An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (H^sub x^O^sub y^) Species

Abstract

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (H^sub x^O^sub y^) and selected recommended values for H, O, OH, H^sub 2^O, HO^sub 2^, H^sub 2^O^sub 2^, O^sub 3^, HO^sub 3^, and H^sub 2^O^sub 3^. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO^sub 3^ and H^sub 2^O^sub 3^ (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

Headnote

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (H^sub x^O^sub y^) and selected recommended values for H, O, OH, H^sub 2^O, HO^sub 2^, H^sub 2^O^sub 2^, O^sub 3^, HO^sub 3^, and H^sub 2^O^sub 3^. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO^sub 3^ and H^sub 2^O^sub 3^ (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.

Key words: ab initio thermochemistry; atomization energies; bond dissociation energies; enthalpy of formation; hydrogen-oxygen species; thermochemical network; thermodynamic properties.

Accepted: March 11, 2016

Published: March 30, 2016

http://dx.doi.org/10.6028/jres.121.005

1. Introduction

We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. Compared to uncertainties for the recommended values in the NIST-JANAF tables (1998) [1] and the thermochemical tables of Gurvich et al. (1989) [2] , the updated values are (50 to 100) times more precise for H atom, O atom, and O3, (5 to 10) times more precise for OH and HO2, and (25 to 35)% more precise for H2O and H2O2. Enthalpies of formation for the species HO3 and H2O3, which are important in atmospheric chemistry, are not found in prior thermochemical evaluations. For these species, we also provide molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions (Cp, S°, H°, and ΔfH°).

This compilation of gas phase enthalpies of formation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. We list not only recent, more precise values, but older values for archival purposes. Uncertainties (where available) are given along with the enthalpies of formation. The uncertainties listed are in general 2σ (a coverage factor of 2 having a level of confidence of approximately 95 %) [3]. Many workers did not explicitly state whether the uncertainties are 1σ (standard uncertainty) or 2σ - in these cases, we provide the uncertainties as reported.

In the tables of enthalpies of formation for each species, we also provide a column identifying the (experimental or computational) method used to derive the enthalpies of formation. A glossary for the notations used in the methods column is provided in Sec. 4. We also provide the reported values for dissociation energies, heats of reaction, appearance energies, or other quantities used to derive the enthalpy of formation. We provide these values in the original reported units. We utilized the following conversion factors: 1 kJ mol-1 ≡ 83.593472(4) cm-1, 1 eV ≡ 96.4853365(21) kJ mol-1, 1 eV ≡ 8065.544005(50) cm-1, 1 hartree ≡ 2625.49962(13) kJ mol-1, and Rydberg Constant (R∞ ) ≡ 109737.31568539(55) cm-1 taken from the CODATA values for the fundamental constants by Mohr et al. [4] and 1 kcal mol-1 = 4.184 kJ mol-1 from the NIST-JANAF tables [1].

For each of the species, we provide a table of gas phase enthalpies of formation along with a short discussion in Sec. 2.1 to Sec. 2.9. This is followed by a summary table of the selected values of the enthalpies of formation in Sec. 2.10.

Many of the values selected for the HxOy species are based on the ATcT (Active Thermochemical Tables) thermochemical network approach of Ruscic and coworkers [5-10]. We only include those ATcT values from published work and not those available only online (which have neither documentation nor references) [11, 12].

In addition to the compilation of gas phase enthalpies of formation for these hydrogen-oxygen species, in Sec. 3, we provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics. Zero point energies (ZPEs) are necessary when deriving ground state total atomization energies (ΣD0) used to compute enthalpies of formation ΔfH°(0 K) from electronic total atomization energies (ΣDe) obtained from quantum chemical calculations. In Sec. 3.1, we provide a table with vibrational frequencies, both experimental fundamental frequencies and calculated (or derived) harmonic frequencies. In Sec. 3.2, molecular geometries, vibrational frequencies, and torsional potentials for two species, HO3 and H2O3, are given, along with discussion of their use in computing thermochemical functions. In Sec. 3.3, ion reaction energetics, such as ionization energies, electron affinities, and appearance energies, are provided. These quantities are utilized to compute enthalpies of formation using thermochemical cycles involving ions.

