Article pubs.acs.org/JPCA
Thermochemistry of HO2 + HO2 → H2O4: Does HO2 Dimerization Affect Laboratory Studies? Matthew K. Sprague*,# and Karl K. Irikura* Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States S Supporting Information *
ABSTRACT: Self-reaction is an important sink for the hydroperoxy radical (HO2) in the atmosphere. It has been suggested (Denis, P. A.; Ornellas, F. R. J. Phys. Chem. A, 2009, 113 (2), 499−506) that the minor product hydrogen tetroxide (HO4H) may act as a reservoir of HO2. Here, we compute the thermochemistry of HO2 self-reactions to determine if either HO4H or the cyclic hydrogen-bound dimer (HO2)2 can act as reservoirs. We computed electronic energies using coupled-cluster calculations in the complete basis set limit, CCSD(T)/CBS[45]//CCSD(T)/cc-pVTZ. Our model chemistry includes corrections for vibrational anharmonicity in the zero-point energy and vibrational partition functions, core− valence correlation, scalar relativistic effects, diagonal Born−Oppenheimer, spin−orbit splitting, and higher-order corrections. We compute the Gibbs energy of dimerization to be (−20.1 ± 1.6) kJ/mol at 298.15 K (2σ uncertainty), and (−32.3 ± 1.5) kJ/mol at 220 K. For atmospherically relevant [HO2] = 108 molecules per cm3, our thermochemistry indicates that dimerization will be negligible, and thus H2O4 species are atmospherically unimportant. Under conditions used in laboratory experiments ([HO2] > 1012 molecules per cm3, 220 K), H2O4 formation may be significant. We compute two absorption spectra that could be used for laboratory detection of HO4H: the OH stretch overtone (near-IR) and electronic (UV) spectra. been made using laser magnetic resonance.33−35 All of these studies involved HO2 number densities of [HO2] = 1012−1014 molecules per cm3, roughly 4−6 orders of magnitude higher than in the atmosphere. In the presence of methanol11,13,17,30 or water,11,17−19 the rate of reaction 1 is enhanced by a chaperone mechanism, in which HO2 forms a complex with methanol or water before reacting with another HO2 molecule. Analyses of experimental kinetics data typically assume that HOOH is the only stable product formed from the HO2 selfreaction in significant quantities. However, additional reaction pathways leading to combination products (generically denoted H2O4, reaction 2) have been postulated since the 1960s.22,36−43 Two H2O4 products have been suggested: the straight chain isomer, hydrogen tetroxide (HO4H), and a cyclic, doubly hydrogen-bound complex (HO2)2. The three conformers of HO4H (labeled #1, #2, and #3) and (HO2)2 are illustrated in Figure 1.
1. INTRODUCTION The reactions of the hydroperoxy radical, HO2, play a key role in the atmospheric oxidation of volatile organic compounds and consequently the concentrations of tropospheric ozone, aerosols, and greenhouse gases.1−3 Typical atmospheric [HO2] ranges from 106 to 108 molecules per cm3.1−3 In regions with high concentrations of nitrogen oxides (high [NOx]), HO2 will react with NOx as part of chemical cycles leading to ozone and smog production. In regions with low [NOx], self-reaction of HO2 becomes important. The major products of this self-reaction are hydrogen peroxide (HOOH) and triplet molecular oxygen (O2) (reaction 1).4−6 The (+M) above the arrow in reaction 1 indicates that both bimolecular and termolecular pathways exist. (+M)
