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Quality Structures, Vibrational Frequencies, and Thermochemistry of the Products of Reaction of BrHg• with NO2, HO2, ClO, BrO, and IO Yuge Jiao and Theodore S. Dibble* Department of Chemistry, College of Environmental Science and Forestry, State University of New York, Syracuse, New York 13210, United States S Supporting Information *

ABSTRACT: Quantum chemical calculations have been carried out to investigate the structures, vibrational frequencies, and thermochemistry of the products of BrHg• reactions with atmospherically abundant radicals Y• (Y = NO2, HO2, ClO, BrO, or IO). The coupled cluster method with single and double excitations (CCSD), combined with relativistic effective core potentials, is used to determine the equilibrium geometries and harmonic vibrational frequencies of BrHgY species. The BrHg−Y bond energies are refined using CCSD with a noniterative estimate of the triple excitations (CCSD(T)) combined with core−valence correlation consistent basis sets. We also assess the performances of various DFT methods for calculating molecular structures and vibrational frequencies of BrHgY species. We attempted to estimate spin− orbit coupling effects on bond energies computed by comparing results from standard and two-component spin−orbit density functional theory (DFT) but obtained unphysical results. The results of the present work will provide guidance for future studies of the halogen-initiated chemistry of mercury. Reaction 2 has been investigated theoretically,12,15 and it possesses a high rate constant due to being a barrierless reaction. Nevertheless, the atmospheric significance of reaction 2 and 3 is likely to be small because the atmospheric concentrations of Br• and OH• are much lower than those of other radicals. We recently suggested that atmospherically abundant radicals, Y• (Y = NO2, HO2, ClO, or BrO), can react with BrHg• via:16,17

1. INTRODUCTION Mercury is a neurotoxin, whose compounds can damage human health and the well-being of ecosystems.1 Roughly 90% of mercury in the atmosphere exists as gaseous elemental mercury (Hg(0)), which has a long lifetime (∼1 year) and does not readily enter ecosystems because of its relatively high equilibrium vapor pressure and its low solubility in water.2 Oxidized mercury, mostly Hg(II), is more prone to enter ecosystems.3 However, the mechanisms of Hg(0) oxidation in the atmosphere are not well-known.4−6 Bromine atom initiates atmospheric oxidation of Hg(0) in the marine boundary layer7 and polar mercury depletion events.8 Modeling studies suggest that bromine atom also dominates the global oxidation of atmospheric Hg(0)9,10 via the following initiation reaction: Br • + Hg + M → BrHg • + M

BrHg • + • Y → BrHgY

Our previous quantum chemical calculations indicated that the BrHg−Y bonds formed in these reactions render these BrHgY compounds thermally stable in the atmosphere. Introducing reaction 4 into atmospheric models greatly increases the rate of Hg(II) formation.18,19 None of the proposed BrHgY species have been detected in experiments, although we recently described how proton-transfer mass spectrometry might be used to detect these species.17 In the absence of experimental data on BrHgY, quantum chemistry can provide reliable structures (shown in Figure 1), spectra, and thermochemical data. Previous quantum calculations16 were limited by three factors: (1) use of a density functional method that could not provide high-accuracy equilibrium geometries; (2) neglect of the effects of spin− orbit coupling; (3) neglect of correlation of the core electrons.

(1)

where M is a third body. While the kinetics of reaction 1 has been investigated both experimentally11 and theoretically,12−14 the atmospheric fate of BrHg• radical is unknown. Currently, no experimental data is available on the kinetics or products of reactions of BrHg• with other atmospheric species. Until recently, only two reactions were included in atmospheric models oxidizing BrHg• to Hg(II) compounds: BrHg • + •Br → HgBr2 •

(2)

•

BrHg + OH → BrHgOH © 2015 American Chemical Society

(4)

Received: May 21, 2015 Revised: September 24, 2015 Published: September 24, 2015

(3) 10502

DOI: 10.1021/acs.jpca.5b04889 J. Phys. Chem. A 2015, 119, 10502−10510

Article

The Journal of Physical Chemistry A

correlation consistent basis sets denoted as cc-pVnZ-PP (n = T or Q) developed by Peterson and co-workers21,22,24 for use with those AREPs (PP stands for pseudopotential). Other atoms (H, N, O, and Cl) were treated with the all-electron correlation consistent basis sets cc-pVnZ.25−28 To improve the performance of these basis sets, diffuse functions were also added to those basis sets; these are denoted as aug-cc-pVnZ-PP or aug-cc-pVnZ. For simplicity, we refer to those combinations of basis sets as VnZ (unaugmented) or AVnZ (augmented) in the remainder of this paper. Geometries of BrHgX and BrHgY species were optimized via coupled cluster theory with single and double excitations (CCSD)29 with the AVDZ, VTZ and AVTZ basis sets. The frozen core approximation (denoted as FC) was used for coupled cluster calculations except where noted. Harmonic vibrational frequencies were computed with CCSD using numerical second order derivatives. The AVTZ basis set was used to compute vibrational frequencies for BrHgX and the smaller BrHgY, but the VTZ basis set was used for BrHgNO2, BrHgONO, and BrHgOOH due to computational requirements that exceeded our resources. The results were compared with the harmonic vibrational frequencies calculated by density functional theories. Single point energies were refined via coupled cluster theory with single, double, and a noniterative estimate of triple excitations (CCSD(T))30 combined with the AVTZ basis sets at CCSD/AVTZ geometries. For open-shell species, we used UHF-based coupled cluster methods. To include the correlation from core electrons, we computed the CCSD(T) energies with all electrons correlated (denoted as FULL) using aug-cc-pwCVTZ-PP basis sets for Br, I, and Hg,24,31 and aug-cc-pwCVTZ basis sets for N, O, and Cl (denoted as AwCVTZ basis sets). These basis sets are explicitly optimized for calculation of core−valence correlation. Also the CCSD(T)/aug-cc-pwCVQZ energies were computed with all electrons correlated for selected species. For these species, the CCSD(T) energies were extrapolated to the complete basis set (CBS) limits using the 2-point extrapolation formula32,33