2. Hydrogen-Oxygen Species

2.1 H Atom

Literature values for the gas phase enthalpy of formation of H atom are given in Table 1. The majority of the measurements are based on the dissociation energy of H2. The selected enthalpy of formation ΔfHo(298.15 K) for H atom is based on the H2 photoionization measurements of Liu et al. (2009) [20] and Zhang et al. (2004) [22] who determined the dissociation energy to 0.0004 cm-1 and 0.01 cm-1, respectively. These values translate to an uncertainty of on the order of less than 0.0001 kJ mol-1 in the enthalpy of formation of H atom (such a small uncertainty is not important from any practical chemical perspective). Earlier, Eyler, and Melikechi (1993) [24] measured substantially the same dissociation energy, but with a higher uncertainty of 0.04 cm-1. We select the experimentally-derived value from Zhang et al. (2004), because the higher precision value from Liu et al. (2009) is partially dependent upon quantum calculations for D0(H2+) in an ion thermochemical cycle (although the uncertainty in the theoretical component for D0(H2+) is negligible). In addition, the difference between two values is less than 0.0001 kJ mol-1 - a chemically-negligible amount. The measured value of the dissociation energy is essentially identical to that from the relativistic-corrected Born-Oppenheimer energy quantum calculations of Piszczatowski et al. (2009) [36]. Ruscic et al. (2013, 2004) [6, 9] have evaluated the enthalpy of formation for H atoms using a thermochemical network approach and recommend the same value within the uncertainty limits.

2.2 O Atom

Literature values for the gas phase enthalpy of formation of O atom are given in Table 2. The selected enthalpy of formation for O atom is largely derived from the photodissociation measurements of O2 [arrow right] O(3P) + O(1D) by Gibson et al. (1991) [54] and Lewis et al. (1985) [55]. The singlet excited O(1D2) state produced in the reaction is 15867.862 cm-1 (189.82178 kJ mol-1) above the ground state O(3P2) oxygen atom [51]. A weighted average of the results from the photodissociation measurements shown in the table yields a value ΔfHo(298.15 K) = 249.225 ± 0.005 kJ mol-1, while the thermochemical network evaluation of Ruscic et al. (2013) [9] provides a value of 249.229 ± 0.002 kJ mol-1 with a slightly lower uncertainty. Ruscic et al. corrected the bond dissociation energies reported by others to the lowest rovibrational level of O2, and we select the recommended (and corrected) value from Ruscic et al.

Values from the quantum chemical calculations of Feller et al. (2014) [62] and Bytautas et al. (2010) [64] are in excellent agreement with the experimental enthalpy of formation of O atom (within about 0.2 kJ mol-1). Please note that in order to derive the enthalpy of formation from the calculated dissociation energies of De = 42030.1 cm-1 from both Feller et al. and Bytautas et al., we used the experimentallyderived ZPE of 787.4 cm-1 (see Sec. 3.1) rather than the computed anharmonic ZPEs that were used in those studies.

2.3 OH (hydroxyl radical)

The selected value of the gas phase enthalpy of formation of OH is derived from the experimental work of Boyarkin et al. (2013) [76] and Maksyutenko et al. (2006) [77] who both directly measured the dissociation energy of water by determining the onset of the dissociative continuum D0(HO-H) = 41145.9(0.1) cm-1. Ruscic et al. (2014) [9] have evaluated the enthalpy of formation for OH using a thermochemical network approach using these two measurements and other input data and recommend a value that is within the uncertainties of the direct experimental determinations.

The selected value is in excellent agreement with the high level quantum calculations of Boyarkin et al. (2013) [76] (within 8 cm-1 or 0.1 kJ mol-1 - the estimated uncertainty in the calculations). The range of other quantum calculations given in Table 3 are almost as good, providing values within about 0.3 kJ mol-1 of the selected value.

2.4 H2O (water)

The gas phase enthalpy of formation of H2O (water) is largely based on the combustion measurements of liquid water by Rossini (1939) [102-104] decades ago. The gas phase enthalpy of formation was computed using the heat of vaporization for water (see Rossini). Ruscic and coworkers [6, 9, 100] included H2O in thermochemical network evaluations (ATcT) - and the most recent ATcT value differs by only about 0.04 kJ mol-1 from the original value of Rossini (on the order of the uncertainty in the measurement). We select the slightly more precise recommended value from the thermochemical network approach of Ruscic et al. The high level quantum chemical calculations of Feller et al. [92] are in excellent agreement with the experimentally-derived value (within about 0.04 kJ mol-1). All available literature values for the gas phase enthalpy of formation of H2O are given in Table 4.