HO2 + HO2 ⎯⎯⎯⎯→ HOOH + O2
(1)
Reaction 1 is highly exothermic, with ΔrxnH298.15 = −160.04 ± 0.35 kJ/mol7 (2σ uncertainty) and ΔrxnG298.15 = −154.81 kJ/mol (calculated from combining the entropy from ref 8 with the enthalpy from ref 7, uncertainty at least ±0.35 kJ/mol). Atmospheric hydrogen peroxide is unreactive; it is removed from the atmosphere primarily through dissolution into water.9−11 Consequently, the HO2 self-reaction acts as a sink for HO2. The kinetics of reaction 1 have been well-studied for temperatures 200 to 500 K and bath gas pressures up to 0.1 ̃ X̃ absorption of MPa (1 bar), typically by monitoring the B− HO2 in the ultraviolet (UV) region (190 to 250 nm) and subtracting absorption features from HOOH.5,11−27 Some studies monitor other spectroscopic bands of HO2: ν3 (HOO bend) at 1117 cm−14,6,28,29 or 2ν1 (OH stretch overtone) at 6640 cm−1.30−32 Low-pressure measurements (50% of the initial HO2 is bound as H2O4 over the first 100 ms. Under these conditions of high [HO2] (1014 molecules per cm3) and low temperature (220−240 K), H2O4 acts as a significant reservoir for HO2. 3.5. Uncertainty on ΔdimerG, Kc, Dimerization Fraction. We consider two contributions to the 2σ uncertainties on ΔdimerG: errors in ab initio thermochemistry from our quantum chemical method as assessed by wave function diagnostics, and the spread on derived ΔdimerG values from using different reference reactions. Wave function diagnostics can be used to estimate uncertainties on atomization energies quantitatively.71 Table 4 contains the %TAE[(T)] diagnostic72 for each of our molecules, defined as F
DOI: 10.1021/acs.jpca.5b04265 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Table 5. Estimate of 2σ Uncertainties on ΔdimerG(T) and log10 Kc, CCSD(T)/CBS[4,5]. All Energies in kJ/mol, Kc in cm3 per Molecule wave function diagnostics alternative schemes total 2σ uncert on ΔdimerG(T) total 2σ uncert on log10 Kc
200 K
220 K
240 K
260 K
280 K
298.15 K
300 K
320 K
0.25 1.51 1.53 0.92
0.25 1.46 1.48 0.81
0.25 1.48 1.51 0.75
0.25 1.44 1.47 0.68
0.25 1.52 1.54 0.66
0.25 1.54 1.56 0.63
0.25 1.56 1.58 0.63
0.25 1.55 1.57 0.59
Table 6. log10(Kc,298.15/cm3 per molecule) for HO2 + HO2 → H2O4, Calculated at Various Levels of Theory and Bases
a
basisa
HF
B3LYP
MP2(FC)
QCISD
CCSD
CCSD(T)
pVTZ aVTZ pVQZ aVQZ pV5Z aV5Z CBS[45] VTZ-F12 VQZ-F12 CBS[34]-F12
−24.4 −24.7 −24.6 −24.8 −24.7 −24.8 −24.9
−19.4 −20.6 −20.2 −20.7 −20.6 −20.7 −20.8
−9.1 −8.0 −8.3 −7.9 −7.9 −7.7 −7.5
−20.7 −20.8 −20.9 −20.9 −21.0 −21.0 −21.0
−20.6 −20.3 −20.6 −20.4 −20.4 −20.3 −20.3
−16.8 −16.0 −16.4 −16.0 −16.0 −15.9 −15.9
CCSD(T*)-F12a
CCSD(T*)-F12b
−15.4 −15.5
−15.7 −15.7 −15.7
pVxZ = cc-pVxZ, aVxZ = aug-cc-pVxZ, VxZ-F12 = cc-pVxZ-F12. Energies calculated at the cc-pVTZ or VTZ-F12 optimized geometries.