Figure 1. Structures of anti- and syn-BrHgONO, BrHgNO2, BrHgOOH, BrHgOCl, BrHgOBr, and BrHgOI with bond lengths (Å) at the CCSD/AVTZ level of theory.

E(n) = ECBS +

The goal of this paper is to accurately determinate the geometries and vibrational spectra of BrHgY, and the thermochemistry of BrHg• + Y reactions. As suggested by Wang et al.,18 we introduce IO• radical to the list of Y• previously studied. We first describe the methods for quantum chemical calculations, and then evaluate our methods by comparing results for BrHg−X (X = Cl, Br, or I) against experimental data and previously published high-level ab initio calculation results. We then provide harmonic vibrational frequencies of BrHgY as well as BrHg−Y bond energies. In addition, we assess the performance of different density functionals for computing geometries, harmonic vibrational frequencies, and BrHg−Y bond energies.

D n3

(5)

where n = 3 and 4. The evaluation of spin−orbit coupling effects on relative energies (ΔESO) was performed using the NWChem program suite.34 ΔESO was evaluated as the difference between bond energies computed with spin−orbit density functional theory (SO−DFT)35 and normal DFT.36,37 We optimized the geometries of BrHg•, Y• and BrHgY species using both standard DFT and SO−DFT using the B3LYP,38,39 PBE0,40,41 M06,42 and M06-2X42 functionals with AVTZ basis sets. We then calculated BrHg−Y bond energies and compared the DFT results with the corresponding SO−DFT results. These calculations used Stuttgart/Köln spin−orbit ECPs (SOREPs) for Br, I, and Hg, which were specifically developed for twocomponent spin−orbit calculations. For SO−DFT/AVTZ calculations, we used uncontracted versions of AVTZ basis sets for all elements.43 For open-shell species, we used UDFT method. We also computed ΔESO using the CRENBL (Christiansen, Ross, Ermler, Nash, Bursten, and Large valence shape-consistent) type pseudopotentials44−47 as well as their two-component spin−orbit potentials and the corresponding valence part of the basis sets for all atoms except hydrogen (for which the aug-cc-pVTZ basis set was used). We do not rely on the CRENBL pseudopotentials for CCSD(T) calculations,

2. COMPUTATIONAL METHODS Quantum chemical calculations were carried out on Gaussian09 revision D20 except where noted. Averaged relativistic effective core potentials (AREPs) for Br, I, and Hg are used to account for the scalar relativistic effects in present study. We mostly employed the small-core energy-consistent AREPs of the Stuttgart/Köln type that substitute for the innermost 10 electrons for Br,21 28 electrons for I,22 and 60 electrons for Hg.23 The remaining electrons of Br (3s23p63d104s24p5), I (4s24p64d105s25p5), and Hg (5s25p65d106s2) were treated with 10503


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Table 1. Comparison of Present Calculations of BrHg−X (X = Cl, Br, I) Bond Lengths (Å), and Vibrational Frequencies (cm−1) at CCSD/AVTZ with Benchmark Theoretical Calculations (in Italics) and Experimental Results (in Parentheses) frequencies species

R(Hg−Br)

R(Hg−X)

bend

symmetric stretch

asymmetric stretch

HgBrCl HgBr2 HgBrI

2.375, 2.3685a 2.384, 2.3770a 2.396, 2.3785c

2.266, 2.2535a (2.378 ± 0.005)b 2.556, 2.534c

87.1, 86.6a (83d) 70.5, 69.4a (68d) 61.8, 62.2c (66,j 60d)

257.1, 258.8a (253e) 225.6, 225.9a (220,f 218,e 229,g 222h) 185.5, 188.0c (182,e 187.6k)

391.2, 390.8a (385e) 296.4, 296.3a (293i) 273.9, 278.1c (266,e 272.0k)

a From ref 50. bFrom ref 49. cFrom ref 51. dFrom ref 52. eFrom ref 53. fFrom ref 54. gFrom ref 55. hFrom ref 56. iFrom ref 57. jFrom ref 58. kFrom ref 59.

Table 2. Spin−Orbit Coupling Corrections (ΔESO) to BrHg−X Bond Energies (kcal mol−1) and Average Values for the Four Functionals, Where the Geometries Are Optimized at the Corresponding DFT or SO−DFT Level species

pseudopotentials

B3LYP

M06

PBE0

M06-2X

average

best calculated (MRCI)

BrHg−Cla

Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL

−0.04 −0.36 −2.43 −2.70 −5.77 −6.50

0.07 0.70 −1.39 −2.59 −6.50 −7.46

−0.04 −0.22 −0.90 −1.97 −4.18 −4.83

−0.45 0.16 −3.66 −5.05 −4.07 −4.47

−0.12 0.07 −2.09 −3.08 −5.13 −5.82

−1.01b

BgHr−Br BrHg−I a

−3.32b −5.35c

After subtracting the zero-field splitting of Cl, as described in the text. bFrom ref 62. cFrom ref 51.

