High-Accuracy Theoretical Thermochemistry of Atmospherically

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High-Accuracy Theoretical Thermochemistry of Atmospherically Important Nitrogen Oxide Derivatives Peter Szakacs,* Jozsef Csontos, Sanghamitra Das, and Mihaly Kallay Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Budapest P.O. Box 91, H-1521 Hungary

bS Supporting Information ABSTRACT: High-accuracy quantum chemical calculations were performed for several atmospherically important nitrogen oxide derivatives, such as HOONO, HOONO2, NH2NO2, FNO, FNO2, FONO, FONO2, ClNO, ClONO, ClONO2, and ClOONO. The stable conformers of the molecules were identified, and the corresponding heats of formation (ΔfH0° and ΔfH298°) and entropy values (S298°) were computed. On the basis of the thermodynamic functions, equilibrium constants were also calculated for a couple of reactions with importance in the chemistry of the atmosphere. In a number of cases this study provides more reliable estimates for the investigated thermodynamic properties than those can be collected from previous reports.

’ INTRODUCTION Because of their direct link to vital global issues like climate change1,2 and ozone depletion3,4 atmospherically important molecules have received a great deal of publicity during the last decades. Since climate change and global warming are menacing problems of our age, the understanding and the accurate evaluation of the underlying thermochemical processes are crucial. It is well-known that nitrogen oxides and nitrogen oxide derivatives play a significant role in the chemistry of the atmosphere.57 The families of XNO and XNO2 molecules (X = F, Cl) are known to be degradation products of hydrohalocarbons. These molecules are easily photolyzed in the atmosphere yielding radicals that have a significant role in ozone depletion.8 On the other hand, CF3O radicals, which catalyze the ozone depletion cycles, can be degraded via the reaction CF3O þ NO = CF2O þ FNO too.9 FNO also arises as a result of the 2NO þ F2 = 2FNO reaction.10 The reaction of FO and NO was reported to come off through the trans-FONO intermediate, which then isomerizes to FNO2.11 The inorganic nitrates, XONO2, as well as XONO molecules (X = H, F, Cl) also play an important role in the chemistry of the stratosphere. The recombination of OH and NO2 radicals may come to pass as OH þ NO2 þ M = HONO2 þ M or OH þ NO2 þ M = HOONO þ M.12Analogously, the reaction of ClO and NO2 species may yield ClONO2 or ClOONO. These products act as a temporary reservoir of HO, ClO, and NO2 radicals, which are catalysts of O3 degradation cycles.13 Peroxynitric acid, HOONO2, is an effectual oxidant in the troposphere, although it exists only in low concentration. It r 2011 American Chemical Society

springs up and degrades via the HO2 þ NO2 H HOONO2 reaction,14 and consequently, it is a significant reservoir for both the HO2 and NO2 species. It also plays a fundamental role in the development of photochemical smog and in the formation of ozone in the upper troposphere.15,16 Although numerous studies have been carried out to determine the essential thermochemical properties of these molecules, large uncertainties in the values and deviations among the available data in relevant databases, such as NIST-JANAF,17 JPL,18 and the Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion,19 still exist. The lack of accurate and consistent data can be anticipated because the experimental investigation of reactive species is usually challenging. Nevertheless, due to the constant and rapid development of algorithms and hardware architecture, theoretical model chemistries2033 have became a powerful tool providing accurate thermochemical quantities, and nowadays, the reliability of the rigorous model chemistries is comparable with that of sophisticated cutting-edge experiments .27,31,3441 Previously the heats of formation and entropies of several fluorinated and chlorinated methane derivatives42 as well as formaldehyde derivatives43 have been determined accurately by some of us. In this study high-accuracy theoretical heat of formation and entropy values are presented for various atmospherically important nitrogen-oxide derivatives. Furthermore, a couple of reactions which play a crucial Received: December 21, 2010 Revised: February 23, 2011 Published: March 23, 2011 3144

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The Journal of Physical Chemistry A

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role in the atmosphere and involve the selected molecules are also investigated, and accurate reaction heats, reaction entropies, reaction Gibbs energies, and equilibrium constants are provided.

’ THEORETICAL METHODS The theoretical approach used in this study was proven to provide accurate thermodynamic functions including heats of formation at 0 and 298 K as well as standard entropies.42 The details of the approach can be found in ref 42; nevertheless, a brief outline of the utilized calculations is given in the following. The equilibrium geometries of the molecules were determined at the CCSD(T)/cc-pVQZ level. The total energies of the molecules were calculated, assuming the additivity of the various contributions, according to the following scheme E ¼ EHF þ ΔECCSDðTÞ þ ΔECCSDT þ ΔECCSDTðQ Þ þ ΔEcore þ ΔEZPE þ ΔEDBOC þ ΔEREL

ð1Þ

EHF is the basis set limit HartreeFock energy extrapolated44 from aug-cc-pCV(T,Q,5)Z energies. ΔECCSD(T) is the correlation energy calculated by CCSD(T) method using the frozen core approximation and extrapolated45 to the basis set limit using aug-cc-pV(Q,5)Z results. ΔECCSDT = ECCSDT ECCSD(T) and ΔECCSDT(Q) = ECCSDT(Q) ECCSDT are obtained with the cc-pVTZ and cc-pVDZ basis sets, respectively. ΔEcore, which is defined as the energy difference between the all electron and frozen-core approximation, was calculated with the CCSD(T) method extrapolating the ccpCVTZ and cc-pCVQZ basis set results.45 The zero-point vibrational energy, ΔEZPE, is calculated relying on vibrational perturbation theory46 using the CCSD(T) method with the cc-pVTZ basis set. The diagonal BornOppenheimer correction47 (ΔEDBOC) was calculated at the CCSD/cc-pCVTZ level. The relativistic contributions (ΔEREL) were taken into account by evaluating the expectation value of the mass-velocity and one- and two-electron Darwin operators at the CCSD(T)/cc-pCVTZ level. CCSDT(Q) calculations were carried out with the MRCC suite of quantum chemical programs49 interfaced to the CFOUR package,50 while all other calculations came from CFOUR. Standard enthalpies (HT°) and entropies (ST°) were computed at T = 0 and 298.15 K at pressure of 1 bar via the standard formulas of statistical thermodynamics (STD) within the ideal gas approximation.51 For the rotational and vibrational degrees of freedom the rigid-rotor, harmonic oscillator (RRHO) approximation was invoked. For species with separable internal rotation a one-dimensional hindered rotor model5257 was used. The potential energy surface (PES) for the rotation was determined by a relaxed systematic scan, i.e., the appropriate torsional angle was changed by 15° increments, and the obtained conformations were partially optimized keeping the torsional angle fixed. The Fourier grid Hamiltonian method of Marston and Balint-Kurti58,59 was implemented and the one-dimensional Schr€odinger equation p2 d 2 ψ þ V ðθÞψ ¼ Eψ 2Ir dθ2 was solved, where Ir and V(θ) are the reduced moment of inertia and the potential for the rotating top, respectively. To obtain an analytical form for V(θ), it was expanded in a 6-term Fourier series 6

