.250 1.31 6.36 8.81 13.9 136

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

mode

A' A'' A' A' A' A'

BrHgX bend Out-of-plane bend HgXO bend BrHg stretch HgX stretch XO stretch

BrHgClO ν 54.0 79.6 145 249 341 742

BrHgBrO

S 4.79 0.039 0.423 17.1 5.85 159

ν 49.6 63.3 122 274 207 682

S 3.89 0.098 0.396 17.9 6.40 95.9

BrHgIO ν 47.1 55.7 118 260. 171 692

S 3.24 0.176 1.33 23.1 5.78 72.3

Vibrational frequencies of BrHgOX and BrHgXO species are listed in Tables 1 and 2, respectively, along with the integrated intensities. The shorter XO bond lengths in BrHgXO than in BrHgOX are accompanied by slightly higher vibrational frequencies. Note that, in BrHgXO, the ordering of the BrHg and HgX stretches changes from X=Cl to X=Br, as might be expected from the atomic masses. In BrHgXO the BrHg and HgX stretch modes are much more strongly coupled for X = Br and I than for X = Cl. For all six species the XO stretch has the highest absorption intensity, although in BrHgOCl the HgO stretch is almost as intense as the ClO stretch. We compare the vibrational frequencies computed here at CCSD(T)/AVTZ with those previously calculated for the BrHgOX species using the same basis set and MP221, CCSD, and four density functionals (B3LYP, PBE0, M06, and M06-2X).20 Of most relevance to thermodynamics, the ZPEs computed with all methods fall within 0.15 kcal/mol of the CCSD(T)/AVTZ values. This means that reliable zero-point energies can be obtained at very low computational cost. The MP2 values of Shepler for BrHgOCl and BrHgOBr show the highest deviation from the CCSD(T) results, followed by CCSD. Curiously, the best performance comes from the venerable B3LYP functional. It consistently underestimates the ZPE by 0.04-0.05 kcal/mol. B3LYP yields the lowest root mean square (RMS) deviation in absolute terms (cm-1) for all three species, although the M06 functional performs slightly better than B3LYP for the RMS deviation of the percent error in frequencies for BrHgOI. Recall that the analyses in this paragraph only apply to the BrHgOX species, since there are no previous studies of the BrHgXO species. 8 ACS Paragon Plus Environment

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Table 3. Basis set effect on De for BrHg-OX and BrHg-XO (kcal/mol, exclusive of zero-point energy corrections) using CCSD(T) on geometries at CCSD(T)/AVQZ+ΔCV+ΔSOC. ΔEQZa ΔE5Zb ΔECBSc De(AVTZ) BrHg-OCl 51.28 1.07 0.34 0.20 BrHg-ClO 21.82 1.85 0.72 0.42 BrHg-OBr 54.04 1.30 0.44 0.26 BrHg-BrO 25.01 1.95 0.64 0.37 BrHg-OI 55.88 1.11 0.45 0.27 BrHg-IO 31.19 1.94 0.72 0.42 a. Defined as De (AVQZ) – De (AVTZ). b. defined as De (AV5Z) – De (AVQZ). c. defined as De (CBS) – De (AV5Z).

We now turn to discussing the various factors influencing D0. Those who just want the final values of D0 should skip ahead to the discussion of the final results. Table 3 shows that increasing the size of the basis set at CCSD(T) consistently increases bond energies, due to the much better description of bonding with the larger basis sets.42,71 The increase in D0 in going from AVTZ to the CBS limit is at least 1.6 kcal/mol and as much as 3.1 kcal/mol. The effect of increasing the basis set from AVTZ to AVQZ, i.e., ΔEQZ, is larger than in going from AVQZ to the complete basis set limit. Basis set effects are 50-90% larger for BrHgXO than BrHgOX. The larger basis set effects in BrHgXO than BrHgOX appear to reflect the need for very large basis sets to recover the correlation energy for hypervalent halogen atoms. To illustrate this, we compare the changes in energy differences between BrHgBrO and BrHgOBr versus basis set; the comparison is made for both the Hartree–Fock (HF) energy and the CCSD(T) correlation energy (values of both quantities can be found in Table S6 for all BrHgOX and BrHgXO). The difference in the HF energy between those two species in going from AVTZ to AVQZ falls by 0.20 miliHartree (mH), and changes by only 0.01 mH in going from AVQZ to AV5Z. The difference in the CCSD(T) correlation energy decreases by 0.82 mH from AVTZ to AVQZ and by 0.32 mH in going from AVQZ to AV5Z. So at the HF level the relative energies of the two isomers is well-converged using the AVQZ basis set, but the correlation energy difference between the isomers changes by 0.3 kcal/mol in going from AVQZ to AV5Z.