heavier than bromine. Thus, the effect of spin−orbit coupling on BrHgY geometries will not be as large as in HgBrI. Our CCSD/AVTZ vibrational frequencies are in very good agreement with the available data. As noted by Peterson and co-workers,50,51 experimental spectra obtained in the gas phase were of sufficiently low resolution that peak locations are uncertain; spectra obtained in matrices were subject to matrix shifts of peak locations. Harmonic vibrational frequencies for BrHgX species are very close to benchmark calculations at CCSD(T)/CBS+CV+SO+SR level of theory. The discrepancies between our results and those of Peterson and coworkers’ are no more than 1.7 cm−1 for HgBr2 and HgBrCl, and no more than 4.2 cm−1 for HgBrI. Table 2 shows our results for ΔESO on BrHg−X bond energies (D0) as well as literature results calculated by multireference configuration interaction (MRCI) method using Stuttgart/Kö ln relativistic pseudopotentials for all atoms. These MRCI values are the only ones of which we are aware for these systems. ΔESO for the BrHg−X and BrHg− Y bond energies should be negative because spin−orbit effects stabilize the radical fragments much more than the closed-shell species.60 For the BrHg−Cl bond, Stuttgart/Köln pseudopotentials (only used for Br and Hg) consistently predict the incorrect sign of ΔESO. This is in large part attributable to the absence of spin−orbit potential of Cl atom with AVTZ basis sets used in current study. By contrast, the CRENBL pseudopotentials already include a spin−orbit potential for Cl atom. If we correct the SO−DFT/AVTZ value of the BrHg−Cl bond energy by subtracting the experimental zero-field splitting value of Cl atom 0.84 kcal mol−1 (the difference between javeraged value and the j = 3/2 value),61 the resulting ΔESO values will be negative (except at M06/AVTZ). The CRENBL results are qualitatively correct for the B3LYP and PBE0 functionals but not the M06 or M06-2X functionals. However, both functionals with CRENBL pseudopotentials underestimate ΔESO for BrHg−X by more than 0.6 kcal mol−1 compared to the MRCI results. For BrHg−Br and BrHg−I, both types of pseudopotentials predict the correct sign of ΔESO. In particular for BrHg−I, the SO−DFT values are in good agreement with MRCI values. In our calculation of BrHg−X

because they yield mediocre equilibrium geometries and bond energies for mercury halides,48 probably because their valence basis sets are somewhat small.37 The thermochemical data at 298.15 K and 1 atm is also computed at the CCSD(T, FULL)/ AwCVTZ//CCSD/AVTZ level of theory. Bond energies listed in the text are D0 values (0 K including zero-point energy differences) unless otherwise specified.

3. RESULTS AND DISCUSSION 3.1. Validation of Methods by analysis of BrHgX (X = Cl, Br, I) systems. As can be seen from Table 1, our computed bond length for HgBr2 is in very good agreement with that derived from electron diffraction.49 For HgBrCl and HgBr2, our CCSD/AVTZ geometries are in good agreement with literature results50 that were computed at CCSD(T)/CBS+CV+SO+SR (CV means core−valence corrected, SR means scalar relativity corrected). As can be seen from Table 1, the discrepancies of Hg−Br bond lengths are no more than 0.007 Å and that of Hg−Cl bond length is 0.012 Å. The agreement of the present results with experimental results and higher level calculations includes a significant contribution from cancellation of errors. By comparing our CCSD/AVTZ geometries with Balabanov and Peterson’s50 CCSD(T)/AVTZ geometries of HgBr2 and HgBrCl, we find that adding the noniterative triple excitations can increase these bond lengths by 0.004−0.012 Å. Fortunately the basis set extrapolation we have not carried out for determining geometries can shrink these bond lengths by 0.009−0.011 Å (at CCSD(T)), which largely offsets the neglect of the effect of triple excitation on geometries. Balabanov and Peterson also indicated that spin−orbit coupling and scalar relativistic effects have very small impacts on these bond lengths (less than ±0.001 Å). For HgBrI, the discrepancy between our CCSD/ AVTZ bond lengths and those computed by Shepler et al.51 at CCSD(T)/CBS+CV+SO+SR increases to about 0.02 Å. We infer that these larger discrepancies are derived from the stronger spin−orbit coupling effect in HgBrI versus HgBr2 and HgBrCl. It should be noted that for all BrHgY species in current study, the mercury atom does not bond to any atoms 10504


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Table 3. BrHg−X Bond Energies (kcal mol−1 at 0 K) at CCSD(T)//CCSD/AVTZ and Corrections for Spin−Orbit Coupling (ΔESO), Core−Valence Correlation (ΔECV), and Zero-Point Energy (ΔEZPE)a CCSD(T, FC)

CCSD(T, FULL)

species

AVTZ

AwCVTZ

AwCVQZ

CBS

ΔEZPE

ΔESO

D0

BrHg−Cl BrHg−Br BrHg−I

79.80 74.46 67.46

79.84 73.14 66.60

81.93 75.24 68.60

83.46 76.78 70.06

−0.92 −0.69 −0.57

−1.01 −3.32 −5.35

81.5, 81.8b 72.8, 73.0b (71.86,c 72.33d) 64.1, 64.4e

a D0 values at CCSD(T, FULL)/CBS including all corrections, with benchmark theoretical calculations (in italics) and experimental results (in parentheses). ΔESO values are from refs 62 and 51. bFrom ref 60. cFrom ref 63. dFrom ref 15, calculation based on experimental results. eFrom ref 51.

