The Journal of
Physical Chemistry VOLUME 98, NUMBER 18, MAY 5, 1994
0 Copyright 1994 by the American Chemical Society
LETTERS Ideal Gas Thermodynamic Properties of HOBr M. P. McGrath' and F. S. Rowland Department of Chemistry, University of California, Irvine, California 9271 7 Received: January 28, 1994; In Final Form: March 16, 1994'
On the basis of the Gaussian-2 theory of molecular energies, supplemented with empirical data, we have determined the ideal gas heat of formation of HOBr, AZf~fO(300),to be-14.2 f 1.6 kcal mol-'. This is in contrast to the widely used estimate of -19 kcal mol-' and the recently suggested value of -9 kcal mol-'. Thermodynamic data for HOBr are derived in the 0-500 K range and used to compute reaction energies of importance to atmospheric chemistry. Introduction Hypobromous acid, HOBr, is a potentially important trace gas in the atmosphere. It can be formed by reactions 1 and 2, whose kinetics have been studied previously.',*
+ -
+ HO BrO + HOO Br,
Although products of the Br observed, reaction 3
Br
+ HOOH
HOBr + Br HOBr + 0,
(1)
(2)
HOOH reaction have not been
HOBr + HO
(3)
is probably a minor channel; the major products are likely to be HBr H00.1.2 Recent interest in tropospheric HOBr has centered on its possible uptake into sulfuric acid aerosols and possible subsequent condensed-phase chemistry.' Presumably an important loss process of HOBr is photolysis
+
HOBr + hv
-
+
HO + Br
(4)
BrO + H
(5)
where, by analogy with HOC1, reaction 4 is expected to be the major channel.lJ Reactions 2 and 4 are the key reactions involving stratospheric HOBr in the catalytic destruction of ozone. This Abstract published in Advance ACS Absrracrs, April 15, 1994.
cycle has received renewed interest since the recent remeasurement of the rate constant of reaction 2.4-5 Although the geometrical structure6 and infrared spectra' of HOBr have been determined, its thermodynamic properties, until very recently, have been limited to a single estimate of A H f O (300) = -19 kcal mol-' by Benson.8 This value has been incorporated into the thermochemical compilations used in atmospheric chemistry.Iv2 Monks et al.9 have challenged Benson's estimate and suggested a much higher value, -9 kcal mol-', for AHfO(300) of HOBr. This value is based on the observed ionization energy of HOBr and an estimated heat of formation of the cation, HOBr+(ZA").gb In view of the discrepancy between the two previous estimates of the heat of formation of HOBr, and the need for thermochemical data to study atmospheric processes, we report an accurate determination of various ideal gas thermodynamic properties of HOBr, based on the Gaussian-2 (G2)lo theory of molecular energies, supplemented with empirical data.
Theoretical Methods The G2 theory of molecular energies was proposed by Curtiss et al.10asa more accurate replacement for the original, Gaussian-1 (Gl)" theory. Thus, for 55 small molecules composed of atoms above the third row (i.e.,H-Cl), G1 predicts total atomization energies with an average absolute deviation of 1.56 kcal mol-' from well-established experimental values, whereas the average absolute deviation in the G2 predictions is 1.16 kcal mol-l.10 For
0022-3654/94/2098-4173%04.50/0 0 1994 American Chemical Society
4774
Letters
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994
TABLE 1: HOBr
(kcal mol-')
+ C10
theoretical method' MP2/6-31G(d) MP2/6-31 lG(d,p) MP2/6-31l+G(Zdf,p) MP2/6-311+G(3df,2p)
-
HOC1 + BrO Reaction Energies theoretical method'
AE, 4.3 3.4
4.0 4.5
QCISD(T)/6-31 lG(d,p) Glb G2'
AE,
0
1.8 2.2 2.8
100 200 300 400
Used MP2/6-31G(d) geometries. b Does not include the zero-pint correction. The respective G1 energies E, of BrO and HOBr are -2647.595 92 and -2648.262 47 hartrees. CDoes not include the zeropoint correction. The respective G2 energies E, of BrO and HOBr are -2647.602 85 and -2648.271 04 hartrees. a
example, the atomization energies of HOCl at G1 and G2 are 156.1 and 156.8 kcal mol-',lo respectively, which compare favorably to the experimentalI2J3value of 156.3 f 0.5 kcal mol-'. G 1 theory was extended for use in bromine-containing molecules, and results of comparable accuracy were demonstrated, as long as empirical spin-orbit corrections are explicitly i n c l ~ d e d . ' ~ Subsequently, both G 1and G2 theories were extended to molecules containing any of the third row, main group elements.'6 The G1 and G2 energies in this work were computed using the GAUSSIAN 92 program system.17