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Table 4. Spin-orbit coupling corrections (ΔESOC) on bond energies for BrHg-OX and BrHg-XO at CCSD(T)/AVQZ+ΔCV+ΔSOC geometries (in kcal/mol, exclusive of zero-point energy corrections) and approximate contribution of halogen oxides to ΔESOC (-ZFS(XO)/2). ΔESOCa -ZFS(XO)/2b BrHg-OCl -0.65 (-0.90)c -0.41 BrHg-ClO -0.65 BrHg-OBr -1.43 (-1.54)c -1.25 BrHg-BrO -1.62 BrHg-OI -2.54 -2.66 BrHg-IO -3.45 a. Total SOC effect. b. -1/2 the zero-field splitting (ZFS) of the halogen oxide as calculated in the present work. c. Shepler’s results at SO-CISD/AVTZ level with spin-orbit pseudopotentials.21 The SOC corrections to bond energies are presented in Table 4. All ΔESOC values are negative, indicating that SOC always decreases the strength of the BrHg-OX and BrHg-XO bonds. In the two cases (BrHg-OCl and BrHg-OBr) where values were previously reported,21 our results agree reasonably well. The value of ΔESOC grows from X = Cl to Br to I and is larger for BrHgIO than BrHgOI (by 0.9 kcal/mol). By contrast, there is no difference in ΔESOC between BrHgOCl and BrHgClO, and only a 0.2 kcal/mol difference between BrHgOBr and BrHgBrO. It should also be pointed out that the ground state of BrHg• (2Σ+) possesses no first-order SOC effect. If the L-S coupling rules did not break down significantly as one goes down the periodic table from Cl to I, the effect of SOC of the halogen oxides, alone, on D0 for BrHgOX and BrHgXO, would be -½ the zero-field splitting (ZFS) of the XO. The ZFS is the energy difference between the 2Π3/2 state and 2Π1/2 state of the halogen oxide. We list the value of –ZFS/2 in the second column of Table 4 to help compare how well (or poorly) ΔESOC is accounted for by the contribution of SOC of the halogen oxides. It appears that one may use -ZFS/2 as a first-order approximation of SOC corrections to D0 for these bonds. This is partly due to the fact that the second-order SOC effect of BrHg• is partially cancelled by that of BrHgOX or BrHgXO.

Table 5. Additive contributions to D0 for BrHg-OX and BrHg-XO (in kcal/mol). literature ΔECBS ΔECV ΔET ΔE(Q) ΔECV-4f ΔESR ΔESO ΔZPE Total BrHg-OCl 50.8a, 50.6b 52.89 0.45 -0.79 0.38 0.15 0.14 -0.65 -1.20 51.4 BrHg-ClO 24.82 0.34 -0.57 0.44 0.10 -0.02 -0.65 -0.84 23.6 BrHg-OBr 56.05 0.60 -0.98 53.6a, 53.5b 0.41 0.15 0.14 -1.43 -1.17 53.8 BrHg-BrO 27.96 0.15 -0.71 0.44 0.09 0.11 -1.62 -0.71 25.7 54.8b BrHg-OI 57.72 0.53 -1.17 0.32 0.16 -0.09 -2.54 -1.16 53.8 BrHg-IO 34.27 0.39 -0.97 0.46 0.11 -0.11 -3.45 -0.72 30.0 a. From Shepler’s thesis21 at CCSD(T)/CBS+ΔCV+ΔSO. b. From Jiao and Dibble20 at CCSD(T, Full)/AwCVTZ//CCSD/AVTZ.


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QZ

5Z

CBS

CV

ΔT

(Q)

CV4f

SR

SOC

5.0 4.0 3.0 2.0 ΔE (kcal/mol)

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1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 BrHgOCl

BrHgClO

BrHgOBr BrHgBrO

BrHgOI

BrHgIO

Figure 3. Additive corrections, ΔE, to BrHg-OX and BrHg-XO bond energies (compared to CCSD(T)/AVTZ). Positive values mean a correction term increases the computed value of D0, while negative values mean the correction term reduces the computed value of D0.