Table 4. Critical Bond Lengths Lengths (in Ångstroms) and Bond Angles (in Degrees) of BrHgY Optimized at Various Levels of Theories, Where All DFT Calculations Use the AVTZ Basis Set molecule BrHgNO2 anti-BrHgONO

syn-BrHgONO

BrHgOOH

BrHgOCl

BrHgOBr

BrHgOI

parameter

B3LYP

PBE0

M06

M06-2X

CCSD/AVDZ

CCSD/VTZ

CCSD/AVTZ

Hg−Br/Å Hg−Y/Å Hg−Br/Å Hg−Y/Å A(Br−Hg−Y) Hg−Br/Å Hg−Y/Å A(Br−Hg−Y) Hg−Br/Å Hg−Y/Å A(Br−Hg−Y) Hg−Br/Å Hg−Y/Å A(Br−Hg−Y) Hg−Br/Å Hg−Y/Å A(Br−Hg−Y) Hg−Br/Å Hg−Y/Å A(Br−Hg−Y)

2.424 2.148 2.403 2.030 177.5 2.423 2.133 172.2 2.414 2.023 178.3 2.406 2.025 177.2 2.407 2.018 176.8 2.407 2.011 176.5

2.392 2.111 2.372 2.009 177.6 2.391 2.105 172.1 2.384 1.998 178.5 2.375 2.002 177.5 2.375 1.996 177.2 2.376 1.989 176.8

2.418 2.148 2.396 2.029 177.6 2.418 2.157 170.3 2.407 2.018 178.9 2.398 2.021 177.8 2.399 2.012 177.2 2.400 2.004 176.9

2.398 2.112 2.383 2.022 177.8 2.397 2.102 173.0 2.393 2.008 178.9 2.386 2.016 177.7 2.387 2.011 177.5 2.388 2.002 177.1

2.393 2.094 2.385 2.016 177.2 2.395 2.089 172.8 2.391 2.008 179.0 2.385 2.013 177.4 2.386 2.009 177.2 2.388 2.002 176.8

2.381 2.084 2.370 2.000 177.6 2.380 2.064 173.6 2.378 1.991 178.9 2.372 1.996 177.6 2.373 1.992 177.4 2.374 1.986 177.1

2.371 2.077 2.363 1.996 177.5 2.372 2.061 173.3 2.369 1.987 178.8 2.364 1.993 177.4 2.365 1.988 177.2 2.365 1.982 176.8

not be that large for BrHg−Y bond energies (see Section 3.4), where the Hg is bonded to a first-row element. Several energy terms are not computed in present study, but they are believed to account for only modest effects on BrHg− Y bond energies. Those include pseudopotential error (ΔEPP) that derives from the ECP we used for heavy atoms rather than all-electron basis sets, scalar relativistic effect (ΔESR) for light atoms including N, O, and Cl, core−valence correlation derived from Hg 4f electrons (ΔECV‑4f), and the Lamb shift (ΔELamb) arising from quantum electrodynamics.64 Table S4 in the Supporting Information presents the literature values of these corrections on BrHg−X bond energies. Every individual energy correction term is no larger than 0.8 kcal mol−1 and, and the net effects of all these terms are no more than 0.8 kcal mol−1. Having validated our computational approach, we now turn to the BrHgY species which have yet to be reported in any experiment. 3.2. BrHgY Equilibrium Geometries. Table 4 shows the Hg−Br and Hg−Y bond lengths and Br−Hg−Y bond angles for equilibrium geometries of all BrHgY species optimized at various level of theory. Figure 1 displayed the structures with CCSD/AVTZ bond lengths. It should be noted that the equilibrium geometry of HgBrOI is the first reported for this species. The T1 diagnostic values of all BrHg−Y species are less than 0.02, supporting the reliability of CCSD and CCSD(T) calculations of these molecules.65

bond enthalpies below (see Table 2), we used MRCI results from reference51,62 for our spin−orbit corrections, as these are the only results available and are expected to be fairly reliable. In the following calculations, we will evaluate spin−orbit coupling on BrHgY bond energies and geometries by SO−DFT with both CRENBL and Stuttgart/Köln pseudopotentials. Table 3 displays constituent energy contributions to the BrHg−X bond energies and the D0 values. Our bond energies show minor discrepancies (less than 0.3 kcal mol−1) compared with the experimental data for HgBr2 and benchmark calculations at CCSD(T)/CBS+CV+SO+SR+PP level for HgBrCl and HgBr2. Our results also agree well with for HgBrI with previous results at CCSD(T)/CBS+CV+CV4f+SO +LAMB level of theory (PP denotes correction to pseudopotential error, CV4f denotes core−valence correlation from 4f electrons, and Lamb denotes Lamb shift). In Peterson and coworkers’ studies50,61 on BrHg−Cl, the aug-cc-pV(n+d)Z basis set was used for Cl atom. The relatively small differences between our BrHgCl geometry, vibrational spectra and bond energy with their results indicate that the additional tight exponent on the d-shell has only a tiny impact. It should be noted that for most BrHgY molecules we are limited to CCSD(T, FULL)/AwCVTZ energies. The extrapolation from triple-ζ quality basis sets to CBS limit can increase BrHg−X bond energies by 3.5−3.6 kcal mol−1. However, that effect may 10505