(295 K) have the same shape.26,75 Vertical transition frequencies and oscillator strengths are listed in the Supporting Information. The simulated electronic spectra of HOOH, HO2, and a mixture of HO4H at 240 K are shown in Figure 3, over the
and relatively large basis sets (up to quintuple zeta). For larger chemical systems (e.g., self-reaction of alkyl peroxides); such calculations may be too computationally expensive. Thus, we are interested in whether calculations with smaller basis sets or at lower levels of theory can reproduce our computed thermochemistry. Table 6 contains log10Kc for reaction 2 at 298.15 K, computed at various levels of theory and bases, using the procedures described in the Theoretical Methods section. (Energies of formation can be found in the Supporting Information.) The 2σ uncertainty on log10 Kc is 0.7 at 298.15 K (from Table 5). We note that all of the CCSD(T*)-F12 calculations are able to reproduce Kc to within this uncertainty. Furthermore, all CCSD(T) calculations using the aug-cc-pVTZ basis or larger can also reproduce Kc. This suggests that reducing the basis set size or using explicitly correlated coupled-cluster calculations are two ways to reduce computational expense. In contrast, HF, B3LYP, MP2, QCISD, and CCSD yield values of Kc 3−10 orders of magnitude different than our model chemistry. Furthermore, singlet (HO2)2 is predicted to be lower in energy than HO4H for HF, B3LYP, QCISD, and CCSD. None of these methods appears suitable for modeling the thermochemistry of peroxy radical dimerization. 3.7. Predicted Spectroscopic Bands of HO4H. As stated in the Introduction, HO2 self-reaction kinetics have been widely studied by monitoring the time dependence of spectroscopic ̃ X̃ electronic absorption bands of HO2, typically either the B− (220 nm) or the 2ν1 OH stretch vibrational overtone (6600 cm−1). If HO4H forms in appreciable quantities, it may have detectable spectroscopic features in these regions. Here, we predict the positions of these features. Vertical electronic transition frequencies and oscillator strengths of HO2, HOOH, and the three conformers of HO4H were computed at the EOM-CCSD/aug-cc-pVDZ level,74 as implemented in Gaussian 09.58 All spin-allowed transitions (i.e., singlet−singlet) corresponding to λ > 130 nm were computed. The transitions were convolved with a Gaussian function with a full width at half-maximum (fwhm) of 55 nm. This width was chosen so that the computed and experimental spectra of HO2
Figure 3. Predicted UV absorption spectra for HOOH (top), HO2 (middle, black), and HO4H (bottom, 240 K), calculated at EOMCCSD/aug-cc-pVDZ. Transitions were convolved with a Gaussian function (fwhm = 55 nm). The 295 K experimental UV spectrum of HO226,75 is shown for comparison (middle, blue).
wavelength range of 150−300 nm. At 220 nm, the absorption cross section of HO4H is nearly equal to that of HOOH, both of which are an order of magnitude less than that of HO2. Significant H2O4 formation would have a measurable impact on an experimental UV spectrum. Consider an experiment at 240 K in which the initial [HO2] is 1014 molecules per cm3. According to the simple kinetics model discussed in section 3.4, 50% of the HO2 will be bound as H2O4 after 1 ms. In this case, the absorption at 220 nm would be 55% of what would be expected if dimerization did not occur. G
DOI: 10.1021/acs.jpca.5b04265 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 7. Calculated OH Stretch Fundamental and Overtone Frequencies (cm−1). Literature Values in Parentheses νOH 2νOH
HO2
HOOH
CH3OH
HO4H #1
HO4H #2
HO4H #3
3435 (3436a) 6667 (6651c)
3616/3616 (3610/3618a) 7056/7056 (7045d)
3692 (3681a) 7214 (7195e)
3557/3570 (3537/3554b) 6939/6964
3568/3570 (3550/3553b) 6961/6965
3565/3566 (3550/3553b) 6955/6956
a Experimental frequency from ref 79. bComputed frequencies from ref 43. cExperimental frequency from ref 80. dExperimental ν1+ν5 combination band frequency from ref 81. eExperimental frequency from ref 82.