V ðθÞ ¼

∑ pi ð1 cosðiθÞÞ i¼1

Furthermore, Ir was calculated using the frequency scheme as described previously,60,61 and its dependence on θ was neglected. The partition function for the hindered rotor, which was obtained by direct eigenvalue summation, was used to correct the ZPE, entropy, and thermal correction values. To obtain the heats of formation from the calculated enthalpies the elemental reaction approach was used.31 The reference state of the elements were defined as it is standard in thermochemistry. The errors introduced by the various approximations were also investigated thoroughly in ref 42. It was found, by comparison to accurate experimental or theoretical data, that for firstrow molecules the root-mean-square (rms) deviation was 0.51 kJ/mol with a maximum error of 1.06 kJ/mol, and for molecules containing chlorine atoms the corresponding errors were 2.10 and 4.54 kJ/mol, respectively. To define an error estimate, which depends on the size of the molecular system the rms deviations were recalculated on a per-atom basis, and 0.20 kJ/mol as well as 0.75 kJ/mol were obtained for first-row and chlorine atoms, respectively. Consequently, the 95% confidence limit for a given species was estimated as twice the above rms values, i.e., for every first-row atom 0.4 kJ/mol and for every chlorine atom 1.5 kJ/mol was taken as uncertainty and then these uncertainties were summed. Accordingly, the error bar, e.g., for the ΔfH°(ClONO T 2) values can be estimated as 1.5 kJ/mol þ 4 0.4 kJ/mol = 3.1 kJ/mol. On the basis of a statistical analysis of a benchmark set of 15 molecules and radicals the current protocol yielded a rms deviation of 0.6 J/K 3 mol against accurate entropy values in ref 42. Thus, our conservative estimate is 1.5 J/K 3 mol for the error associated with our entropy data. Nevertheless, to further test the validity of the above error estimates we collected the nitrogen oxides and NO derivatives for which accurate data are available and calculated the corresponding thermochemical properties. These molecules include NO, HNO, and NO2. For ΔfH0°(NO), ΔfH°298(NO), and S°298 (NO) our approach yielded 90.0 ( 0.8 kJ/mol, 90.5 ( 0.8 kJ/mol, and 210.6 ( 1.5 J/K 3 mol, respectively. The corresponding best ATcT estimates, which are combined experimental and theoretical values, are 90.6 ( 0.1 kJ/ mol,62 91.1 ( 0.1 kJ/mol,62 and 210.8 J/K 3 mol.17 For ΔfH0°(HNO), ΔfH°298(HNO), and S°298 (HNO) our approach yielded 110.9 ( 1.2 kJ/mol, 107.7 ( 1.2 kJ/mol, and 220.7 ( 1.5 J/K 3 mol, respectively. The corresponding most accurate estimates are 109.8 ( 0.1 kJ/mol,19 106.8 ( 0.1 kJ/mol,19 and 220.7 J/K 3 mol.17 Finally, for ΔfH0°(NO2), ΔfH°298(NO2), and S°298 (NO2) our protocol gave 37.4 ( 1.2 kJ/mol, 34.6 ( 1.2 kJ/mol, and 239.9 ( 1.5 J/K 3 mol, respectively, while the corresponding best estimates are 36.8 ( 0.1 kJ/mol,62 34.0 ( 0.1 kJ/ mol,62 and 240.0 ( 0.1 J/K 3 mol.17 It can be observed that the appropriate values agree well supporting our error estimates associated with our protocol introduced in ref 42; for further details please see Table 1 in the Supporting Information.

’ RESULTS Conformational Analysis. To determine all the relevant conformational isomers of the investigated species a systematic search at the CCSD(T)/cc-pVTZ level was conducted around the torsional angles of FONO, ClONO, HOONO2, ClOONO, and HOONO. Every geometrical variable was relaxed but the scanned torsional angle. Figure 1 shows the potential energy curve (PEC) and the ZPEs for FONO, ClONO, HOONO2, and ClOONO. In the case of FONO the global minimum is the cis conformer; the trans conformation is less stable by 11.3 kJ/mol. The barrier height between the conformers is 46.0 kJ/mol, which is larger than the 3145

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Figure 1. PECs calculated at the CCSD(T)/cc-pVTZ level of theory; every molecular coordinates were fully relaxed except the scanned torsional angle. The dashed line indicates the amount of the ZPE for the given conformer. (a) FONO; (b) ClONO; (c) HOONO2; (d) ClOONO.

Figure 2. PES of HOONO calculated at the CCSD(T)/cc-pVTZ level of theory; every molecular coordinates were fully relaxed except the scanned torsional angle.

ZPEs of the conformers. The PEC of ClONO is very similar to that of FONO; the trans conformer is higher in energy by 13.9 kJ/mol, and the ZPEs are smaller than the rotational barrier, 39.7 kJ/mol, between the conformers. On the PEC of HOONO2 two minima exist; the so-called periplanar structure, where the HO bond is nearly perpendicular to the plane of the ONO2 group, is the global minimum, and the less stable planar structure which is stabilized by an H-bond. The ZPE for the global minimum, 76.9 kJ/mol, is

substantially larger than the rotational barrier; therefore, only the periplanar structure is considered in the following computations. In the case of ClOONO two conformers exist; the energies of the minima differ by only 7.1 kJ/mol. However, the rotational barrier is 38.3 kJ/mol, which is higher than the ZPEs of the conformers. HOONO is the most flexible among the investigated molecules, and Figure 2 shows the PES of HOONO. In the global minimum both torsional angles have cis conformation (cc), 3146



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Figure 3. PECs calculated at the CCSD(T)/cc-pVTZ level of theory; all molecular coordinates were fully relaxed except the scanned torsional angle. The dashed line indicates the amount of the ZPE for the given conformer. (a) FONO2; (b) ClONO2; (c) NH2NO2.

which is stabilized by a H-bond. We note here that in the analog ClOONO molecule the cc conformation is a transition state between the two cp conformers, which are stereoisomers. In the second most stable conformer of HOONO the HO bond is approximately perpendicular to the plane defined by the ONO group (cp), and it is separated by a really shallow, less than 1 kJ/mol, barrier from the cc conformer. In the energetically least favorable isomer, which lies 7.8 kJ/mol above the cp conformer, the OO-NO torsional angle is trans and the HO bond is nearly perpendicular to the plane defined by the trans torsional angle. Nevertheless, since the ZPEs are larger than the separating barriers only the most stable cc conformer is considered in the following. The results obtained for those conformers which are not discussed here can be found in the Supporting Information. Internal Rotation. Besides HOONO and HOONO2, where shallow rotational barriers exist as mentioned above, NH2NO2, FONO2, and ClONO2 can also be identified as molecules with possible internal rotations. Figure 3 shows the PEC around the torsional angles of NH2NO2, FONO2, and ClONO2. It can be seen that although the ZPEs are larger than the corresponding barriers, the barriers are still high in energy, 49.4, 36.7, and 29.5 kJ/mol, respectively. Consequently, the rotations are probably welldescribed within the HO approximation as torsional vibrations. Nevertheless, to further test this assumption the one-dimensional hindered rotor model was applied to their torsional motion. For NH2NO2, FONO2, and ClONO2 the torsional motion is decoupled from the vibrations and the one-dimensional Schr€odinger

equation provides a meaningful approximation for the internal rotation. (The obtained eigenvalues can be found in the Supporting Information.) Treating the torsional motion as hindered rotation instead of vibration had a relatively little impact on the thermodynamic functions calculated in this study at 0 and 298.15 K. The heat of formation values changed less than 0.1 kJ/mol. The entropy of NH2NO2 is decreased by 0.1 J/K 3 mol, and that of ClONO2 increased by 0.6 J/K 3 mol; the entropy value of FONO2 was practically not effected. Unfortunately, in HOONO2 the two torsional modes are strongly coupled and in HOONO the torsional motions are coupled to two vibrational modes. Therefore an appropriate treatment would have required the numerical solution of a two-dimensional Schr€odinger equation, which was out of the scope of the present work. Consequently, because the largest correction, obtained for ClONO2, was 0.6 J/K 3 mol the error bars for the entropy of HOONO and HOONO2 were increased by 1.5 J/K 3 mol. Thermochemistry. HOONO. The JPL compilation18 recommends the data of McGrath and Rowland13 who reported the results of their G2 study in 1994 and listed ΔfH°298(HOONO) = 23.8 kJ/mol and ΔfH0°(HOONO) = 15.1 kJ/mol. On the basis of G2 calculations Tsai and his co-workers63 estimated the heat of formation of HOONO from ΔfH°298(OONO)64 and reported 25.1 ( 8.4 kJ/mol at 298 K. Dixon and associates using a CCSD(T)-based composite approach calculated 3.2 kJ/mol for ΔfH0°(HOONO).65 In a QCISD(T) study with the relatively small cc-pVDZ basis set Golden and co-workers presented 9.3 kJ/mol 3147