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Table 5. Harmonic Vibrational Frequencies (cm−1) of BrHgY Species at B3LYP, PBE0, M06, and M06-2X with the AVTZ Basis Set and CCSD with either the VTZ or AVTZ Basis Sets (As Noted)a frequencies BrHgNO2 (C2v)

anti-BrHgONO (Cs)

syn-BrHgONO (Cs)

BrHgOOH (C1)

BrHgOCl (Cs)

symmetry

B2

B1

B2

A1

CCSD/VTZ B3LYP/AVTZ PBE0/AVTZ M06/AVTZ M062X/AVTZ

63.1 58.3 61.1 56.0 60.1

71.9 65.2 68.8 64.3 68.6

237.3 238.9 243.4 229.6 229.1

242.5 210.8 226.7 216.0 228.4

A1

symmetry

A′

A″

A″

A′


61.8 58.1 60.2 59.1 59.1

98.2 89.5 93.9 92.6 88.4

164.4 165.0 169.7 170.6 155.7

195.4 181.8 187.2 182.5 186.0

symmetry

A′

A″

A′

A′


71.1 63.4 66.5 59.4 68.8

89.2 79.0 82.6 74.4 81.1

150.2 129.1 139.1 140.9 152.3

257.7 228.7 242.9 230.0 242.2

symmetry

A

A

A

A


77.1 71.9 74.8 70.5 73.9

121.6 112.1 117.3 112.8 113.4

223.7 211.8 221.9 214.2 212.6

252.2 256.9 268.1 260.9 247.0

B1

321.1 505.8 283.7 497.2 301.1 514.2 289.0 497.3 299.5 494.2 frequencies A′ 267.3 248.1 260.6 253.6 254.3 frequencies A″ 362.0 360.9 380.5 340.7 367.4 frequencies

A1

A1

B2

850.1 825.5 846.3 836.8 856.0

1411.3 1355.1 1409.7 1405.3 1444.4

1619.9 1564.6 1637.7 1637.7 1628.0

A′

A′

A′

A′

425.8 395.0 412.0 406.1 408.3

801.5 694.1 770.7 767.3 823.1

941.0 893.9 943.7 945.6 970.3

1743.6 1708.0 1750.0 1751.5 1774.2

A′

A′

A′

A′

436.8 384.8 394.9 398.3 396.5

894.0 885.8 909.8 903.9 914.2

1071.4 1056.0 1135.0 1164.3 1144.3

1600.3 1526.2 1578.1 1552.4 1600.0

A

A

272.1 587.8 289.0 545.5 293.6 570.5 288.9 557.4 259.3 563.5 frequencies

A

A

A

935.0 908.2 965.2 968.7 1005.2

1374.1 1346.9 1375.3 1364.0 1371.1

3847.1 3748.5 3807.8 3797.7 3835.7

symmetry

A′

A″

A′

A′

A′

A′

CCSD/AVTZ B3LYP/AVTZ PBE0/AVTZ M06/AVTZ M062X/AVTZ

62.1 58.1 60.5 59.7 54.5

120.4 115.3 122.2 119.2 112.2

173.5 168.6 171.8 167.0 166.2

270.4 250.5 263.2 256.2 254.4

538.3 505.0 530.3 521.9 517.3

781.1 738.7 786.6 779.9 811.6

frequencies BrHgOBr (Cs)

symmetry

A′

A″

A′

A′

A′

A′


51.3 48.1 49.7 49.3 46.5

120.8 114.2 121.8 114.7 123.1

131.1 127.8 129.8 127.2 127.0

269.0 248.7 261.8 254.6 253.2

506.4 480.3 505.7 499.1 495.8

721.6 673.7 712.0 713.2 736.5

symmetry

A′

A′

A″

A′

A′

A′


45.1 43.4 43.9 43.2 42.6

112.2 108.9 110.3 107.7 108.6

120.3 117.7 121.2 115.0 118.6

268.3 247.5 260.7 253.4 251.8

474.0 451.4 476.0 465.1 470.0

711.9 660.1 688.6 685.5 713.1

frequencies BrHgOI (Cs)

a

syn- and anti-BrHgONO are listed with Cs symmetry, although some levels of theory/basis sets predicted minute deviations from Cs symmetry.

BrHgNO2, the equilibrium geometry has C2v symmetry at all levels of theory. For syn-BrHgONO and anti-BrHgONO, the CCSD/AVTZ geometries deviate from Cs symmetry by less than 1.0 degrees in the Br−Hg−O−N dihedral angle, and the electronic energies of C1 geometries are only 10−7−10−6 Hartree more positive than those of optimized Cs geometries.

All spin−orbit-free DFT/AVTZ calculations used here yield Br−Hg and Hg−Y bond lengths larger than the corresponding CCSD/AVTZ values. As compared to CCSD, B3LYP and M06 overestimate bond lengths the most, by an average of 0.044 and 0.041 Å, respectively. PBE0 and M06-2X perform the best, with deviations of only 0.016 and 0.025 Å, respectively. For 10506


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Table 6. BrHg−Y Bond Energies (kcal mol−1 at 0 K) at CCSD(T, FULL)/AwCVTZ//CCSD/AVTZ+ ΔEZPE Level of Theorya

a

CCSD(T, FC)

CCSD(T, FULL)

species

AVTZ

AwCVTZ

ΔEZPE

D0

previously calculatedb

BrHg−NO2 anti-BrHg−ONO syn-BrHg−ONO BrHg−OOH BrHg−OCl BrHg−OBr BrHg−OI

37.22 38.54 45.03 43.77 53.59 55.97 57.53

35.79 37.10 43.50 42.80 51.93 54.78 56.02

−1.70 −0.81 −1.14 −1.69 −1.30 −1.26 −1.25

34.1 36.3 42.4 41.1 50.6 53.5 54.8

35.6 38.4 43.7 42.5 52.7 55.6 −

Previously calculated values of D0 are at the CCSD(T)//B3LYP/AVTZ + ΔEZPE level of theory. bFrom refs 16 and 17.