Results and Discussion The atomization energy of HOBr is predicted to be 150.4 kcal mol-' at G1 and 150.8 kcal mol-' a t G2. Using the JANAF Thermochemical Tables12 for the atoms H, 0, and Br, these energies imply respective HOBr AHfO(0) values of -11.6 and -1 2.0 kcal mol-l. We could use the -1 2.0 kcal mol-' value, along with the observed molecular properties of HOBr, as a basis for generating a set of ideal gas thermodynamic properties. However, we choose a second, independent method to determine the A H f O (0) of HOBr. In order to further the accuracy of our G2 based thermochemistry, we have calculated reaction energies for the isodesmic, isogyric, halogen-exchange reaction HOBr
+ C10
-
HOCl
+ BrO
(6)
This reaction was chosen to encourage error cancellation, by matching both the number and type of reactant and product covalent bonds and valence nonbonded electrons. The total electronic energy changes AEe using various theoretical methods are shown in Table 1. Note that since the number of paired and unpaired valence electrons is the same on both sides of the arrow in reaction 6, the empirical "higher level" contributions to the G1 and G2 reaction energies cancel; so all of the AE, in Table 1 may be regarded as a b initio. Because G1 and G 2 reaction energies are good approximations to the actual QCISD(T)/6-3 l l + G (2df,p) and QCISD(T)/6-31 l+G(3df,2p) values,'* we can compare MP2 and QCISD(T) AE, as the basis set is extended from 6-31 lG(d,p) to 6-31 1+G(2df,p) to 6-311+G(3df,2p). For both levels of theory, each basis extension increases AE,by 0.50.6 kcal mol-l. But raising the level of theory from MP2 to QCISD(T) decreases Meby 1.7-1.8 kcal mol-' in the three comparisons. Thus, a relatively high level of theory and a n extended basis set are needed to calculate the energy of reaction 6, despite the error cancellation evident in the MP2/6-3 1G(d) AE,. We estimate the residual difference in the G2 reaction energy, from the unknown exact, nonrelativistic AE,, to be within i 0 . 5 kcal mol-l. To our G2 reaction energy of 2.85 f 0.50 kcal mol-', we need to add spin-orbit (A&) and zero-point vibrational (AEzPE) energy corrections. The empirical spin-orbit correction for the C10 and BrO radicals is calculated from their ground state 211~/2* l l 3 / 2 splittings19*20as
AEso = -'/,(968.0 - 321.8) cm-'
TABLE 2
Ideal Gas Thermodynamic Properties of HOBP
0 7.97
0 50.1 55.7 59.3 62.0 64.2
0
0.80 1.61 8.45 2.49 9.18 3.44 9.83 500 10.33 4.45 0 Units: Tin K; CPoand So in cal mol-'
-11.7 -11.9 -12.4 -14.2
K-l;
-11.7
-18.1
-13.0 -13.9 -14.5 -13.8
-18.2
-12.7
otherwise kcal mol-l.
The spin-orbit corrections for the closed-shell singlets HOCl and HOBr, which we have not included, are expected to be much smaller and to partially cancel. The zero-point vibrational energy change, AEZPE= 40.3 cm-1, is calculated from the observed fundamental vibrational frequencies of C10,21 Br0,22 HOCl,23 and HOBr,7 weighting the isotopic variations using the natural abundances of 35~3~Cl and 79.81Br. After applying these two corrections, the A Z f O ( 0 ) of reaction 6 emerges as 2.35 f 0.55 kcal mol-' . Now the experimentally based AHfO(0) (kcal mol-' units) of C10 (24.15 f 0.02),24BrO (31.90 f 0.57),25 and HOCl (-17.10 f O.50)l2J3can be combined with the semiempirical A H O ( 0 ) of reaction 6 derived above, to determine the AHf"(0) of HOBr, -1 1.7 f 1.6 kcal mol-'. Here we have treated the uncertainties conservatively by simply adding them. Note that this agrees with the value of -12.0 kcal mol-' determined using the G2 atomization energy of HOBr, which has a somewhat larger uncertainty associated with it. We used the AHfO(0) of HOBr, along with theobserved (rs) structure6and fundamental vibrational freq~encies,~ to derive ideal gas heat capacities Cpo(T),entropies So(T),heats of formation AHfo(T), and freeenergies of formation AGfO(7') in the usual rigid rotor, harmonic oscillator approximation.26 Weighted averages for H079Brand H08'Br were taken. The results are displayed in Table 2 for several