The Journal of Physical Chemistry A for ΔfH0°(HOONO).66 More recently CBS and G3 calculations were performed by Mak and Wong in order to determine thermochemical parameters for reactive nitrogen oxide species,67 and the heat of formation of the most stable cc conformation of HOONO at 298 K was determined using CBS-Q (31.1 kJ/mol), CBS-QB3 (31.8 kJ/mol), CBS-APNO (25.1 kJ/mol), G3 (17.6 kJ/ mol), and G3X (22.7 kJ/mol) methods. They noted that the large deviation in the values is due to the possibly inaccurate geometry and suggested the G3 result, 17.6 ( 5.1 kJ/mol, as the best ° (HOONO). Our calculated ΔfH298 ° (HOONO) estimate for ΔfH298 = 15.5 ( 2.0 kJ/mol value agrees within the given error bar with the G3 result of Mak and Wong, while our ΔfH0°(HOONO) = 6.4 ( 2.0 data is in line with that of Dixon and associates. However, it substantially deviates from the G2 value of ref 13, which is currently accepted by the JPL. Since our protocol is clearly superior to that of G2, a revision might be in order for ΔfHT°(HOONO). By use of the available entropy data for H2O2 and HONO, Richeson and associates68 applied empirical rules to calculate the entropy of HOONO; they reported 284.5 ( 4.2 J/K 3 mol for ° (HOONO). On the basis of estimated thermodynamic S298 functions, both in the fluid and gas phase, Tsai and co-workers63 predicted 288.7 ( 30.0 J/K 3 mol for S298 ° (HOONO). G2 ° (HOONO) = 274.0 J/K 3 mol.13 calculations resulted in S298 Our study yields a more reliable estimate, 271.0 ( 3.0 J/K 3 mol, ° (HOONO) than the previous ones. for S298 HOONO2. Baldwin and Golden studied the transition state of the HOO-NO2 H HO2 þ NO2 reaction and based on the dissociation energy of the ON bond, derived the first heat of formation data for HOONO2, 57.3 kJ/mol.69 More recent experimental studies yielded data between 52.3 and 53.1 kJ/ ° (HOONO2); see Table 1 and other works.7073 mol for ΔfH298 Our ΔfH298 ° (HOONO2) value, 52.4 ( 2.4 kJ/mol, agrees well within the given error bars with those obtained from experiments and presents the best estimates for ΔfH°298(HOONO2). On the basis of a second-law analysis Sander and Peterson71 obtained S298 ° (HOONO2) = 308.8 ( 8.4 J/K 3 mol. Regimbal and Mozurkewich72 using a HF/6-31G geometry and two estimated frequencies reported 294.0 ( 3.0 J/K 3 mol for the entropy, and this value was also accepted by the authors of the ° (HOONO2) JPL database. Chen and Hamilton14 calculated S298 = 297.5 J/K 3 mol at the B3LYP/6-311þþG(d,p) level of theory. In a third-law analysis study Gierczak and co-workers obtained ° (HOONO2) = 297.1 ( 2.9 J/K 3 mol. Our calculations S298 ° (HOONO2), which yielded 296.2 ( 3.0 J/K 3 mol for S298 reasonably agrees with the above values. NH2NO2. In an attempt to determine the heats of formation of di- and trinitramid at 0 K, Michels and Montgomery calculated, as auxiliary data, ΔfH0°(NH2NO2) = 17.2 ( 8.4 kJ/mol using G2 theory.74 Chen and Hamilton also evaluated ΔfH0°(NH2NO2) at different levels of theory, and their best estimate was 15.9 ( 4.2 kJ/ mol obtained in a CBS-APNO calculation.75 With the CBS-QB3 ° (NH2NO2).76 method Cobos reported 5.4 kJ/mol for ΔfH298 Wilcox and associates developed empirical atom/group corrections to the B3LYP/6-31G(d,p) calculations and got 9.8 kJ/mol for the heat of formation of NH2NO2 at 298 K;77 they also ° (NH2NO2) = 6.7 kJ/mol. Later, they reported a G2 result, ΔfH298 revised these values,78 and the average of the G3 and CBS-QB3 ° (NH2NO2) = 2.4 kJ/mol, was suggested.78 results, ΔfH298 Although Gurvich’s recommendation, ΔfH298 ° (NH2NO2) = 26.0 ( 10.0 kJ/mol, is broadly different from the above values the JPL database18 adopted his data.79 Our calculations yielded

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ΔfH0°(NH2NO2) = 18.3 ( 2.4 kJ/mol and ΔfH0°(NH2NO2) = 4.2 ( 2.4 kJ/mol. It can be seen that our result confirms the data of refs 7478 but disagrees with that of Gurvich. ° (NH2NO2) Gurvich reported 268.5 J/K 3 mol without For S298 ° (NH2NO2) = 268.2 J/K 3 mol was obtained at both error bars. S298 the B3LYP/6-31G(d) and B3LYP/6-31G(d,p) levels of theory.77,78 Our calculations, in agreement with the above values, yielded 268.0 ( 1.5 J/K 3 mol for the standard entropy of NH2NO2 at 298 K. It can be observed in Table 1 that our study provides the more reliable estimates both for the heats of formation and for the entropy of NH2NO2, than the previously reported ones. FNO. The only experimental investigation dealing with the heat of formation of nitrosyl-fluoride was conducted by Johnston and Bertin10 in 1959. In a calorimetric study they investigated the 2NO þ F2 = 2FNO reaction and determined 65.7 ( 1.7 kJ/mol ° (FNO), which was also adopted by the authors of the for ΔfH298 NIST-JANAF database.17 The computational studies are also rather scarce. Martin and associates using a CC-based approach with empirical corrections80,81 pointed out that the experimental result might need a revision and suggested 79.9 ( 4.2 kJ/mol for ° (FNO).82 In line with the findings of Martin and coΔfH298 workers, Bakowies reported ΔfH298° = 84.1 ( 8.9 kJ/mol using the so-called ATOMIC protocol.83 Our calculations support the ° theoretical studies yielding 87.2 ( 1.2 kJ/mol for ΔfH298 (FNO), nevertheless, our protocol is more accurate than those utilized in the theoretical investigations above. On the basis of the vibrational frequencies and moments of inertia obtained by Stephenson and Jones in a spectroscopic ° (FNO) = 248.1 study,84 the NIST-JANAF database suggests S298 kJ/K 3 mol without an attached uncertainty.17 Our result, 247.6 ( 1.5 J/K 3 mol, agrees well with the experimental value and it comes with a well-defined error bar. FNO2. The first reports about the heat of formation of FNO2 were published by MacLaren and his co-workers.85,86 In a calorimetric measurement they obtained 83.7 ( 20.9 kJ/mol for the heat of formation at 298 K.85 On the basis of a revised value of ref 85, ΔfH298° = 79.5 ( 8.4 kJ/mol, Tschuikow-Roux suggested ΔfH0° = 73.6 ( 8.4 kJ/mol.87 In their final technical report Breazeale and MacLaren revised the previous values to ° (FNO2) = 108.8 ( 20.9 kJ,86 and this value was also ΔfH298 adopted in the NIST-JANAF database.17 About 20 years later Lee presented results determined using the calculated energy of the HNO2 þ FNO = HNO þ FNO2 reaction.88 In his CCSD(T)/ANO study ΔfH298° = 86.2 ( 4.2 kJ/mol together with ΔfH298° = 92.5 ( 4.2 kJ/mol were reported. Our calculation ° (FNO2) = 108.7 ( 1.6 and ΔfH298 ° (FNO2) = yielded ΔfH298 114.9 ( 1.6, which agree, within a given error bar, with those obtained from experiment and recommended by the IUPAC89 or the NIST-JANAF database17 but considerably deviates from those obtained in previous theoretical investigations. Moreover, it can be easily recognized from Table 1 that our values provide more reliable estimates for the heats of formation of FNO2, than the former results. From the moments of inertia measured by Smith and Magnuson90 using microwave spectroscopy and from the frequencies determined by Dodd and associates91 Tschuikow-Roux ° (FNO2) = 260.2 J/ and the NIST-JANAF database suggest S298 ° (FNO2) = 260.3 J/K 3 mol, respectively. Our K 3 mol and S298 ° (FNO2). It is notable that value is 258.5 ( 1.5 J/K 3 mol for S298 the experimental entropies are based on an estimated geometry; Smith and Magnuson90 assumed that the ONO angle is 125°; while in the derivation of the NIST-JANAF value it was 3148