2.5 HO2 (hydroperoxyl radical)

We have selected the gas phase enthalpy of formation for HO2 from the Active Thermochemical Tables (ATcT) work of Ruscic et al. (2006) [73], but with a slightly higher uncertainty. Our rationale for assigning a higher uncertainty is as follows. The neutral and ion reaction energetics available to derive the enthalpy of formation for HO2 as compiled in Table 5 all have uncertainties of about (1.5 to 2.5) kJ mol-1 (much higher than the 0.25 kJ mol-1 assigned by Ruscic et al.), while the quantum chemical calculations have (reported) uncertainties of about (0.3 to 0.8) kJ mol-1. Thus, the ATcT value and its uncertainty are strongly influenced by theoretical values. Additionally, the enthalpies of formation from quantum calculations are dependent upon computed ZPEs (zero point energies) and there is about a 16 cm-1 (0.2 kJ mol-1) uncertainty in computing anharmonic ZPEs (see Sec. 3). Although enthalpies of formation from the quantum calculations are much more precise than those derived from experimental measurements, we suggest a higher uncertainty (0.35 kJ mol-1) than assigned by Ruscic et al. considering the factors above. We do not recommend use of the value from the thermochemical network approach of Ganyecz et al. (2015), because of the limited data used in their thermochemical network and their value is substantially inconsistent with most experimentally-derived and calculated values.

2.6 H2O2 (hydrogen peroxide)

As shown in Table 6, there are only two relatively direct measurements leading to a value for the gas phase enthalpy of formation of H2O2 - the calorimetry measurement of Giguere (1955) [140] and the D0(O-O) dissociation energy of Luo et al. (1992) [138]. We have selected the inherently more precise spectroscopic value from Luo et al., but assigned a higher uncertainty of 0.16 kJ mol-1 in consideration of the (0.33 kJ mol-1) range of recommended values by Ganyecz et al. (2015) [71], Ruscic (2013) [134], Ruscic (2010) [72], and Ruscic et al. (2006) [73]. In the ATcT evaluations by Ruscic and coworkers, there are no details given on either the reactions used to compute the enthalpy of formation of H2O2 or why the two ATcT values differ outside their uncertainties.

The enthalpies of formation derived from quantum chemical calculations are within about 1.0 kJ mol-1 of the selected value. These values depend upon the zero point energy (ZPE) of the molecule and different anharmonic corrections were computed. In Sec. 3.1 "Zero Point Energies and Vibrational Frequencies," we show that the computed anharmonic ZPEs have an apparent uncertainty of about 0.4 kJ mol-1 and this may contribute to part of the difference between the computed and experimentally-derived values.

2.7 O3 (ozone)

The selected gas phase enthalpy of formation for O3 (ozone) is taken from Ruscic et al. (2004) [6] which is largely based on the photofragment excitation measurements of Masumi and coworkers (1997, 1999) [149, 150]. The other experimental determinations shown in Table 7 are in good agreement with this value within their stated uncertainties. Ruscic et al., in a thermochemical network evaluation, corrected the bond dissociation energies of Masumi and coworkers to the lowest rotational (J=0) level for the O2 products - changing the computed enthalpy of formation by about 0.15 kJ mol-1. The quantum chemical calculations of Dixon and coworkers (2008, 2009) [89, 92] are within about 0.1±1.6 kJ mol-1 of the recommended value - excellent, and likely fortuitous, agreement given the unpaired electrons in ozone (multiconfigurational character causes problems for single reference methods).

2.8 HO3 (hydrotrioxyl radical)

HO3 has been termed an "elusive" radical [160, 164, 167, 169] with regard to detection, molecular structure, vibrational frequencies, and enthalpy of formation - from both experimental and theoretical points of view. The first measurement of its gas phase enthalpy of formation was derived indirectly from correlations in electron transfer efficiencies of the positive ion HO3+ with the ionization energies of a series of neutral electron donors by Speranza (1996) [165]. This value had a very high uncertainty (about 20 kJ mol-1). Subsequent high level quantum chemical calculations, however, put the enthalpy of formation on the order of (20 to 40) kJ mol-1 higher - and the quantum calculations showed a wide spread (see Table 8). Thus, the experimental value from Speranza was much lower (about 25 kJ mol-1) than the currently accepted value and the theoretical values were much higher (about (10 to 15) kJ mol-1) than the currently accepted value.