Table 5 lists the corrections to the CCSD(T)/CBS bond energies from higher order clusters, core-valence effects, spin-orbit coupling, scalar relativity, and zero-point energies. Figure 3 graphically shows how these effects (with respect to CCSD(T)/AVTZ bond energies, other than zero-point energy differences) contribute to strengthening and weakening the bonds. The sign of all these effects are the same across all six species. The only two effects that reduce the computed value of D0 are the use of the full triples excitations (ΔET) and the spin-orbit correction (ΔESOC). These two corrections take on rather similar values for BrHgOX as for BrHgXO for any one X. All the other effects tend to increase the computed value of D0, with increases in D0 with basis set summing to the largest of these effects. The effect of a perturbative estimate of the quadruples excitations, ΔE(Q), cancels a significant fraction of the effect of the ΔET correction. The ΔE5Z + ΔECBS corrections, together, may be as large as 1 kcal/mol, but computing AV5Z energies is very expensive. One could use a more affordable two-point extrapolation to the CBS limit from AVTZ and AVQZ (CBS(AVTZ/AVQZ)) using Equation (7). This strategy yields an absolute error of 0.1 kcal/mol compared to the three-point extrapolation with AVT/Q/5Z using Equation (6). The ΔZPE values are essentially the same as those previously obtained with CCSD and density functional theory with AVTZ basis sets for BrHg-OX.20 As a result, using CBS(AVTZ/AVQZ) to get the CCSD(T)/CBS energy together with 11 ACS Paragon Plus Environment


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a DFT value of ΔEZPE provides an inexpensive and reasonably good approximation of the most expensive parts of the calculation. Calculation of ΔECV and, most importantly, ΔESOC, are still necessary to approach the precision obtained here. By contrast core-valence correlation from the 4f electrons of Hg and scalar relativistic effects from light elements (O and Cl) are usually small (absolute values less than 0.2 kcal/mol), and could be ignored if one is not pursuing high accuracy. Figure 4 depicts the binding energies of all six species together with the energies of the asymptotes for BrHgO + X and BrHgX + O. Thermodynamic data on all six species is listed in the Supporting Information in Table S10. Binding energies are much larger for BrHgOX than BrHgXO. In going from Cl to Br bond energies increase by nearly the same amount (~2.2 kcal/mol) for BrHg-XO as for BrHg-XO. In going from Br to I, the BrHgOX bond energy is unchanged but the BrHg-XO bond energy increases by 4.3 kcal/mol. Our preliminary results at PBE0/AVTZ (see Figures S1 and S2) show that there is no energy barrier for formation of either BrHgOBr or BrHgBrO from BrHg• + BrO•.

Figure 4. Bond energies (kcal/mol) for BrHg-OX and BrHg-XO for X= Cl, Br, and I. The thermodynamics of BrHgO + X and BrHgX + O relative to BrHg• + XO are taken from the work of Peterson and coworkers.27,46,70 Figure 4 also shows the relative energies of the BrHgX + O and BrHgO + X asymptotes. Except for BrHgO + Cl, all the asymptotes lie below BrHg• + XO. This means that the kinetics of the dissociation of BrHgOX and BrHgXO need to be investigated. The T1 diagnostic72 for BrHg• and the BrHgOX and BrHgXO species are below 0.03 (see Table S9), indicating only modest multireference character. By contrast, the value of the T1 diagnostic for the halogen oxides rises steadily form 0.036 for ClO to 0.055 for IO. The largest absolute value of the t2 amplitudes for three halogen oxides are no more than 0.06 at CCSD/AVTZ, suggesting that they do not possess extensive multireference character. Consistent with this, the structure and vibrational frequencies of BrO73 and IO74 are reproduced well at CCSD(T)/6-311+G(3df) and at the CBS limit, 12 ACS Paragon Plus Environment