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Table 1. Heats of Formation (in kJ/mol) as well as Entropies (in J/K 3 mol) for the Nitrogen Oxide Derivatives Studied in This Work species HOONO

ΔfH°0 6.4 ( 2.0

15.1

HOONO2

ΔfH°298

S298 °

15.5 ( 2.0

271.0 ( 3.0

this work

4.2 ( 4.2 25.1 ( 8.4

284.5 ( 4.2 288.7 ( 30.0

ref 68, NF ref 63, G2

23.8

274.0

refs 13 and 18, G2

3.2

ref 65, CC

9.3

ref 66, QCISD(T)

41.3 ( 2.4

31.1

ref 67, CBS-Q

31.8

ref 67, CBS-QB3

25.1

ref 67, CBS-APNO

17.6 22.7

ref 67, G3 ref 67, G3X

52.4 ( 2.4

296.2 ( 3.0

this work

53.1 ( 2.5

294.0 ( 3.0

refs 18 and 72

52.7 ( 4.2

297.1 ( 2.9

52.7 ( 4.5 52.7 ( 8.4 46.9 NH2NO2

18.3 ( 2.4

308.8 ( 8.4

ref 111

57.3 57.0

ref 69 ref 112

4.9 ( 2.4

268.0 ( 1.5

ref 74, G2 2.4

268.5 268.2

6.7 268.2

ref 76, CBS-QB3 ref 77, B3LYP

84.7 ( 1.2

87.2 ( 1.2

247.7 ( 1.5

this work

65.7 ( 1.7

248.1

refs 10 and 17, JANAF ref 82, CCSD(T)

84.1 ( 8.9

ref 83, ATOMIC

109.6 ( 44.4 108.7 ( 1.6

114.9 ( 1.6

86.2 ( 4.2

92.5 ( 4.2 109.0 ( 8.0

73.6 ( 8.4

79.5 ( 8.4

ref 113, B3LYP 258.5 ( 1.5

102.9 ( 20.9 47.1 ( 1.6

108.8 ( 20.9 42.6 ( 1.6

260.2

ref 87

260.3

refs 17 and 86

274.0 ( 1.5

this work

275.5 ( 1.5

this work

ref 85

39.8 58.4 ( 1.6

this work ref 88, CCSD(T) ref 89

83.7 ( 20.9

ref 94, CCSD(T)

54.2 ( 1.6 56.9 ( 8.4b 54.0 ( 12.5b

ref 92, NF ref 93, NF

67.0

refs 18 and 114, NF

19.8 ( 2.0

12.3 ( 2.0

291.3 ( 1.5

this work

18.0 ( 2.1

10.5 ( 2.1

292.9

refs 17, 18, 95

17.6 ( 3.8

ref 115

13.0 ( 8.4 ClNO

ref 78, G3 and CBS-QB3

63.3 ( 1.7

79.9 ( 4.2

FONO2

refs 18 and 79, NF ref 77, G2

5.4 9.8

trans-FONO

this work ref 75, CBS-APNO

26.0 ( 10.0

cis-FONO

ref 71

52.3 ( 8.4

17.2 ( 8.4

FNO2

ref 70 ref 73

15.9 ( 4.2

FNO

sourcea

ref 116, CCSD(T)

53.6 ( 0.4

51.7 ( 0.4

261.7 ( 0.2

ref 17

56.2 ( 1.4

52.7 ( 0.5 54.3 ( 1.4

261.6 261.0 ( 1.5

refs 18 and 79 this work, HEAT

47.3

ref 98, CBS-Q

3149



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Table 1. Continued species cis-ClONO

ΔfH°0 59.6 ( 2.7 64.4 ( 6.3

ΔfH°298

S298 °

55.2 ( 2.7 60.7 ( 6.3

282.8 ( 1.5

61.1 ( 7.5 72.4 ( 2.7

ref 99

68.4 ( 2.7

286.1 ( 1.5

75.3 ( 6.3

ref 101, CCSD(T) 26.4 ( 0.8

302.5

ref 102

33.8 ( 3.1

22.9 ( 2.0 26.7 ( 3.1

302.4 301.9 ( 1.5

refs 18 and 105 this work

31.0

ref 106, CCSD(T)

29.3

23.0

ref 108, G3

ClONO2

135.5 ( 3.1

130.0 ( 3.1

136.0 ( 4.1

131.8 ( 4.1

312.2 ( 1.5

106.7

101.7b

315.9b

refs 13 and 18, G2(MP2)

143.0 ( 3.1 143.9 ( 4.1

136.4 ( 3.1 138.9 ( 4.1

315.1 ( 1.5

this work ref 108, G3

113.4

108.4b

318.8b

ref 13, G2(MP2)

this work ref 108, G3

137.6 tp-ClOONO

this work ref 100, CCSD(T)

73.6 ( 7.5

cp-ClOONO

this work ref 100, CCSD(T) ref 101, CCSD(T)

56.1 trans-ClONO

sourcea

ref 109, CCSD(T)

143.9

ref 109, CCSD(T)

a

Unless otherwise noted, the data are obtained from experiment. If a composite scheme is used in a theoretical study, only the highest-level method is indicated. For further details on the experimental setup or on the theoretical methods please refer to the appropriate literature. NF - empirical result, no direct experimental findings. CC - coupled-cluster based model chemistry. b The data is given at 300 K.