More recently, Lester and coworkers [161-164] measured the vibrational predissociation of HO3 putting an upper limit on its bond dissociation energy D0(HO-OO) moving the estimate for the enthalpy of formation upward by about (10 to 15) kJ mol-1. In 2010, Le Picard et al. [160], using a spectroscopic kinetic/equilibrium measurement at low temperatures (87 K to 100 K), determined the bond dissociation energy (D0) relatively precisely (reportedly within about 0.5 kJ mol-1) and thus, pinned down the enthalpy of formation of HO3 with an acceptable level of uncertainty. Beames et al. (2011) [158] have since revised the dissociation energy D0 from Le Picard et al. measurements by treating the torsional potential correctly in computing thermochemical functions [156] (see also Sec. 3.2.1). Since then there have been a number of high level quantum chemical calculations that confirmed the experimentally-derived value to within about (2 to 3) kJ mol-1. The earlier "high" enthalpies of formation from theory were because of the inability of the single reference methods employed to properly treat HO3 due to significant spin contamination and the multi-reference character of the wavefunctions (see discussion in references in Table 8). With the use of multi-reference configuration interaction methods and other treatments this problem was apparently solved. Thus, both the experimental and quantum chemical methods have converged to similar values for the enthalpy of formation of HO3.

We selected an enthalpy of formation using the revised D0 from Beames et al. and using a thermal correction from an enthalpy H° calculated treating the molecule as a rigid rotor harmonic oscillator (RRHO), plus using the scaled torsional potential of Beames et al. to compute the contribution of the hindered rotor (see Sec. 3.2.1 for more details). We also increased slightly the uncertainty assigned by Beames et al. (from 0.5 kJ mol-1 to 0.6 kJ mol-1) to reflect the uncertainty (est. 0.3 kJ mol-1) in the contribution of the torsion to the free energy (considering uncertainties in both enthalpy H° and entropy S°).

We note that the quantum chemical calculations used a wide range of ZPEs (about 500 cm-1 ≡ 6 kJ mol-1) and this contributes to some of the spread in the theoretical values (see Sec. 3.1 and Table 11). In Table 11, we suggest the use of the ZPE from Grant et al. (2009) [89], which is an average of experimental fundamental and computed harmonic frequencies.

2.9 H2O3 (hydrogen trioxide)

There are no experimental determinations for the gas phase enthalpy of formation of H2O3. Hence, we have selected an enthalpy of formation based on the high level ab initio calculations of Grant et al. (2009) [89]. We have assigned an estimated (liberal) uncertainty of 1.2 kJ mol-1 considering the uncertainties in the quantum chemical calculations (see Table 9 for the range of computed values), zero point energies, and the contribution to the enthalpy from the torsions. We have corrected the Grant et al. value slightly using the anharmonic ZPE computed by Hollman and Schaefer (2012) [200] and treating the torsions as hindered rotors (Grant et al. treated them as vibrations). These corrections increased the ZPE (and ΔfH° at 0 K) by about 0.5 J/mol and the enthalpy H°(298.15 K) by about 0.3 kJ mol-1 for an increase in ΔfH°(298.15 K) of about 0.8 kJ mol-1 relative to value provided by Grant et al. (There is also a substantial change in entropy S° and thus, in free energy ΔfG° and the equilibrium constant/stability of H2O3). See Sec. 3.2.2 for more details.

2.10 Summary of Selected Values for Gas Phase Enthalpies of Formation

Table 10 is a summary of the selected values for the gas phase enthalpies of formation for each hydrogen-oxygen HxOy species as outlined in previous sections.

The gas phase enthalpies of formation of H atom, O atom, OH, H2O, and O3 have uncertainties of less than 0.1 kJ mol-1. Compared to uncertainties associated with the values in the JANAF [1] and Gurvich et al. [2] thermochemical tables, the updated values in Table 10 are (50-100) times more precise for H atom, O atom, and O3 and about 7 times more precise for OH. The precision for H2O is only slightly better (about 33 %). For all of these species (except O3), the values from quantum chemical calculations also agree to within 0.1 kJ mol-1. In the case of ozone (O3), the quantum chemical calculations agree to within the uncertainty of the calculations (estimated at 1.6 kJ mol-1). This is excellent, and likely fortuitously, agreement given the unpaired electrons in ozone (requiring multiconfigurational calculational approaches).