Table 7. Spin−Orbit Coupling Corrections ΔESO (kcal mol−1) on BrHg−Y Bond Dissociation Energies (De, kcal mol−1) Calculated by Various DFT and SO−DFT Methods with CRENBL and Stuttgart/Köln Pseudopotentials species

pseudopotentials

ΔESO‑B3LYP

ΔESO‑M06

ΔESO‑PBE0

ΔESO‑M06‑2X

average ΔESO

std. dev. ΔESO

BrHg−NO2

Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL Stuttgart/Kölnb CRENBL Stuttgart/Köln CRENBL Stuttgart/Köln CRENBL

0.78 0.34 0.79 0.29 0.60 0.19 0.90 0.33 0.57 0.31 0.66 0.34 −0.20 0.41

0.67 0.38 0.77 0.32 0.60 0.21 1.00 0.37 0.66 0.33 2.29 0.28 −1.99 a

0.78 0.37 0.75 0.28 0.55 0.19 0.88 0.34 0.54 0.31 0.67 0.33 −0.05 0.34

1.08 0.17 0.26 0.04 0.08 −0.07 0.52 0.10 0.16 0.09 0.57 0.17 1.02 0.42

0.83 0.32 0.65 0.23 0.46 0.13 0.83 0.29 0.48 0.26 1.05 0.28 −0.31 0.39

0.18 0.10 0.26 0.13 0.25 0.13 0.21 0.12 0.22 0.11 0.83 0.08 1.25 0.04

anti-BrHg−ONO syn-BrHg−ONO BrHg−OOH BrHg−OCl BrHg−OBr BrHg−OI a

Calculation fails due to convergence failure. bAfter subtracting the experimental spin−orbit splitting of OCl, as described in the text.

3.3. BrHgY Vibrational Frequencies. The harmonic vibrational frequencies at the B3LYP/AVTZ, PBE0/AVTZ, M06/AVTZ, M06-2X/AVTZ, and CCSD/(A)VTZ levels of theory are presented in Table 5. As stated previously, to reduce the computational demand, we omitted the diffuse functions in computing CCSD frequencies for BrHgNO2, BrHgONO, and BrHgOOH. If we take the CCSD frequencies as a standard, the PBE0 functional gives the most accurate frequencies among four functionals with an average deviation of 2.8%, while B3LYP functional provides the least accurate frequencies with an average deviation of 5.8%. M06 and M06-2X have moderate performances on vibrational frequencies with average deviations of 4.7% and 4.2%, respectively. Qualitative descriptions of these modes are available in the Supporting Information to ref 16. 3.4. BrHg−Y Bond Energies. Table 6 lists BrHg−Y bond energies at the CCSD(T,FULL)/AwCVTZ//CCSD/AVTZ level of theory, with comparisons to previously calculated results at CCSD(T)//B3LYP/AVTZ.16 All BrHg−Y bond energies are in the range of 34−55 kcal mol−1. The synBrHgONO has an Hg−O bond energy 6.1 kcal mol−1 larger than the anti-BrHgONO and 8.3 kcal mol−1 larger than the Hg−N bond energy of BrHgNO2. This which confirms our previous report17 that the syn-conformer is the most stable in the BrHg + NO2 system. The difference between the present CCSD(T, FC)//CCSD/AVTZ bond formation enthalpies and the previously published results at CCSD(T, FC)//B3LYP/ AVTZ are rather modest: −0.1 to 0.7 kcal mol−1 (neglecting ΔEZPE for both). Including core−valence correlation at the CCSD(T, FULL)/AwCVTZ level decreases the bond energies by 1.0 to 1.7 kcal mol−1. Because of the limitation of our

Note that after including zero-point energy at B3LYP/AVTZ, the energy of the Cs symmetry energy is more negative than that of the C1 geometry. As a result of these observations, we suspect these deviations from Cs symmetry are artifacts. A detailed comparison of C1 energies and Cs energies at various level of theory is presented in the Supporting Information. Of the two BrHgONO conformers, the syn conformer has a longer Hg−Br bond (by 0.01−0.02 Å) and Hg−O bond (by 0.07− 0.13 Å) bonds and a smaller Br−Hg−O bond angle (3.8−7.4 deg) than the anti conformer. For BrHgOOH, the optimized geometries have no symmetry, whereas all three BrHgOX species possess Cs symmetry. Spin−orbit coupling effect on equilibrium geometries can be evaluated by comparing the geometries of spin−orbit-free DFT with those of the corresponding SO−DFT using both types of pseudopotentials (Table S5). Although the various functionals yield different geometries, the differences between DFT geometries and SO−DFT geometries (ΔSO) among the four functionals are very consistent. The spin−orbit effect always reduces the Hg−Br bond and Hg−Y bond length by less than 0.01 Å. Comparing the CCSD geometries computed with AVDZ, VTZ, and AVTZ basis sets (shown in Table 4) allows us to assess the effect of basis set size on equilibrium geometries. The increase from a double-ζ to a triple-ζ valence basis set decreases Hg−Br and Hg−Y bond lengths by about 0.02 Å. Adding diffuse functions shortens these bonds by no more than 0.01 Å. The Br−Hg−Y bond angles do not show obvious trends with basis set. 10507