temperatures. Note that because the reference state of Br2 changes from crystal to liquid at 265.9 K and from liquid to ideal gas a t 332.5 K, the temperature dependences of AHfo(T) and AGfo(T) are not as smooth as might be expected based on cursory examination of the analogous functional dependencies for HOC1.l2 It is of interest to address the differences between the present determination of the AHfO(300) of HOBr (-14.2 kcal mol-') and ref 9b (-9 kcal mol-'), where the observed adiabatic ionization energy (IE) of HOBr (245 kcal mol-') was subtracted from a semiempirical estimate of AHfo(300) of HOBr+ (236 kcal mol-l), which was derived by combining the experimentally based heats of formation of H+ (ion convention)12and BrO25 with a theoretical proton affinity of Br0,9b,29calculated using the CASSCF+ 1+2/ CEP-SVP method. In this method of electron correlation, all singly and doubly excited configurations of the valence electrons from the multiconfigurational complete active space, selfconsistent-field (CASSCF) reference wave function are constructed; the "atomic orbital" or one-electron basis is of splitvalence plus single polarization (SVP) quality, and the core electrons of oxygen ( N = 2) and bromine ( N = 28) are described by compact effective potentials (CEP). The G2 IE of HOBr is 10.64 eV a t both 0 and 300 K,16 in agreement with the experimental value of 10.62 f 0.04 eV a t 300 K.9b Adding the G2 IE to the AHfO(300) of HOBr (Table 2) gives the AHf"(300) of HOBr+, 231.2 i 3.0 kcal mol-l. Here we have conservatively added the maximum uncertainty in the G2 IE (evidently 0.06 eV) to the uncertainty in the heat of formation of HOBr (1.6 kcal mol-'). Therefore, the psIr0(3O0) value for HOBr+ derived in ref 9b is too large by at least 1.8 kcal mol-'. Benson's determination of AHfO(300) of HOBr(g), in part, involved taking a heat of formation of the undissociated weak acid in aqueous solution, HOBr(ao), and subtracting an estimate of the heat of hydration: (-31) - (-12) = -19 kcal mol-1.8,30 AHfO(300) of HOBr(ao) is given as -27.0 kcal mol-' in ref 25a,
Letters
The Journal of Physical Chemistry, Vol. 98, No. 18, 1994 4775
TABLE 3 Ideal Cas Entbalpy and Free Energy Changes (kcal mol-') for Reactions 1-5
--- -
reaction
LW'(0)
G(300)
AG'(300)
+ H O HOBr + Br BrO + H O O HOBr + 02 Br + H O O H HOBr + H O HOBr H O + Br HOBr BrO + H
-3.8 -47.1 0.5 49.2 95.2
4.2 47.1 1.o 50.3 96.4
-3.8 -46.1 -0.6 42.4 88.9
Brz
which implies (Table 2) a heat of hydration of -12.8 kcal mol-' at 300 K. Assuming the entry in ref 25a is reliable, the major source of error in the -19 kcal mol-l value lies in the AHfo(300) of HOBr(ao) that was used.
Conclusions In contrast to two previously reported8.9bvalues of AHfO(300) of HOBr, -19 and -9 kcal mol-', we have determined the A H f O (300) to HOBr to be -14.2 f 1.6 kcal mol-'. Indeed, the compilation of Table 2 is the only reliable set of ideal gas thermodynamicdata currently available for HOBr. Using Table 2, along with the best available thermochemical data for H,I2 Br,IZ Br2,I2 HO,' Br0,2S HO0,27 and HOOH,28 energies for reactions 1-5 were calculated. The results, shown in Table 3, are of course quite different from values calculated using the previously recommended's2 AHfO(300) of -19 kcal mol-I. For example, the peroxide insertion reaction 3 is actually close to being thermoneutral.
Acknowledgment. M.P.M. thanks the Joan Irvine Smith and Athalie Clark Foundation for postdoctoral fellowship support. The research was supported by Department of Energy Contract DE-FGO3-86ER-13469. References and Notes (1) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Troe. J. J . Phys. Chem. Re/. Data 1992, 21, 1125. (2) 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 for Use in Stratospheric Modeling; Evaluation Number 10; NASA JPL Publ. 1992, No. 92-20. (3) (a) Fan, S.-M.; Jacob, D. J. Nature 1992,359,522. (b) FinlaysonPitts, B. J.; Livingston, F. E.; Berko, H. N. Nature 1990, 343, 622. (4) Poulet, G.; Pirre, M.;Maguin, F.; Ramaroson, R.; Le Bras, G. Geophys. Res. Lett. 1992, 19, 2305. (5) Bridier, I.; Veyret, B.; Lesclaux, R. Chem. Phys. Lett. 1993, 201, 563. (6) Koga, Y.; Takeo, H.; Kondo,S.; Sugie, M.; Matsumura, C.; McRae, G. A.; Cohen, E. A. J . Mol. Spectrosc. 1989, 138, 467.