The gas phase enthalpy of formation of H2O2 is also known relatively well (to less than 0.2 kJ mol-1) being derived largely from a spectroscopic measurement of the D0(HO-OH) dissociation energy (with a precision of about 3 cm-1). The precision is only slightly better (about 25 %) compared to values in the JANAF and Gurvich thermochemical tables which are largely based on the calorimetric measurements of decades ago for the decomposition of H2O2 by Matheson and Maas (1929) [142] and Giguere et al. (1955) [140].

The uncertainty in the gas phase enthalpy of formation for hydroperoxyl radical HO2 is somewhat larger - about 0.4 kJ mol-1. The energies of neutral and ion reactions involving HO2 have uncertainties of about (1.5 to 2.5) kJ mol-1, while high level quantum chemical calculations have (estimated) uncertainties of about (0.2 to 0.4) kJ mol-1. The selected value for the enthalpy of formation for HO2 is now about 10 times more precise than the values in the JANAF and Gurvich et al. thermochemical tables.

The gas phase enthalpies of formation of the HO3 radical and for H2O3, which are important species in atmospheric chemistry, are not found in prior evaluation. We provide recommended values here, as well as supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials for these species in Sec. 3.2. These data can be used to compute thermochemical functions (Cp, S°, H°, and ΔfH°) for these species.

For many years, the enthalpy of formation of the HO3 radical was elusive both from an experimental and theoretical point of view. The experimental values were "too low" by (10 to 20) kJ mol-1 (compared to the now accepted value), while the theoretical values were "too high" by (10 to 15) kJ mol-1. In the last 5 years (since 2010), both the experimental and quantum chemical methods converged to similar values - the experimental value (derived from a spectroscopic kinetic/equilibrium measurement) has an uncertainty of about (0.5 to 0.8) kJ mol-1 and the quantum chemical values are known to about (2 to 3) kJ mol-1.

There are no experimental measurements for the enthalpy of formation of H2O3. However, different high level quantum chemical methods predict similar values. We assigned a liberal (and estimated) uncertainty of about 1.2 kJ mol-1 to the selected value considering the uncertainties in the contribution of the torsions to the enthalpy H°, zero point energy (ZPE), and the quantum chemical calculations.

3. Supplementary Data

3.1 Zero Point Energies and Vibrational Frequencies

Table 11 and Table 12 provide zero point energies (ZPEs) and vibrational frequencies, respectively, for the hydrogen-oxygen species. ZPEs are necessary for correcting electronic total atomization energies ΣDe to ground state total atomization energies ΣD0 (at T=0 K). The ZPEs are derived from vibrational frequencies including anharmonic terms.

The zero point energies (ZPEs) given in cm-1 (standard spectroscopic units) for the hydrogen-oxygen species are given in Table 11. For the selected values, the ZPEs in kJ mol-1 are given, along with uncertainties (2σ) (in parenthesis). The ZPEs for the diatomics H2, O2, and OH come from the review and analysis by Irikura [193, 194] and that for H2O from the evaluation by Irikura et al. [195]. These ZPEs for H2, O2, OH, and H2O are derived from experimental spectroscopic constants.

The ZPEs compiled in Table 11 used by different workers consist of a mix from experimental fundamental frequencies, computed harmonic frequencies, scaled computed harmonic frequencies (equivalent to fundamental frequencies), and averages of the harmonic and anharmonic frequencies (a relatively good approximation). In some cases anharmonic ZPEs were computed (more accurately) using the vibrational configuration interaction (VCI) [188] or second-order vibrational perturbation theory (VPT2) [189] methods. Some discussion regarding uncertainties in computed ZPEs can be found in work by Barone (2004) [190], Irikura et al. (2009) [195], Kesharwanti et al. (2015) [191], and references contained therein.

For each species in Table 11, for reference purposes, we have also provided ZPEs computed directly from the experimental fundamental frequencies (ZPEf = ½Σνi) and from the computed harmonic frequencies (ZPEh = ½Σωe). We have also computed an empirical estimate of anharmonic ZPEs using the relationship ZPEemp = (1/2)(ZPEh+ZPEf) + (1/8)(ZPEh-ZPEf) (the average of harmonic and anharmonic frequencies plus a correction) from the work of Csonka et al. (2005) [192] who found that the anharmonic ZPEs for a series of polyatomic molecules obeyed this relationship to about 7 cm-1 (0.08 kJ mol-1). We have used these values to screen our selected ZPE values and find a MAD (mean absolute deviation) of about 11 cm-1 (0.13 kJ mol-1) for this set of molecules - consistent with that estimated by Csonka et al.