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Table 8. BrHg−Y Bond Dissociation Energies (De, kcal mol−1) Calculated by Various Spin−Orbit-Free Functionals with AVTZ and CRENBL Pseudopotential/Basis Seta B3LYP

a

M06

PBE0

M06-2X

species

AVTZ

CRENBL

AVTZ

CRENBL

AVTZ

CRENBL

AVTZ

CRENBL

CCSD(T)

BrHg−NO2 anti-BrHg−ONO syn-BrHg−ONO BrHg−OOH BrHg−OCl BrHg−OBr BrHg−OI

29.2 27.5 34.4 34.4 43.5 45.0 46.0

31.9 31.6 37.7 33.8 46.1 45.3 44.8

32.9 30.0 39.0 37.9 47.7 48.7 48.6

39.2 37.2 45.7 39.5 51.7 52.3 51.7

33.0 29.8 37.5 36.8 47.3 49.4 51.0

36.1 33.6 40.4 36.1 50.4 50.2 50.3

32.4 33.2 41.1 37.5 48.7 51.0 53.8

39.5 38.9 45.6 40.1 53.9 54.3 55.1

35.8 37.1 43.5 42.8 51.9 54.8 56.0

CCSD(T) values are at the CCSD(T, FULL)/AwCVTZ//CCSD/AVTZ level of theory.

and vibrational frequencies of BrHg−Y, suggests that B3LYP not be used to study BrHgY species. By contrast, the M06-2X bond strengths have the least deviation compared with CCSD(T) values among four functionals, but it still systematically underestimate the bond energies by 3.5 ± 1.0 kcal mol−1. The PBE0 and M06 functionals both underestimate the bond energies by an average of 5.3 kcal mol−1. Values of De computed with DFT/CRENBL (Table 8) are generally larger than DFT/AVTZ bond energies, and thus closer to the CCSD(T) values than the DFT/AVTZ values. This leads to M06 and M06-2X bond energies that are, on average, within 1 kcal mol−1 of the CCSD(T) values (albeit with standard deviations of 2−3 kcal mol−1, larger than the corresponding DFT/AVTZ values). DFT/CRENBL thus appears to perform better than DFT/AVTZ for BrHg−Y bond energies. One might, therefore, be tempted to rely on DFT/CRENBL for studies of BrHgY. On the other hand, if one recalls the poor performance of CCSD(T)/CRENBL for bond energies, one might hesitate to use DFT/CRENBL for future studies of other aspects of BrHgY chemistry and thermodynamics.48

computational resources, the only BrHgY for which we can compute the CBS extrapolated bond energy is BrHg−OCl (Table S1 in the Supporting Information). Increasing the basis set size from AwCVTZ to AwCVQZ increases the bond energies by 1.0 kcal mol−1, and from AwCVQZ to the extrapolated CBS limit further increases the bond strength by 0.7 kcal mol−1. We estimate that basis-set effects on BrHg−Y bond energies, generally, should be similar to that observed here for BrHg−OCl. Note that, because SO−DFT tends to lead to unphysical values of ΔESO for BrHg−Y bond energies (see below) we do not include ΔESO in calculating D0 in these systems. More reliable calculations of ΔESO in these systems would be desirable. Bond energies of BrHg−Y were calculated by spin−orbit-free DFT and spin−orbit DFT methods with two types of pseudopotentials and four functionals. As stated above, the spin−orbit corrections to bond energies are evaluated by taking the difference between the spin−orbit DFT bond energies and the corresponding spin−orbit-free DFT bond energies with both types of pseudopotentials. Those differences are listed as ΔESO in Table 7. All ΔESO values are positive for all Y except one functional for syn-BrHgONO and three functionals for BrHgOI, indicating that spin−orbit coupling effects almost always strengthen the BrHg−Y bonds. Unfortunately, this contradicts with the fact that spin−orbit coupling decreases the bond energy for a close-shell molecule that dissociates to two open-shell fragments.60 Since the spin−orbit potentials of O and Cl are absent for Stuttgart/Köln pseudopotentials, we also attempt to correct the BrHg−OCl bond energy at the SO− DFT/AVTZ level by subtracting the experimental spin−orbit splitting value of OCl 0.37 kcal mol−1 (the difference between javeraged value and the j = 3/2 value), however, the resulting ΔESO values are still positive. Interestingly, Kim et al.48 also found that SO−DFT yielded larger bond energies than regular DFT for FHg−F and ClHg−Cl with both Stuttgart/Köln and CRENBL pseudopotentials. We therefore infer that SO−DFT is not appropriate to predict ΔESO for BrHg−Y bond energies with those two types of pseudopotentials when mercury is binding to a relatively light atom (such as Cl, O, N, and F). Turning to spin−orbit-free DFT results, we evaluate the performances of four functionals by comparing (see Table 8) the DFT/AVTZ bond dissociation energies (De, without any corrections) to the CCSD(T, FULL)/AwCVTZ//CCSD/ AVTZ values. The four functionals with AVTZ basis sets underestimate the BrHg−Y bond strengths by values ranging from 2.8 to 10.0 kcal mol−1 (depending on the functional and the identity of Y•). The B3LYP bond energies are 8.9 ± 2.4 kcal mol−1 (mean ± 2 s.d.) smaller than CCSD(T) values. This fact, and the poor performance of B3LYP for equilibrium geometries