presumed that the ONO angle is the same, namely, 129.5°, in ClNO2 and FNO2. According to our CCSD(T)/cc-pVQZ geometry optimization it is 135.6°. FONO. With an empirical bond additivity method, Colussi and Grela determined the heat of formation of trans-FONO and ° (trans-FONO).92 Later, reported 56.9 ( 8.4 kJ/mol for ΔfH300 based on new bond additivity contributions they corrected this ° (trans-FONO) result to 54.0 ( 12.5 kJ/mol.93 Our result, ΔfH300 = 54.2 ( 1.6 kJ/mol, is in an excellent agreement with this value. Lee and Rice examined the relative energetics of the FNO2, cisFONO, and trans-FONO species using the CCSD(T) method with various basis sets,94 and it was reported that the cis conformer is lower in energy by about 10 kJ/mol. Furthermore, ° (cis-FONO) the enthalpy of the reaction to determine ΔfH298 2FONO þ H2O = 2HONO þ F2O was calculated, and ΔfH298° (cis-FONO) = 39.8 kJ/mol was derived.94 Our calculation ° (cisyielded the most reliable heats of formation data, ΔfH298 ° (trans-FONO) = 54.2 ( FONO) = 42.6 ( 1.6 kJ/mol. ΔfH298 1.6 kJ/mol. For FONO no entropy data has been published in the ° (cis-FONO) = 274.0 ( 1.5 literature. This study presents S298 ° (trans-FONO) = 275.5 ( 1.5 J/K 3 mol. J/K 3 mol, and S298 FONO2. In a calorimetric study Rewick and his co-workers measured the reaction enthalpy of the F2 þ NaNO3 = FONO2 þ NaF process95 and from the appropriate heats of formation ° (FONO2) = 10.5 ( 2.1 kJ/mol was established. This value ΔfH298 is also adopted by both the JPL18 and NIST-JANAF17 databases. With the help of CCSD(T)/ANO calculation, Lee investigated several isodesmic reactions to determine the heat of formation of ° (FONO2) = 13.0 ( 8.4 FONO2, and his best estimate was ΔfH298 kJ/mol. Our results, ΔfH0°(FONO2) = 19.8 ( 2.0 kJ/mol and ° (FONO2) = 12.3 ( 2.0 kJ/mol, are in line with those ΔfH298 recommended by the JPL and NIST-JANAF databases.

The standard entropy value of NIST-JANAF database, 292.9 J/K 3 mol, was determined using the estimated vibrational frequencies of Palm and Kilpatrick96 and structure of Pauling and Brockway;97 no error estimate is given for the entropy. ° (FONO2) = 291.3 ( 1.5 J/K 3 mol. We obtained S298 ClNO. In his book Gurvich suggests 52.7 ( 0.5 kJ/mol for the heat of formation of ClNO at 298 K,79 which is also listed in the JPL compilation of data. The NIST-JANAF compendium pre° (ClNO) = sents ΔfH0°(ClNO) = 51.7 ( 0.4 kJ/mol and ΔfH298 53.6 ( 0.4 kJ/mol.17 Among various other quantities, Jursic calculated the heat of formation of ClNO with several methods such as G2, G2MP2, and CBS-Q,98 and, as the most accurate estimate, he relied on the CBS-Q value, ΔfH0°(ClNO) = 47.3 kJ/ mol. Utilizing a slightly modified HEAT protocol43 our calcula° tions yielded ΔfH0°(ClNO) = 56.2 ( 1.4 kJ/mol and ΔfH298 (ClNO) = 54.3 ( 1.4 kJ/mol. It can be observed in Table 1 that our data at 298 K overlaps with that of Gurvich and practically rules out the value given in the NIST-JANAF database. Furthermore, the fairly thin, 0.3 kJ/mol, overlapping region might also indicate some problem with the experimental value listed by Gurvich. In line with the accurate NIST-JANAF, 261.7 ( 0.2 J/K 3 mol, and the JPL, 261.6 J/K 3 mol, entropy data at 298 K, our ° (ClNO) = 261.0 ( 1.5 J/K 3 mol. investigation resulted in S298 ° ClONO. The experimental heat of formation value, ΔfH298 (ClONO) = 56.1 kJ/mol, was obtained without considering the separation of the cis and trans isomers.99 In a CCSD(T)/ANO4 study, Lee investigated the cis/trans-HONO þ HOCl = cis/transClONO þ H2O reactions and ΔfH0°(cis-ClONO) = 64.4 ( 6.3 ° (cis-ClONO) = 60.7 ( 6.3 kJ/mol as well as kJ/mol, ΔfH298 ΔfH0°(trans-ClONO) = 75.3 ( 6.3 kJ/mol were derived.100 The JPL database18 adopted Lee’s values; however, it accidentally lists the 0 K data at 298 K. Zhu and Lin also evaluated the enthalpies 3150



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Table 2. Calculated Standard Reaction Enthalpies (ΔrHo [kJ/mol]), Standard Reaction Entropies (ΔrSo [J/mol.K]), Standard Gibbs Energies of Reaction (ΔrGo [kJ/mol]), Equilibrium Constants (K [cm3/molecule]), and Uncertainty Factors (f) at 298 K reactiona OH þ NO2 f HOONO HO2 þ NO2 f HOONO2 ClO þ NO2 f ClONO2 ClO þ NO2 f ClOONO

ΔrHo

ΔrSo

ΔrGo

K

f 12

86.8 ( 2.4

152.7 ( 3.1

41.3 ( 3.3

0.7 10

98.0 ( 2.9 108.9 ( 3.3

172.9 ( 3.2 163.2 ( 2.1

46.5 ( 3.9 60.3 ( 3.9

0.6 1011 1.5 109

4.8 4.9

5.7 ( 3.3

152.9 ( 2.1

39.9 ( 3.9

4.2 1027

4.9

3.8

a

Heat of formation data for NO2, OH, and ClO were taken from ref 18; the heat of formation of HO2 is from ref 34. The entropy data for NO2, OH, and HO2 are from ref 17; the entropy of ClO is from ref 18.