Table 12 provides vibrational frequencies for the species. The first line for each species lists the experimental fundamental frequencies (ν) for that species [note: the ν2 mode of HO3 is the only mode derived from a quantum calculation]. The second line for each species lists the harmonic frequencies (ωe) for that species. For most of these species the harmonic frequencies are derived from experimental spectroscopic rotational-vibrational lines, while for H2O2, HO3, and H2O3 the harmonic frequencies are derived from ab initio calculations.

Experimental values for the vibrational frequencies for HO2 and H2O2 can be found in the review by Jacox [206, 207]. There is a single high resolution measurement of the vibrational frequencies of H2O3 by Engdahl and Nelander [219]. Much earlier, Arnau and Giguere [208] measured ν3, ν4, and ν8 for H2O3 at 857,400, and 755 cm-1, respectively - about a 21 cm-1 mean deviation from the values of Engdahl and Nelander.

There is some uncertainty in the vibrational modes (and thus in computed ZPEs) for two of the molecules - H2O2 and HO3.

The torsion potential in H2O2 is a double well with two torsional frequencies 371 cm-1 (ungerade) and 255 cm-1 (gerade). For the other modes, there is good agreement between the computed anharmonic frequencies and the observed fundamental frequencies (mean absolute deviation of 11 cm-1). For the torsional mode, however, there is a discrepancy where the computed anharmonic and harmonic frequencies are 316 cm-1 and 380 cm-1, respectively. That is, the harmonic frequency is comparable to the fundamental frequency (9 cm-1 higher) when one might expect it to be (20 to 35) cm-1 higher. In addition, the computed anharmonic frequency is substantially different than the measured fundamental frequency. See Sec. 3.2.2 for more discussion.

The torsional potential in HO3 is a double well with a cis form about (0.9 to 1.2) kJ mol-1 less stable than trans form and a trans-to-cis barrier of about (3 to 4) kJ mol-1 - or ΔE=(75 to 100) cm-1 and V=(250 to 330) cm-1, respectively. Beames et al. (2011) [158] have computed the torsional potential. The experimental torsional frequency for the trans form is 129 cm-1 and the computed value for the cis form is slightly lower at 122 cm-1. Accurate representation of this torsional potential is necessary to properly compute the thermochemical functions (particularly the entropy) at low temperatures (100 to 300) K which are relevant to atmospheric chemistry. See Sec. 3.2.1 for more discussion.

3.2 Supplementary Data for HO3 and H2O3

In this section, we provide and discuss supplementary data for HO3 and H2O3 consisting of molecular geometries, vibrational frequencies, and torsional potentials. These data are not provided in prior evaluations and can be used to compute thermochemical functions (Cp, S°, H°, and ΔfH°). Both HO3 and H2O3 are important species in atmospheric chemistry. HO3 is considered to be a key intermediate, but is difficult to detect.

3.2.1 Data for HO3

Suma et al. (2005) [177] derived a molecular geometry for HO3 from rotational spectra yielding r0(OO*)=1.225 Å, r0(OO)=1.688 Å, θ0(OOO)=111.02°, r0(OH)=0.972 Å, and θ0(OOH)=90.04° for the trans (most stable) form assuming a planar geometry. More recently, McCarthy et al. (2012) [221] similarly derived a molecular structure and found r0(OO*)=1.235(4) Å, r0(OO)=1.684(3) Å, θ0(OOO)=110.7(3)°, r0(OH)=0.913(26) Å, and θ0(OOH)=92.4(14)°. Their measured rotational constants correspond to moments of inertia {Ia,Ib,Ic} = {57.76, 50.60, 7.140} amu Å2 or {9.59, 8.40, 1.186}x10-46 kg m2 in SI units. We utilize the molecular structure from the work of McCarthy et al. We note that later Suma et al. (2013) [204] derived values for equilibrium structure (re, θe) using the isotopic rotational constants from their earlier work and that of McCarthy et al. plus theoretically-derived vibration-rotation interaction constants.

Experimental vibrational frequencies for HO3 come from the work of Derro et al. (2008) [218] except they did not observe ν2. Anglada et al. (2010) [141] computed harmonic vibrational frequencies using the CASSCF(19,15) level of theory. In this work, we used a scaled harmonic ν2 from Anglada (see vibrational frequencies table in Sec. 3.1). The experimental fundamental and computed harmonic vibrational frequencies are given in Table 12.