Computational Chemistry Comparison and Benchmark Database89 for OH (−0.833 kJ/mol) and triplet O atom (−0.933 kJ/ mol). (Explicit calculation of the spin−orbit matrix elements using MOLPRO yielded corrections within 0.02 kJ/mol of the experimental values.) (6) The contribution of higher-order coupled-cluster excitations (denoted as T(Q)−(T)) was estimated as the difference between CCSDT(Q)/cc-pVDZ and CCSD(T)/ cc-pVDZ energies. DBOC was calculated using CFOUR 1.0,90 CCSDT(Q) calculations were performed in MRCC (release date 22-Aug2013),91 and calculations for the other corrections used MOLPRO 2012.1.61
The OH stretch overtone frequencies of HO2, HOOH, conformers of HO4H, and CH3OH were computed using the Fourier Grid Hamiltonian method of Marston and BalintKurti,76 as implemented in the FGH1D program of Johnson.77 A local mode approximation78 was used for the OH stretch; the potential surface was generated by performing rigid energy scans along a single O−H bond coordinate to 30000 cm−1 above the minimum (22000 cm−1 for HO2). The reduced mass was chosen such that when spectroscopic constants (Te, ωe, ωexe) are fitted to the first four eigenstates, the harmonic frequencies ωe are equal to those obtained from harmonic frequency calculations. All energy scans were performed at CCSD(T*)-F12a/VTZ-F12. Table 7 contains the calculated OH stretch fundamental and overtone frequencies, and a comparison to literature values when available. Our method is able to reproduce the experimental overtone frequencies of HO2, HOOH, and CH3OH to within 25 cm−1, and we take this as the 2σ uncertainty in absolute overtone frequencies for HO4H. Our model predicts that for all conformers of HO4H, 2νOH will appear distinct from the overtones of molecules typically found in the HO2 self-reaction experiments: HO2, HOOH, and CH3OH.
A.2 Corrections to Thermochemistry
(1) A correction for anharmonicity was estimated using the Simple Perturbation Theory (SPT) of Truhlar and co-workers,68 which uses fundamental frequencies in the RRHO partition function rather than harmonic frequencies. Fundamental CCSD(T)/cc-pVTZ frequencies were estimated by taking the harmonic CCSD(T)/cc-pVTZ frequencies and subtracting the difference between harmonic and anharmonic frequencies at B3LYP/aug-cc-pVTZ, using vibrational perturbation theory (VPT2)92 as implemented in Gaussian 09.58 These fundamental frequencies were used to compute S and H(T) − H(0), and can be found in the Supporting Information. (2) Corrections were also applied to the entropy and integrated heat capacity to account for hindered rotors in HO4H and HOOH, using the analysis of Pitzer and Gwinn,93 as implemented in Gaussian 09.58 Parameters can be found in the Supporting Information.
4. CONCLUSIONS Our calculated Gibbs energies of dimerization, (−20.1 ± 1.8) kJ/ mol at 298.15 K and (−32.3 ± 1.7) kJ/mol at 220 K, indicate that H2O4 species are atmospherically unimportant, but may affect low-temperature laboratory studies that use elevated [HO2]. Our simulated electronic and OH-stretch overtone spectra of HO4H indicate that these bands could be used for experimental detection of HO4H.
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APPENDIX B: SPECIAL CASES The following deviations were made from the procedures described in the Theoretical Methods and Thermochemical Corrections sections: (1) The anharmonic ZPE correction for diatomic molecules (H2, O2, OH) was calculated as the difference in harmonic and anharmonic ZPE at CCSD(T*)-F12a/VTZ-F12. The anharmonic ZPE was calculated by mapping out the potential energy surface up to 1000 cm−1, then fitting to a sixth-order polynomial to obtain spectroscopic constants, using the “Diatomic” macro in MOLPRO 2012.1.61 The resulting constants were used in a standard formula to obtain the ZPE.94 (2) To reduce computational expense, the VCI calculations on H2O4 species were performed on potential energy surfaces with up to two-mode couplings (“ZPVE” macro in MOLPRO). (3) HOOH is a chiral molecule (C2 point group), and thus a racemic mixture of stereoisomers will have additional entropy of mixing. To account for this, R ln 2 was added to the ab initio entropy of HOOH. (4) The individual HO4H conformers are also chiral (C1 or C2 point group), so R ln 2 was added to their ab initio entropies to account for a racemic mixture of stereoisomers. Furthermore, the overall entropy of singlet H2O4 includes a contribution from conformational entropy, Sconf.