of the above reactions with various methods, such as B3LYP/6311Gþ(3df,2p), CCSD(T)/6-311Gþ(3df,2p)//B3LYP/6311Gþ(3df,2p), G3, and G3B3, and the average values, 61.1 ( 7.5 and 73.6 ( 7.5 kJ/mol, were suggested for ΔfH0°(cisClONO) and ΔfH0°(trans-ClONO), respectively.101 Our computations resulted in ΔfH0°(cis-ClONO) = 59.6 ( 2.7 ° (cis-ClONO) = 55.2 ( 2.7 kJ/mol, ΔfH0°(transkJ/mol, ΔfH298 ° (trans-ClONO) = ClONO) = 72.4 ( 2.7 kJ/mol, and ΔfH298 68.4 ( 2.7 kJ/mol. As it is demonstrated in Table 1 our data agree, within the given uncertainties, with the available literature values, nevertheless, our study presents the most accurate estimates for the heats of formation of ClONO. Furthermore, this study provides the first data on the entropies of the ClONO ° (cis-ClONO) = 282.8 ( 1.5 J/K 3 mol, and S298 ° isomers; S298 (trans-ClONO) = 286.1 ( 1.5 J/K 3 mol. onle and ClONO2. In their reaction kinetic study, Sch€ ° (ClONO2) = 26.4 ( 0.8 kJ/mol associates102 quoted ΔfH298 referring to previous experimental studies.103,104 The authors of the JPL database18 recommend the data of Anderson and Fahey, who measured the rate constant of the ClONO2 decomposition reaction, and after a third-low analysis, determined 22.9 ( 2.0 kJ/mol for the heat of formation at 298 K.105 Lee and Rice calculated the enthalpy of the ClONO2 þ H2O = HOCl þ HONO2 reaction at the MP2/DZP, CCSD/DZP, CCSD(T)/ DZP, CCSD(T)/DZ2P levels of theory, and based on the ° (ClONO2) = 31.0 kJ/mol was CCSD(T) computations ΔfH298 established.106 Our calculations yielded ΔfH0°(ClONO2) = 33.8 ( 3.1 kJ/mol ° (ClONO2) = 26.7 ( 3.1 kJ/mol. Although our heat and ΔfH298 of formation at 298 K agrees within the given uncertainties with both data suggested in two previous studies (22.9 ( 2.0 kJ/ mol)105 and (26.4 ( 0.8 kJ/mol),102 it is closer to that of ref 102. Therefore, the revision of the currently accepted heat of formation data might be necessary. ° (ClONO2) = 301.9 ( 1.5 J/K 3 mol, is Our entropy value, S298 in line with the experimental result, 302.4 J/K 3 mol, obtained from the spectroscopic study of Miller and associates.107 ClOONO. By use of an empirical bond additivity scheme Colussi and Grela calculated the heat of formation of ClOONO at 300 K, 148.1 ( 8.4 kJ/mol,92 and later this value was revised to 135.1 ( 12.5 kJ/mol.93 Nevertheless, it is not clear which conformation was taken into account. Both the cc and cp conformation of ClOONO were investigated theoretically with the G2(MP2) method by McGrath and Rowland; and ΔfH0°(cc-ClOONO) = 106.7 kJ/mol, ΔfH°300(ccClOONO) = 101.7 kJ/mol, ΔfH0°(tp-ClOONO) = 113.4 kJ/mol, ΔfH°300(tp-ClOONO) = 108.4 kJ/mol were established.13 Lesar and co-workers also studied both conformations and suggested ΔfH0°(ccClOONO) = 136.0 ( 4.1 kJ/mol, ΔfH°300(cc-ClOONO) = 131.8 ( 4.1 kJ/mol, ΔfH0°(tp-ClOONO) = 143.9 ( 4.1 kJ/mol, ΔfH°300(tpClOONO) = 138.9 ( 4.1 kJ/mol based on their G3(B3)

calculations.108 B3LYP and CCSD(T) methods with the 6-311þG(3df,2p) basis set were also used in a study conducted by Zhu and Lin, and 137.6 kJ/mol as well as 143.9 kJ/mol were reported, respectively, for ΔfH0°(cp-ClOONO) and ΔfH0°(tp-ClOONO).109 The use of our protocol resulted in ΔfH298 ° (cp-ClOONO) = ° (tp-ClOONO) = 136.4 ( 3.1 kJ/ 130.0 ( 3.1 kJ/mol and ΔfH298 mol as well as ΔfH0°(cp-ClOONO) = 135.5 ( 3.1 kJ/mol and ΔfH0°(tp-ClOONO) = 143.0 ( 3.1 kJ/mol. As it can be seen in Table 1 our results correspond to the most reliable estimates for the heats of formation of the ClOONO isomers. McGrath and Rowland tabulated the entropy values for both cp-ClOONO and tp-ClOONO. On the basis of their G2(MP2) ° (cp-ClOONO) = 315.9 J/K 3 mol and S300 ° (tpcalculations S300 ClOONO) = 318.8 J/K 3 mol were obtained. Our calculations ° (cp-ClOONO) = 312.2 ( 1.5 J/K 3 mol and S298 ° (tpyielded S298 ClOONO) = 315.1 ( 1.5 J/K 3 mol providing the best estimates for these thermodynamic functions. Equilibrium Constants. As aforementioned the species investigated in this study are involved in a number of important atmospheric reactions. Since, in most of the cases, this study presents the best estimates for the heats of formation and for the entropies of the molecules, the standard enthalpies, ΔrH, standard entropies, ΔrS, and standard Gibbs energies, ΔrG°, of reaction were also calculated for four important reactions. Table 2 lists the computed ΔrH°, ΔrS°, and ΔrG° values, the equilibrium constants, as well as the uncertainty factors for the equilibrium constants. For the OH þ NO2 f HOONO and HO2 þ NO2 f HOONO2 reactions the JPL database lists, respectively, 2.2 1012 cm3/molecule with an uncertainty factor of 2.0 and 1.6 1011 cm3/molecule with an uncertainty factor of 1.3.18 It can be observed in Table 2 that our corresponding data, 0.7 1012 cm3/molecule and 0.6 1011 cm3/molecule, agree, within the given uncertainties, with the above values. Zhu and Lin constructed the PES for the ClO þ NO2 f ClONO2 reaction using the CCSD(T)/6-311þG(3df)//B3LYP/ 6-311þG(3df) level of theory .109 On the basis of the predicted low-, and high-pressure limits for the association and dissociation processes 5.7 109 cm3/molecule (without an error estimate) can be calculated for the equilibrium constant at 298 K. Recently, Golden110 also calculated the equilibrium constant for the ClO þ NO2 f ClONO2 reaction at various temperatures and found that the data of Zhu and Lin at 298 K is 60% higher than his value, 3.6 109 cm3/molecule. Our result, 1.5 109 cm3/molecule with the associated uncertainty factor of 4.9, is in line with Golden’s data and disagree with that of Zhu and Lin.

’ CONCLUDING REMARKS High-accuracy theoretical model chemistries can provide a viable alternative to even cutting edge experimental investigations. 3151


The Journal of Physical Chemistry A This study also confirmed the value of theoretical studies in thermochemistry; it presented several heat of formation and entropy values for nitrogen oxide derivatives, which turned out to be the best available estimates for most of the considered molecules. On the basis of our calculations the currently accepted heat of formation values for HOONO, HOONO2, NH2NO2, FNO, FNO2, cis- and trans-FONO, FONO2, ClNO, cis- and transClONO, cp- and tp-ClOONO may need revision.

’ ASSOCIATED CONTENT

bS

Supporting Information. Heats of formation of three test molecules, total energies, equilibrium geometries, rotational constants, harmonic frequencies, and anharmonic corrections. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Financial support has been provided by the European Research Council (ERC) under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement No. 200639, and by the Hungarian Scientific Research Fund (OTKA), Grant No. NF72194. ’ REFERENCES (1) Forster, P.; Ramaswamy, V.; Artaxo, P.; Berntsen, T.; Betts, R.; Fahey, D.; Haywood, J.; Lean, J.; Lowe, D.; Myhre, G.; Nganga, J.; Prinn, R.; Raga, G.; Schulz, M.; Dorland, R. V. Climate Change 2007: The Physical Science Basis; Cambridge University Press: Cambridge, UK, 2007. (2) Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change; Pachauri, R. K., Reisinger, A., Eds.; IPCC: Geneva, CH, 2008. (3) Safeguarding the Ozone Layer and the Global Climate System: Issues Related to Hydrofluorocarbons and Perfluorocarbons; Metz, B., Kuijpers, L., Solomon, S., Andersen, S. O., Davidson, O., Pons, J., de Jager, D., Kestin, T., Manning, M., Meyer, L., Eds.; Cambridge University Press: Cambridge, UK, 2005. (4) Nohende Ajavon, A.-L.; Albritton, D. L.; Watson, R. T. Scientific assessment of ozone depletion: 2006, Global Ozone Research and Monitoring Project—Report No. 50; World Meteorological Organization, 2007. (5) Cox, R.; Derwent, R.; Hutton, A. Nature 1977, 270, 328. (6) Atkinson, R. Atmos. Environ. 2000, 34, 2063–2101. (7) Seinfeld, J.; Pandis, S. From air pollution to climate change. Atmospheric Chemistry and Physics; John Wiley & Sons, New York, 1998. (8) Demaison, J.; Csaszar, A. G.; Dehayem-Kamadjeu, A. J. Phys. Chem. A 2006, 110, 13609. (9) Digle, T. S.; Francisco, J. S. J. Chem. Phys. 1993, 99, 397. (10) Johnston, H. S.; Bertin, H. J., Jr. J. Am. Chem. Soc. 1959, 81, 6402. (11) Ellison, G. B.; Herbert, J. M.; McCoy, A. B.; Stanton, J. F.; Szalay, P. G. J. Phys. Chem. A 2004, 108, 7639. (12) Mollner, A. K.; Valluvadasan, S.; Feng, L.; Sprague, M. K.; Okumura, M.; Milligan, D. B.; Bloss, W. J.; Sander, S. P.; Martien, P. T.; Harley, R. A.; McCoy, A. B.; Carter, W. P. L. Science 2010, 330, 646. (13) McGrath, M. P.; Rowland, F. S. J. Phys. Chem. 1994, 98, 1061. (14) Chen, Z.; Hamilton, T. P. J. Phys. Chem. 1996, 100, 15731.