The most stable form of HO3 is a trans geometry. A number of workers have computed the difference in energy between the cis and trans forms. Braams and Yu (2008) [146] using the density functional method (DFT) HCTH computed that the cis form was 4.6 kJ mol-1 higher with barrier-to-rotation of 8.8 kJ mol-1. Beames et al. (2011) [158] using the EOMIP-CCSD/ANO method computed a torsional potential where the cis form was about 49 cm-1 (0.59 kJ mol-1) higher and there was a trans-to-cis classical barrier-to-rotation of 255 cm-1 (3.05 kJ mol-1). They utilized a scaling factor of 1.35 with the ab initio potential to produce a torsional potential of 132 cm-1 that roughly agrees with the experimental torsional frequency of 129 cm-1. Varandas (2012, 2011) [143, 222] using CCSD(T) and MRCI-Q methods with cc-pVnZ basis sets extrapolated to the complete basis set limit and including higher order corrections calculated the cis form to be (0.5 to 0.6) kJ/mol higher with a barrier-to-rotation of about (3.3 to 4.8) kJ mol-1. Although Varandas computed the torsional potential as a function of torsional angle, unfortunately it is not provided in numerical form for use by others. Hoy et al. (2013) [223] using the 2-RDM density functional method computed that cis-HO3 was about 7.4 kJ mol-1 higher with a barrier-torotation of about 8.5 kJ mol-1 (only slightly higher than the cis form).

We recommend using the scaled torsional potential of Beames et al. (2011) [158] to compute thermochemical functions for HO3 (treating the rest of the molecule as a rigid rotor harmonic oscillator). In our work, RRHO calculations were performed using the program ChemRate [224] and hindered rotor thermochemical functions were computed using the program FGH1D (Fourier Grid Hamiltonian 1-D) [225]. We suggest employing a rotational constant of B=22.93 cm-1 to generate a hindered rotor with a trans form with torsional frequency of 129 cm-1 and a cis form that was 84 cm-1 higher with a torsional frequency of 146 cm-1. We also computed thermochemical functions for the hindered rotor using a simpler analytical torsional potential employing Vncos(nθ) terms with V1=54 cm-1 and V2=257 cm-1. This torsional potential gives a classical barrier of 288 cm-1 with the cis form at 49 cm-1 (0.6 kJ mol-1) relative to the trans form and a torsional frequency of 129 cm-1 (we used a rotational constant of B=22.93 cm-1 from the molecular geometry). We found small differences in the thermochemical functions relative to that computed using the scaled torsional potential of Beames et al.: entropies S° differing by about 0.1-0.4 J mol-1 K-1 and enthalpies H° differing by 0.2-0.4 kJ mol-1 at temperatures of 300 K to 1000 K.

3.2.2 Data for H2O3

Suma et al. (2005) [226] derived a molecular geometry for H2O3 from rotational transitions yielding r0(OO)=1.428 Å, θ0(OOO)=107.0°, r0 (OH)=0.963 Å, θ0(OOH)=101.1°, and [straight phi]0(OOOH)=81.8°. This structure was derived from rotational constants Ba=1.706 cm-1, Bb=0.351 cm-1, and Bc=0.312 cm-1. These correspond to moments of inertia {Ia,Ib,Ic} = {9.88, 47.28, 54.02} amu Å2 or {1.64, 7.85, 8.97}x10-46 kg m2 in SI units. By comparing the measured rotational constants to those derived from structures from their ab initio calculations, they determined that the trans form was more stable than the cis form. We note that the first molecular structures for H2O3 calculated by Blint and Newton (1973) [227] and Cremer (1978) [228] using quantum chemical methods are in fairly good agreement with those experimentally determined by Suma et al.

Engdahl and Nelander [219] measured all of the vibrational frequencies for H2O3 (see Table 12). Earlier, Arnau and Giguere (1974) [208] measured three frequencies: ν3, ν4, and ν8. Hollman and Schaefer (2012) [200] computed anharmonic and harmonic frequencies (the latter are given in Table 12). Jackel (1993) [205] has also computed harmonic frequencies.

The most stable rotational conformer of H2O3 is a trans form. Su et al. (2002) [229] calculated the cis form to be 10.0 kJ mol-1 higher a barrier-to-isomerization of 21.8 kJ mol-1. We note that the first quantum chemical calculations (MP2) of the rotational potential of this molecule were done by Cremer (1978) [228] and predicted the cis form to be about 15.9 kJ mol-1 less stable and that there was a very high barrier-toisomerization of 46.4 kJ mol-1.