(7) (a) McRae, G. A.; Cohen, E. A. J. Mol. Spectrosc. 1990,139,369. (b) Schwager, I.; Arkell, A. J. Am. Chem. Soc. 1%7,89, 6006. (8) Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley: New York, 1976. See also the discussion in ref 9b. (9) (a) Monks, P. S.; Nesbitt, F. L.; Scanlon, M.; Stief, L. J. J. Phys. Chem. 1993, 97, 11699. (b) Monks, P. S.; Stief, L. J.; Krauss, M.; Kuo, S. C.; Klemm, R. B. J . Chem. Phys. 1994,100, 1902. We thank Dr. Stief for a preprint of (b). (10) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys. 1991, 94, 7221. (1 1) (a) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, 5622. (b) Curtiss, L. A,; Jones, C.; Trucks, G. W.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1990,93,2537. (12) Chase, M. W., Jr.; Davies, C. A,; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; J . Phys. Chem. Rej. Data 1985, 14 (Suppl. No. 1). (13) Despite good agreement between thevarious experimental determinations of the heat of formation of HOC1,14 AH~,'(298)ranging between -17.8 and -18.0 kcal mol-', ref 2 assigns an uncertainty of &3 kcal mol-l for this value. (14) (a) Molina, L. T.; Molina, M. J. J . Phys. Chem. 1978,82,2410. (b) Knauth, H.-D.; Alberti, H.; Clausen, H. J. Phys. Chem. 1979,83, 1604. (c) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. Chem. Phys. Lett. 1979,66,325. (d) Ennis, C. A,; Birks, J. W. J. Phys. Chem. 1985,89, 186. (15) McGrath, M. P.; Radom, L. J. Chem. Phys. 1991, 94, 511. (16) Curtiss, L. A.;Davis, N.; McGrath, M. P.; Radom, L. Tobepublished. (17) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foreman, J. B.; Johnson, B. G.; Schlegel, H.B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari. K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92; Gaussian, Inc.: Pittsburgh, 1992. (18) Curtiss, L. A.; Carpenter, J. E.; Raghavachari, K.; Pople, J. A. J . Chem. Phys. 1992, 96,9030. (19) Coxon, J. A. Can. J. Phys. 1979,57, 1538. (20) McKellar, A. R. W. J . Mol. Spectrosc. 1981, 86, 43. (21) (a) Lang, V. I.; Sander, S. P.; Friedl, R. R. J . Mol. Spectrosc. 1988, 132,89. (b) Burkholder, J. B.; Hammer, P. D.; Howard, C. J.; Maki, A. G.; Thompson, G.; Chackerian, C. J . Mol. Spectrosc. 1987, 124, 139. (22) Orlando, J. J.; Burkholder, J. B.;Bopegedera, A. M. R. P.; Howard, C. J. J. Mol. Spectrosc. 1991, 145, 278. (23) (a) Wells, J. S.; S a m , R. L.; Lafferty, W. J. J. Mol. Spectrosc. 1979, 77,349. (b) Lafferty, W. J.; Olson,W. B.J . Mol. Spectrosc. 1986,120,359. (24) Abramowitz, %;Chase, M. W., Jr. PureAppl. Chem. 1991,63,1449. (25) (a) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J . Phys. Chem. Re/. Data 1982, I1 (Suppl. No. 2). (b) Durie, R. A,; Ramsay, D. A. Can. J . Phys. 1958, 36, 35. (26) McQuarrie, D. A. StatisticalMechanics; Harper & Row: New York, 1973; Chapter 8. (27) Bauschlicher, C. W.; Partridge, H. Chem. Phys. Lett. 1993,208,241. (28) (a) Giguere, P. A.; Liu, I. D. J. Am. Chem. Soc. 1955,77,6477. (b) Flaud, J.-M.; Camy-Peyret, C.; Johns, J. W. C.; Carli, B. J . Chem. Phys. 1989, 91, 1504. The torsional potential energy function reported in (b) was used to improve the treatment of internal rotational from that carried out in (a). (29) Monks, P. S.; Stief, L. J.; Krauss, M.; Kuo, S. C.; Klemm, R. B. Chem. Phys. Lett. 1993, 211, 416 and references therein. (30) Benson, S . Private communication, 1994.