4. CONCLUSION In present study, we investigate the equilibrium geometries, vibrational frequencies, and bond energies of BrHgY species. The overall BrHg−Y bond strengths at the CCSD(T, FULL)/ AwCVTZ//CCSD/AVTZ level of theory in the current study are generally smaller than the previously published results by values ranging from 1.3 to 2.1 kcal mol−1. These discrepancies can be mainly attributed to adding core−valence correlation. The complete basis set extrapolation is not fully included in the current study, but we suggest that the use of a triple-ζ quality basis set results in underestimating the bond energy by very roughly 2 kcal mol−1. These discrepancies in bond energies will not change the conclusion of Dibble et al., that BrHg• can form thermodynamically stable compounds with atmospherically relevant radicals Y.16 We find that spin−orbit coupling corrections to BrHg−Y bond energies are unphysical when combining spin−orbit DFT with CRENBL or Stuttgart/Köln SOREPs. Also we find that the PBE0 and M06-2X functionals are systematically better than M06 and B3LYP functionals in predicting geometries, vibrational spectra, and energies for BrHgY. This work not only improves on the level of theory used for geometries, vibrational frequencies, and energies used in Dibble et al.,16 it also extends calculations to Y = IO•, which was recently suggested to be an important reaction partner of BrHg• in the marine boundary layer. 10508


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(12) Goodsite, M. E.; Plane, J. M. C.; Skov, H. A Theoretical Study of the Oxidation of Hg0 to HgBr2 in the Troposphere. Environ. Sci. Technol. 2004, 38, 1772−1776. (13) Shepler, B. C.; Balabanov, N. B.; Peterson, K. A. Hg+Br→HgBr Recombination and Collision-Induced Dissociation Dynamics. J. Chem. Phys. 2007, 127, 164304. (14) Wilcox, J.; Okano, T. Ab Initio-Based Mercury Oxidation Kinetics via Bromine at Postcombustion Flue Gas Conditions. Energy Fuels 2011, 25, 1348−1356. (15) Balabanov, N. B.; Shepler, B. C.; Peterson, K. A. Accurate Global Potential Energy Surface and Reaction Dynamics for the Ground State of HgBr2. J. Phys. Chem. A 2005, 109, 8765−8773. (16) Dibble, T. S.; Zelie, M. J.; Mao, H. Thermodynamics of Reactions of ClHg and BrHg Radicals with Atmospherically Abundant Free Radicals. Atmos. Chem. Phys. 2012, 12, 10271−10279. (17) Dibble, T. S.; Zelie, M. J.; Jiao, Y. Quantum Chemistry Guide to PTRMS Studies of as-yet Undetected Products of the Bromine-Atom Initiated Oxidation of Gaseous Elemental Mercury. J. Phys. Chem. A 2014, 118, 7847−7854. (18) Wang, F.; Saiz-Lopez, A.; Mahajan, A. S.; Gómez Martín, J. C.; Armstrong, D.; Lemes, M.; Hay, T.; Prados-Roman, C. Enhanced Production of Oxidised Mercury over the Tropical Pacific Ocean: A Key Missing Oxidation Pathway. Atmos. Chem. Phys. 2014, 14, 1323− 1335. (19) Toyota, K.; Dastoor, A. P.; Ryzhkov, A. Air−snowpack Exchange of Bromine, Ozone and Mercury in the Springtime Arctic Simulated by the 1-D Model PHANTAS − Part 2: Mercury and Its Speciation. Atmos. Chem. Phys. 2014, 14, 4135−4167. (20) Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. Gaussian, Inc.: Wallingford CT, 2009. (21) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-D Group 16−18 Elements. J. Chem. Phys. 2003, 119, 11113. (22) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110, 13877−13883. (23) Figgen, D.; Rauhut, G.; Dolg, M.; Stoll, H. Energy-Consistent Pseudopotentials for Group 11 and 12 Atoms: Adjustment to MultiConfiguration Dirac−Hartree−Fock Data. Chem. Phys. 2005, 311, 227−244. (24) Peterson, K. A.; Puzzarini, C. Systematically Convergent Basis Sets for Transition Metals. II. Pseudopotential-Based Correlation Consistent Basis Sets for the Group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) Elements. Theor. Chem. Acc. 2005, 114, 283−296. (25) Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007. (26) Davidson, E. R. Comment on “Comment on Dunning’s Correlation-Consistent Basis Sets. Chem. Phys. Lett. 1996, 260, 514− 518. (27) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796. (28) Woon, D. E.; Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. III. The Atoms Aluminum through Argon. J. Chem. Phys. 1993, 98, 1358. (29) Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F. An Efficient Reformulation of the Closed-Shell Coupled Cluster Single and Double Excitation (CCSD) Equations. J. Chem. Phys. 1988, 89, 7382. (30) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (31) Peterson, K. A.; Yousaf, K. E. Molecular Core-Valence Correlation Effects Involving the Post-D Elements Ga-Rn: Bench-

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b04889. Energies of all species at CCSD(T), DFT, and SO−DFT, along with zero-point energies and Cartesian coordinates, as well as thermochemical data at 298.15 K and 1 atm (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*(T.S.D.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS 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 the Blacklight system at the Pittsburgh Supercomputing Center (PSC). We thank Dr. Jochen Autschbach, Dr. Joonghan Kim, and Dr. Philip Christiansen for helpful discussions and the anonymous reviewers for their many helpful comments.

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REFERENCES

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