To compute thermochemical functions for H2O3, we recommend treating the molecule as a rigid rotor harmonic oscillator (RRHO) with the two torsions treated as hindered rotors, and employing the molecular structure of Suma et al. and the vibrational frequencies of Engdahl and Nelander.

We note that in order to correctly compute the hindered rotor partition functions one would need to treat them as two coupled rotors and account for the difference between the trans and cis forms. This is a difficult problem that we cannot solve here. We have treated it as the sum of two identical 1-D rotors. We estimated the uncertainty in the free energy G°(298.15 K) to be about 0.3 kJ mol-1 to account for this approximate treatment (considering uncertainties in both enthalpy H° and entropy S°).

Using the FGH1D program [225], we reproduced the cis-trans energy difference and barrier-to-rotation of 10.0 kJ mol-1 (836 cm-1) and 22.1 kJ mol-1 (1847 cm-1), respectively, using Vncos(nθ) functions with V1=860 cm-1 and V2=1580 cm-1 employing a rotational constant of B=21.09 cm-1 (from the molecular structure). This yielded fundamental frequencies for the trans and cis conformers of 369 cm-1 and 313 cm-1. This frequency for the trans conformer is very close to the average of the symmetric torsional (v9=346 cm-1) and asymmetric torsional modes (v8=387 cm-1).

The enthalpy of formation that we selected for H2O3 was derived from the quantum chemical calculations of Grant et al. (2009) [89] (there are no experimental measurements). We have corrected their value slightly using the anharmonic ZPE computed by Hollman and Schaefer (2012) [200] and treated the torsions as hindered rotors (Grant et al. treated them as vibrations). They used a ZPE of 6474 cm-1 (see Table 11) based on an average of the experimental fundamental frequencies (ν) and computed harmonic frequencies (ωe). We have employed the anharmonic ZPE of 6514 cm-1 computed by Hollman and Schaefer (a difference of +0.47 kJ mol-1) and our computed enthalpy H° of 13.00 kJ mol-1 (a difference of +0.45 kJ mol-1).

Xu and Goddard (2002) [181] reported on a chemical mechanism for the formation of H2O3 from H2 + O3 based on quantum chemical calculations [229] and analysis of experimental data from Engdahl and Nelander (2002) [219] and Goddard and coworkers (2001,2002) [229-231]. They found that the reaction H2O2 + O3 [arrow right] H2O3 + O2 occurs via a set of complex reactions with ring intermediates. The barrier-toaddition of O3 to H2O2 to form an OOOH-OOH adduct is about 6.3 kJ mol-1 and the reaction overall to form H2O3 is about 135 kJ mol-1 exothermic. H2O3 is formed in a cis configuration (from decomposition of a ring). They calculated that cis form was about 10.0 kJ mol-1 (836 cm-1) higher in energy than the trans form and that the barrier-to-isomerization from trans-to-cis was about 22.1 kJ mol-1 (1847 cm-1).

Goddard and coworkers calculated vibrational frequencies for H2O3 both cis and trans using the B3LYP/6-31G** method. They found excellent agreement between the experimental values of Engdahl and Nelander using average scaling factor (expt/theory) of 0.985. The vibrational frequencies of the cis form in general were very similar to the trans form differing by about (0.5 to 1)%. However, the symmetric torsion ν9 for the cis form was 190 cm-1 or much lower than the experimental and calculated values of 346 cm-1 and 347 cm-1, respectively. The ratio of the experimental asymmetric torsion ν8 (387 cm-1) to the symmetric torsion ν9 (346 cm-1) of 1.12 is consistent with slightly different (20 %) rotational constants for the two (opposite) modes on the same potential energy surface. The very low calculated symmetric torsion ν9 for the cis form implies that the two motions are highly coupled (energetically) and that use of a simple 1-D torsion potential energy surface is not fully adequate.

3.3 Ion Energetics

In Table 13, ion reaction energetics, such as ionization energies, electron affinities, and appearance energies, are provided, along with uncertainties. These quantities are utilized to compute enthalpies of formation for a number of the hydrogen-oxygen species using thermochemical cycles involving ion processes. This compilation is of the most precise values available (not all reported values are included). The values are given both in their original reported units and converted to kJ mol-1. The conversion factors employed are given in Sec. 1 "Introduction."

4. Glossary

Notations, acronyms, and abbreviations referred to in this work are provided in Table 14 along with a short description for each. References are also provided for the quantum chemical methods for more information.

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