APPENDIX A: THERMOCHEMICAL CORRECTIONS
A.1 Corrections to Electronic Energies
In addition to the zero-point energy (ZPE) obtained from the harmonic oscillator frequencies, the following corrections were applied to the computed electronic energies: (1) Anharmonicity in the ZPE (denoted as ZPEanharm) was estimated as the difference between harmonic and anharmonic ZPE, computed at B3LYP/aug-cc-pVTZ83,84 (“B3LYP3” in MOLPRO 2012.1). Anharmonic frequencies were calculated using vibrational configuration interaction (VCI)85 up to quadruple excitations, using a potential energy surface with three-mode couplings (3M-VCISDTQ). (2) Core−valence contributions (denoted as CV) were estimated as the difference between frozen-core and corecorrelated energies at CCSD(T)/aug-cc-pwCVQZ.86 (3) Scalar relativistic effects (denoted as DKH) were estimated as the energy difference between using a fourth order Douglas− Kroll−Hess Hamiltonian and a nonrelativistic Hamiltonian, at CCSD(T)/aug-cc-pVTZ-DK.54,55,87 (4) The Diagonal Born−Oppenheimer correction (denoted as DBOC)88 was computed at CCSD/aug-cc-pVDZ. (5) Experimental corrections to account for spin−orbit splitting (denoted as SO) were taken from the NIST H
DOI: 10.1021/acs.jpca.5b04265 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Sconf = −R ∑ xi ln xi i=1
Notes
Certain commercial materials and equipment are identified in this paper in order to specify procedures completely. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified is necessarily the best available for the purpose. The authors declare no competing financial interest.
(7)
Here, R is the universal gas constant, the xi are the equilibrium relative populations of the ith H2O4 conformer (three conformers of HO4H, and (HO2)2 singlet). The xi are calculated from a Boltzmann weight of the Gibbs energies of each conformer.73 The overall Gibbs energy of singlet H2O4, ΔfGsinglets, is
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ACKNOWLEDGMENTS This research was performed while M.K.S. held and was funded by a National Research Council Research Associateship Award at the National Institute of Standards and Technology. We thank Dave Long and Yamil Simon (NIST) for helpful comments and discussions.
4
Δf Gsinglets =
∑ xiΔf Gi − TSconf i=1
(8)
(5) OH is a 2Π molecule with significant spin−orbit splitting (A = −139.2 cm−1).8 The entropy and integrated heat capacity were calculated by explicit computation of rotational energy levels up to 3500 cm−1 using the experimental spin−orbit splitting and ab initio spectroscopic constants. (6) The 3P ground state of atomic oxygen is subject to spin− orbit splitting (J = 2 at 0 cm−1, J = 1 at 158.265 cm−1, and J = 0 at 226.977 cm−1, with degeneracies g = 2J + 1).8 This spin-splitting was included in our calculation of the entropy and integrated heat capacity of atomic oxygen. (7) H2 has two nuclear spin states, ortho-hydrogen and parahydrogen (degeneracies gortho = 3 and gpara = 1).8 The entropy and integrated heat capacity were calculated by explicit computation of rotational energy levels up to 4000 cm−1 using the ab initio spectroscopic constants, assuming equilibrium between both states. (8) O2 is a 3Σg− molecule with spin−orbit splitting (λ = 1.984 cm−1, μ = −8.37 × 10−3 cm−1), and bosonic nuclear spin statistics which permit only rotational states with odd J.8 The entropy and integrated heat capacity were calculated by explicit computation of rovibrational energy levels up to 7000 cm−1 using the experimental spin−orbit splitting and ab initio spectroscopic constants.