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respectively. Despite the high T1 diagnostic value of IO, the I-O bonding can be well described by singlereference CCSDTQ method. This is demonstrated by the fact that the difference between the bond energies at CCSDTQ and full configuration interaction is only 0.09 kcal/mol (using an AVDZ basis set).27 Bross et al.75 showed that the CCSDT(Q)/VDZ atomization energies for eight 3d molecules containing transition metals are within 0.1 kcal/mol of the CCSDTQ/VDZ values except three cases with enormous values of the T1 diagnostic ( > 0.33). Considering the good quality of CCSDT(Q), we do not believe a multireference treatment is needed here. The largest uncertainty in the values of D0 calculated here are the ΔESOC values. Our computed zero-field splittings of the halogen oxides are too small by 0.09 (ClO), 0.29 (BrO) and 0.65 (IO) kcal/mol (see Table S8). If the contribution of this error to D0 is about half of this (as would be the case if L-S coupling was valid), then we would be overestimating D0 by as much as 0.3 kcal/mol. The current study leaves out the Lamb shift. The effects of the Lamb shift were treated for several diatomic HgX and IX species along with IHgO• and IHgX (X=Cl, Br, and I).46 In these cases, the effect of the Lamb shift is to weaken the IHg-X or IHg-O• bond by 0.3 to 0.4 kcal/mol. One might expect a similar effect on the BrHg-OX and BrHg-XO bond energies. The combined effects of errors in spin-orbit coupling corrections and neglect of the Lamb shift may cause our D0 values to be too large by roughly 0.4-0.8 kcal/mol. 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.38,39,76 We do not include the diagonal Born-Oppenheimer correction (DBOC) and anharmonic ZPE correction (both of which are included in some versions of the HEAT method). Our tests on the BrHg-OBr bond energy show that neither the DBOC (at SCF/AVTZ) or the ZPE correction (at PBE0/AVTZ) exceeds 0.01 kcal/mol. The HEAT approach has not been tested for mercury compounds, but there have been a few rigorous comparisons of high-level calculations for molecules containing 3d transition metals. Bross et al.75 studied the atomization energies of a set of 19 of these molecules using a modified Feller-PetersonDixon method with explicitly correlated CCSD(T) and high-level excitation up to CCSDT(Q)Λ. For 16 out of 19 molecules whose experimental uncertainty is less than 3.5 kcal/mol, their calculated results have a mean unsigned deviation of 1.3 kcal/mol and a root mean square deviation of 1.8 kcal/mol. Fang et al.77 studied a set of 20 such diatomic molecules, and claimed their CCSD(T)/CBS + ΔSOC results (with correlation of the valence and outer-core electrons) were mostly accurate to within 1 kcal/mol. Since we included higher excitations in our coupled cluster calculations, we might expect to have obtained slightly better accuracy than this. Lan et al.78 used a variant of the HEAT protocol to study the same set of molecules and found good consistency with experiment. Minenkov et al.79 used the domain-based local pair natural orbital (DLPNO) variant of CCSD(T) with a triple-zeta plus polarization basis set to evaluate a set of 51 reaction enthalpies involving mercury compounds. They found a mean unsigned error of 1.6 kcal/mol. Given the larger basis set used here, and the inclusion of ΔECV and ΔESOC, we feel our results should be more accurate than theirs. The only other composite method that has been significantly tested against transition metals is the correlation consistent composite approach80,81 (ccCA). Laury et al.82 tested a variant of ccCA against 30 molecules containing 4d transition metals, and their computed bond energies tended to agree with experimental data within the experimental error. Their approach extrapolates the correlation energy to the basis set limit using MP2 rather than CCSD(T), and does not use higher order coupled clusters.



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To conclude, in addition to the bias discussed above arising from error in our computed ∆ESOC and neglect of the Lamb shift, we might expect random errors of 0.5 to 1.0 kcal/mol. Let us consider the atmospheric implications of the present results. The large values of D0 for the BrHgOX species means they are thermally stable under all conditions relevant to the troposphere and stratosphere, but there is insufficient information to rigorously compute the thermal stability of the BrHgXO species. It is possible to roughly estimate of the lifetime, τ, of BrHgXO with respect to dissociation (τ=1/kdissoc(T)) from educated guesses about the association rate constant, kassoc, and the equilibrium constants, Keq(T) for BrHg• + XO BrHgXO. Using the harmonic oscillator-rigid rotor approximation and various data compiled here and in the Supporting Information, we find Keq(T) (in units of cm3 molecule-1) is well fit by: 5)6 7 = 3.0 × 10 = >11/

for X = Br

(14)

5)6 7 = 1.8 × 10 = @11/

for X = Cl

(15)

over the range 200-320 K. Based on our kinetic studies of the reactions of BrHg• with NO2 and HOO,15 it is reasonable to think that kassoc for BrHg• + XO → BrHgXO could be as high as 10-10 cm3 molecule-1 sec-1. Given A,BCC'& 7 = A*CC'& 7/5)6 7

(16)

and temperatures typically lower than 260 K in AMDEs, we compute τ(260 K) = 0.4 hours for BrHgClO and 20 hours for BrHgBrO. Polar AMDEs occur in the lowest 1 km of the atmosphere, where lifetimes with respect to deposition are probably a few hours to a day.83,84 While BrHgBrO may be stable over this time period, BrHgClO appears not to be. BrHgIO is more strongly bound than BrHgBrO by 4.4 kcal/mol, so BrHgIO will not dissociate thermally in an AMDE. Note that the potential for isomerization of BrHgXO to BrHgOX has not yet been investigated, and that gas-particle partitioning may remove Hg(II) compounds in competition with deposition.