ARTICLE

(15) Levine, S.; Uselman, W.; Chan, W.; Calvert, J.; Shaw, J. Chem. Phys. Lett. 1977, 48, 528. (16) Jimenez, E.; Gierczak, T.; Stark, H.; Burkholder, J.; Ravishankara, A. J. Phys. Chem. A 2004, 108, 1139. (17) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed.; J. Phys. Chem. Ref. Data, Monograph Vol. 9, 1998. (18) Sander, S. P.; Friedl, R. R.; Golden, D. M.; Kurylo, M. J.; Moortgat, G. K.;Wine, P. H.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J.; Finlayson-Pitts, B. J.; Huie, R. E.; Orkin, V. L. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 15; NASA Jet Propulsion Laboratory Publication, California Institute of Technology: Pasadena, CA, 2006. (19) Burcat, A.; Ruscic, B.; Ruscic, B. Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with updates from Active Thermochemical Tables, ANL-05/20 and TAE 960, Technion-IIT, Aerospace Engineering, and Argonne National Laboratory, Chemistry Division, September 2005. ftp://ftp.technion. ac.il/pub/supported/aetdd/thermodynamics mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html (accessed in March 2010). (20) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (21) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, 7764. (22) Montgomery, J. A., Jr.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 1994, 101, 5900. (23) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A., Jr. J. Chem. Phys. 1996, 104, 2598. (24) East, A. L. L.; Allen, W. D. J. Chem. Phys. 1993, 99, 4638. (25) Csaszar, A.; Allen, W. D.; Schaefer, H. F., III. J. Chem. Phys. 1998, 108, 9751. (26) Martin, J. M. L.; de Oliveira, G. J. Chem. Phys. 1999, 111, 1843. (27) Boese, A. D.; Oren, M.; Atasoylu, O.; Martin, J. M. L.; Kallay, M.; Gauss, J. J. Chem. Phys. 2004, 120, 4129. (28) Karton, A.; Rabinovich, E.; Martin, J. M. L.; Ruscic, B. J. Chem. Phys. 2006, 125, 144108. (29) Feller, D.; Peterson, K. A.; Dixon, D. A. J. Chem. Phys. 2008, 129, 204105. (30) Helgaker, T.; Ruden, T. A.; Jørgensen, P.; Olsen, J.; Klopper, W. J. Phys. Org. Chem. 2004, 17, 913. (31) Tajti, A.; Szalay, P. G.; Csaszar, A. G.; Kallay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vazquez, J.; Stanton, J. F. J. Chem. Phys. 2004, 121, 11599. (32) Bomble, Y. J.; Vazquez, J.; Kallay, M.; Michauk, C.; Szalay, P. G.; Csaszar, A. G.; Gauss, J.; Stanton, J. F. J. Chem. Phys. 2006, 125, 064108. (33) Harding, M. E.; Vazquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. J. Chem. Phys. 2008, 128, 114111. (34) Flowers, B. A.; Szalay, P. G.; Vazquez, J.; Stanton, J. F.; Kallay, M.; Gauss, J.; Csaszar, A. G. J. Phys. Chem. A 2004, 108, 3195. (35) Szalay, P. G.; Thøgersen, L. S.; Olsen, J.; Kallay, M.; Gauss, J. J. Phys. Chem. A 2004, 108, 3030. (36) Willitsch, S.; Merkt, F.; Kallay, M.; Gauss, J. Mol. Phys. 2006, 104, 1457. (37) Tasi, G.; Izsak, R.; Matisz, G.; Csaszar, A. G.; Kallay, M.; Ruscic, B.; Stanton, J. F. ChemPhysChem 2006, 7, 1664. (38) Szalay, P. G.; Tajti, A.; Stanton, J. F. Mol. Phys. 2005, 103, 2159. (39) Demaison, J.; Csaszar, A. G.; Dehayem-Kamadjeu, A. J. Phys. Chem. A 2006, 110, 13609. (40) Karton, A.; Taylor, P. R.; Martin, J. M. L. J. Chem. Phys. 2007, 127, 064104. (41) Karton, A.; Parthiban, S.; Martin, J. M. L. J. Phys. Chem. A 2009, 113, 4802. (42) Csontos, J.; Rolik, Z.; Das, S.; Kallay, M. J. Phys. Chem. A 2010, 114, 13093. (43) Nagy, B.; Csontos, J.; Kallay, M.; Tasi, G. J. Phys. Chem. A 2010, 114, 13213. (44) Feller, D. J. Chem. Phys. 1992, 96, 6104. (45) Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. J. Chem. Phys. 1997, 106, 9639. 3152