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(1) Finlayson-Pitts, B. J.; Pitts, J. N. Chemistry of the Upper and Lower Atmosphere; Academic Press: 1999. (2) Jacob, D. J. Introduction to Atmospheric Chemistry; Princeton University Press: 1999. (3) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: 2006. (4) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. An FTIR study of the mechanism for the gas phase reaction between HO2 radicals. Chem. Phys. Lett. 1980, 73 (1), 43−46. (5) Sander, S. P.; Peterson, M.; Watson, R. T.; Patrick, R. Kinetics studies of the HO2 + HO2 and DO2 + DO2 reactions at 298 K. J. Phys. Chem. 1982, 86 (8), 1236−1240. (6) Su, F.; Calvert, J. G.; Lindley, C. R.; Uselman, W. M.; Shaw, J. H. Fourier transform infrared kinetic study of hypochlorous acid and its absolute integrated infrared band intensities. J. Phys. Chem. 1979, 83 (8), 912−920. (7) Ruscic, B. Active Thermochemical Tables (ATcT) values based on version 1.112 of the Thermochemical Network (2014). http://atct.anl. gov/index.html (accessed 5/4/2015). (8) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances, 4th ed.; Hemisphere: New York, 1989. (9) Herrmann, H. Kinetics of aqueous phase reactions relevant for atmospheric chemistry. Chem. Rev. 2003, 103 (12), 4691−4716. (10) Möller, D. Atmospheric hydrogen peroxide: Evidence for aqueous-phase formation from a historic perspective and a one-year measurement campaign. Atmos. Environ. 2009, 43 (37), 5923−5936. (11) Stone, D.; Rowley, D. M. Kinetics of the gas phase HO2 selfreaction: Effects of temperature, pressure, water and methanol vapours. Phys. Chem. Chem. Phys. 2005, 7 (10), 2156−2163. (12) Andersson, B. Y.; Cox, R. A.; Jenkin, M. E. The effect of methanol on the self reaction of HO2 radicals. Int. J. Chem. Kinet. 1988, 20 (4), 283−295. (13) Christensen, L. E.; Okumura, M.; Sander, S. P.; Salawitch, R. J.; Toon, G. C.; Sen, B.; Blavier, J. F.; Jucks, K. W. Kinetics of HO2 + HO2 → H2O2 + O2: Implications for stratospheric H2O2. Geophys. Res. Lett. 2002, 29 (9), 4. (14) Cox, R. A.; Burrows, J. P. Kinetics and mechanism of the disproportionation of HO2 in the gas phase. J. Phys. Chem. 1979, 83 (20), 2560−2568. (15) DeMore, W. B. Reaction of hydroperoxo radicals with ozone and the effect of water vapor on hydroperoxo kinetics. J. Phys. Chem. 1979, 83 (9), 1113−1118. (16) Dobis, O.; Benson, S. W. Reaction of the ethyl radical with oxygen at millitorr pressures at 243−368 K and a study of the Cl + HO2, ethyl + HO2, and HO2 + HO2 reactions. J. Am. Chem. Soc. 1993, 115 (19), 8798−8809. (17) English, A. M.; Hansen, J. C.; Szente, J. J.; Maricq, A. M. The effects of water vapor on the CH3O2 self-reaction and reaction with HO2. J. Phys. Chem. A 2008, 112 (39), 9220−9228.
ASSOCIATED CONTENT
S Supporting Information *
Derivation of 2σ uncertainties on ΔdimerG; geometries of all molecules at CCSD(T)/cc-pVTZ and CCSD(T*)-F12a/VTZF12; electronic energies; RRHO zero-point energies, entropies, and integrated heat capacities; thermochemical results at additional levels of theory (HF, B3LYP, MP2, QCISD, CCSD, CCSD(T*)-F12a, CCSD(T*)-F12b); electronic energies used to compute thermochemical corrections; electronic energies using multireference methods; fundamental vibrational frequencies used in SPT analysis; and parameters used for Pitzer/Gwinn hindered rotor analysis. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpca.5b04265.
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REFERENCES
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. Tel.: 920-403-3280. Fax: 920-403-4033. *E-mail:
[email protected]. Tel.: 301-975-2510. Fax: 301869-4020. Present Address
# M.K.S.: St. Norbert College, Department of Chemistry, Routing Number 07-3A, 100 Grant Street, De Pere, Wisconsin 54115.
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