Conclusions The vibrational frequencies and intensities reported here might be used to unambiguously identify these compounds in experiments and distinguish between BrHgOX and BrHgXO isomers. Note that the infrared spectrum of the analogous FHgOF compound has been obtained in rare-gas matrix, and interpretation of the spectra was aided by quantum calculations.85 We hope these studies inspire spectroscopists to investigate this series of isomeric pairs. The thermodynamic results presented here suggest that BrHgClO formed in AMDEs may dissociate thermally before depositing to surfaces, but the other species studied here will not. Investigations of the isomerization and photolysis of BrHgXO species and photolysis of BrHgOX species are needed to firmly establish their fate in the atmosphere. The thermodynamic results presented and analyzed here will be invaluable for benchmarking computational studies of the kinetics and mechanism of BrHg• reactions with halogen oxides. The importance of such benchmarking becomes clear when one considers the full complexity of the


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potential energy surface for BrHg• + XO• reactions. Consider that these reactions may form two additional sets of products beyond those described above (see Figure 4). BrHg• + XO• → BrHgX + O

(17a)

BrHg• + XO• → BrHgO• + •X

(17b)

The reactions represented by (17a) are significantly exothermic21,86 and are expected to be barrierless on the ground state surface (by analogy to the absence of a barrier to BrHg• + BrO• → HgBr2 + O and IHg• + IO• → HgI2 + O).46,86 Reaction (17b) is roughly thermoneutral and proceeds without a barrier via a BrHgOX intermediate. The BrHgO• species formed in reaction (17b) is known to be thermally stable,70 but its atmospheric chemistry has not been explored. Treating the kinetics of reactions (2), (5), (17a), and (17b) may require multireference methods, both for bond-breaking on the ground (singlet) surface and to treat the interaction of the ground state with low-lying triplet states (especially in 17a). Furthermore, one might expect that, for each X, there exists one variational transition state (TS) leading to both BrHgOX and BrHgO• + X• and another one leading to both BrHgXO and BrHgX + O. This means that determining product branching ratios would require one to either run ab initio dynamics or build an analytical potential energy surface on which to run dynamics. In either case, one would need to rely on methods less computationally demanding than what is used here. Our thermodynamic results and analysis will provide a means of estimating the sign and magnitude of the errors in dynamical simulations. Finally, we hope this work inspires experimental studies of the kinetics of BrHg• reactions with halogen oxides, so that we may gain a better understanding of how bromine chemistry causes atmospheric mercury depletion events and contributes to the oxidation of Hg(0), globally. Acknowledgements We are grateful for assistance from Dr. Florent Louis, Dr. Fan Wang, and two anonymous reviewers. This work was supported by the Environmental Chemical Sciences program at the National Science Foundation. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant Number ACI-1053575; speciﬁcally, it used Comet at the San Diego Supercomputer Center (SDSC) and Bridges at the Pittsburgh Supercomputing Center (PSC).

Supporting Information Available Energies of all species at all levels of theory, along with zero-point energies and rotational constants; vibrational frequencies and structures of diatomic molecules; scalar relativistic corrections at three levels of theory; values of zero-field splittings of halogen oxides; values of the T1 diagnostic; thermochemical data; figures of energy versus BrHg-OBr and BrHg-BrO bond distance. This material is available free of charge via the Internet at http://pubs.acs.org.



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TOC Graphic


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Schematic of some of the main processes believed to drive the destruction of ozone and mercury in atmospheric mercury depletion events (AMDEs). 244x172mm (220 x 220 DPI)

ACS Paragon Plus Environment


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Bond energies (kcal/mol) for BrHg-OX and BrHg-XO for X= Cl, Br, and I. The thermodynamics of BrHgO + X and BrHgX + O relative to BrHg• + XO are taken from the work of Peterson and co-workers 102x124mm (600 x 600 DPI)


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Additive corrections, ∆E, to BrHg-OX and BrHg-XO bond energies (compared to CCSD(T)/AVTZ). Positive values mean a correction term increases the computed value of D0, while negative values mean the correction term reduces the computed value of D0. 217x186mm (220 x 220 DPI)



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Bond energies (kcal/mol) for BrHg-OX and BrHg-XO for X= Cl, Br, and I. The thermodynamics of BrHgO + X and BrHgX + O relative to BrHg• + XO are taken from the work of Peterson and co-workers. 241x142mm (220 x 220 DPI)


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Structures, Vibrational Frequencies, and Bond Energies of the

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