The Journal of Physical Chemistry A (46) Mills, I. M. In Molecular Spectroscopy: Modern Research; Rao, K. N., Mathews, C. W., Eds.; Academic Press: New York, 1972. (47) Gauss, J.; Tajti, A.; Kallay, M.; Stanton, J. F.; Szalay, P. G. J. Chem. Phys. 2006, 125, 144111. (48) Kallay, M.; Surjan, P. R. J. Chem. Phys. 2001, 115, 2945. (49) MRCC, a string-based quantum chemical program suite written by M. Kallay. See also ref 48 as well as http://www.mrcc.hu/. (50) CFOUR, a quantum chemical program package written by Stanton, J. F.; Gauss, J.; Harding, M. E.; Szalay, P. G. with contributions from Auer, A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J.; Christiansen, O.; Heckert, M.; Heun, O.; Huber, C.; Jagau, T.-C.; Jonsson, D.; J. Juselius, Klein, K.; Lauderdale, W. J.; Matthews, D. A.; Metzroth, T.; D. P. O’Neill, Price, D. R.; Prochnow, E.; Ruud, K.; Schiffmann, F.; Stopkowicz, S.; J. Vazquez, Wang, F.; Watts, J. D.; and the integral packages MOLECULE (J. Alml€of Taylor, P. R.; ), PROPS (Taylor, P. R.; ), ABACUS (Helgaker, T.; H. J. Aa. Jensen, Jørgensen, P.; Olsen, J.; ), and ECP routines by Mitin, A. V.; van W€ullen, C.. For the current version, see http://www.cfour.de. (51) McQuarrie, D. A.; Simon, J. D. Molecular Thermodynamics; University Science Books: Sausalito, CA, 1999. (52) Pitzer, K.; Gwinn, W. J. Chem. Phys. 1942, 10, 428. (53) Pitzer, K. J. Chem. Phys. 1946, 14, 239. (54) Kilpatrick, J.; Pitzer, K. J. Chem. Phys. 1949, 17, 1064. (55) Li, J.; Pitzer, K. J. Phys. Chem. 1956, 60, 466–474. (56) Ercolani, G. J. Chem. Edu. 2000, 77, 1495. (57) Pfaendtner, J.; Yu, X.; Broadbelt, L. Theor. Chim. Acta 2007, 118, 881–898. (58) Marston, C.; Balint-Kurti, G. J. Chem. Phys. 1989, 91, 3571–3576. (59) Balint-Kurti, G.; Dixon, R.; Marston, C. Int. Rev. Phys. Chem. 1992, 11, 317–344. (60) Chuang, Y.; Truhlar, D. J. Chem. Phys. 2000, 112, 1221. (61) Ellingson, B.; Lynch, V.; Mielke, S.; Truhlar, D. J. Chem. Phys. 2006, 125, 084305. (62) Ruscic, B.; updated ATcT thermocemical data based on Core (Argonne) Thermochemical Network [2, 4] ver. 1.110 (2010); available at ATcT.anl.gov. (63) Tsai, H.-H.; Hamilton, T. P.; Tsai, J.-H. M.; van derWoerd, M.; Harrison, J. G.; Jablonsky, M. J.; Beckman, J. S.; Koppenol, W. H. J. Phys. Chem. 1996, 100, 15087. (64) Manuszak, M.; Koppenol, W. H. Thermochim. Acta 1996, 273, 911. (65) Dixon, D. A.; Feller, D.; Zhan, C.-G.; Francisco, J. S. J. Phys. Chem. A 2002, 106, 3191. (66) Golden, D. M.; Barker, J. R.; Lohr, L. L. J. Phys. Chem. A 2003, 107, 11057. (67) Mak, A. M.; Wong, M. W. Chem. Phys. Lett. 2005, 403, 192. (68) Richeson, C. E.; Mulder, P.; Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc. 1998, 120, 7211. (69) Baldwin, A. C.; Golden, D. M. J. Phys. Chem. 1978, 82, 644. (70) Gierczak, T.; Jimenez, E.; Riffault, V.; Burkholder, J. B. J. Phys. Chem. A 2005, 109, 586. (71) Sander, S. P.; Peterson, M. E. J. Phys. Chem. 1984, 88, 1566. (72) Regimbal, J.-M.; Mozurkewich, M. J. Phys. Chem. A 1997, 101, 8892. (73) Miller, C. E.; Lynton, J. I.; Keevil, D. M.; Francisco, J. S. J. Phys. Chem. A 1999, 103, 11451. (74) Michels, H. H.; Montgomery, J. A., Jr. J. Phys. Chem. 1993, 97, 6602. (75) Chen, Z.; Hamilton, T. P. J. Phys. Chem. A 1999, 103, 11026. (76) Cobos, C. THEOCHEM 2005, 714, 147–152. (77) Wilcox, C. F.; Zhang, Y.-X.; Bauer, S. H. THEOCHEM 2000, 528, 95. (78) Wilcox, C. F.; Zhang, Y.-X.; Bauer, S. H. THEOCHEM 2001, 538, 67. (79) Gurvich, L. V.; Veyts, I. V.; Alock, C. B. Thermodynamic Properties of Individual Substances, 4th ed.; Hemisphere: New York, 1992. (80) Martin, J. M. L. J. Chem. Phys. 1992, 97, 5012.

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(81) Martin, J. M. L. J. Chem. Phys. 1994, 100, 8186. (82) Martin, J. M. L.; Francois, J-P; Gijbels, R. J. Phys. Chem. 1994, 98, 11394. (83) Bakowies, D. J. Phys. Chem. A 2009, 113, 11517. (84) Stephenson, C. V.; Jones, E. A. J. Chem. Phys. 1952, 20, 135. (85) Anderson, R.; MacLaren, R. O. 2nd Quarterly Technical Summary Report; United Technology Corporation: Sunnyvale, CA, 1961. (86) Breazeale, D.; MacLaren, R. O., Thermochemistry of Oxygen Flourine Bonding Final Technology; United Technology Corporation: Sunnyvale, CA, 1963. (87) Tschuikow-Roux, E. J. Phys. Chem. 1962, 66, 1636. (88) Lee, T. J. Chem. Phys. Lett. 1993, 216, 194. (89) Wayne, R. P.; Poulet, G.; Biggs, P.; Burrows, J. P.; Cox, R. A.; Crutzen, P. J.; Hayman, G. D.; Jenkin, M. E.; Le Bras, G.; Moortgat, G. K.; Plattm, U.; Schindler, R. N. Atmos. Environ. 1995, 29, 2677. (90) Smith, D. F.; Magnuson, D. W. Phys. Rev. 1952, 87, 226. (91) Dodd, R.; Rolfe, J.; Woodward, L. Trans. Faraday Soc. 1956, 52, 154. (92) Colussi, A. J.; Grela, M. A. J. Phys. Chem. 1993, 97, 3775. (93) Grela, M. A.; Colussi, A. J. J. Phys. Chem. 1996, 100, 10150. (94) Lee, T. L.; Rice, J. E. J. Phys. Chem. 1992, 97, 4223. (95) Rewick, R. T.; Anderson, R.; MacLaren, R. O. J. Chem. Eng. Data 1972, 17, 409. (96) Palm, A.; Kilpatrick, M. J. Chem. Phys. 1955, 23, 1562. (97) Pauling, L.; Brockway, L. O. J. Am. Chem. Soc. 1937, 59, 13. (98) Jursic, B. S. THEOCHEM 1999, 492, 35. (99) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Troe, J. J. Phys. Chem. Ref. Data 1989, 18, 881. (100) Lee, T. J. J. Phys. Chem. 1994, 98, 111. (101) Zhu, R. S.; Lin, M. C. Chem. Phys. Chem. 2004, 5, 1864. (102) Sch€onle, G.; Knauth, H.-D.; Schindler, R. N. J. Phys. Chem. 1979, 83, 3279. (103) Knauth, H.-D.; Martin, H.; Stockmann, W. Z. Naturforsch. A 1974, 29, 200. (104) Alqasmi, R.; Knauth, H.-D.; Rohlack, D. Ber.Bunsen. Phys. Chem 1978, 82, 217. (105) Anderson, L. C.; Fahey, D. W. J. Phys. Chem. 1990, 94, 644. (106) Lee, T. L.; Rice, J. E. J. Phys. Chem. 1993, 97, 6637. (107) Miller, R.; Bernitt, D.; Hisatsune, I. Spectrochim. Acta A 1967, 23, 223–236. (108) Lesar, A.; Prebil, S.; Hodoscek, M. J. Phys. Chem. A 2003, 107, 9168. (109) Zhu, R. S.; Lin, M. C. ChemPhysChem 2005, 6, 1514. (110) Golden, D. Int. J. Chem. Kinet. 2009, 41, 573. (111) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina, M. J.; Chemical Kinetics and Photochemical Data Use on Stratospheric Modeling; NASA JPL: Evaluation no. 12, 1997. (112) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data. 1997, 26, 1329. (113) Cioslowski, J.; Schmeczek, M.; Liu, G.; Stoyanov, V. J. Chem. Phys. 2000, 113, 9377. (114) Atkinson, R.; Baulch, R. A.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data 1997, 26, 521. (115) Talakin, O. G. Russ. J. Phys. Chem. 1962, 36, 561. (116) Lee, T. J. J. Phys. Chem. 1995, 99, 1943.

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