9250
J. Phys. Chem. 1996, 100, 9250-9253
Ab Initio Study of the Electronic Spectrum of HOBr Joseph S. Francisco* Department of Chemistry and Department of Earth and Atmospheric Sciences, Purdue UniVersity, West Lafayette, Indiana 47907-1393
Michael R. Hand and Ian H. Williams School of Chemistry, UniVersity of Bath, Bath BA2 7AY, U.K. ReceiVed: October 6, 1995; In Final Form: March 25, 1996X
The structure and vibrational spectra of HOBr calculated using ab initio post-Hartree-Fock methods are in reasonable agreement with experiment. Vertical excitation energies and oscillator strengths have been computed for transitions to low-lying excited states of HOBr. The peaks at 350 and 280 nm in the gas-phase absorption spectrum reported by Orlando and Burkholder (J. Phys. Chem. 1995, 99, 1143-1150) may be attributed to ˜ 1A′ states, respectively. The calculations predict another absorption with a maximum at the A ˜ 1A′′ and B about 477 nm due to the a˜ 3A′′ state.
I. Introduction The stratospheric chemistry of halogenated compounds is important because of their role in ozone depletion processes. Hypobromous acid, HOBr, an atmospherically significant molecule,1,2 may be formed by reaction (1) of hydroperoxy radicals with bromine monoxide or by hydrolysis (2) of bromine nitrate on or in aerosol particles.3-5 Important loss processes of HOBr are photolysis6,7 (3) and reaction with atomic oxygen (4).8 The HO2 BrONO2 HOBr HOBr
+ + + +
BrO H2O hν O(3P)
f f f f
HOBr HOBr HO HO
+ + + +
O2 HONO2 Br BrO
(1) (2) (3) (4)
significance of HOBr is due to its involvement in the catalytic cycle (5), (6), (1), (3) for destruction of ozone.9,10 Br HO HO2 HOBr net
+ + + +
O3 O3 BrO hν 2O3
f f f f f
BrO HO2 HOBr HO 3O3
+ + + +
O2 O2 O2 Br
(5) (6) (1) (3)
To evaluate the role of HOBr in processes which perturb oddoxygen chemistry in the atmosphere, it is essential to understand its photolysis. No experimental gas-phase UV/visible spectrum was available until the recent observation by Orlando and Burkholder11 of two absorption peaks in the range 200-420 nm. To aid the assignment of these observed features to transitions to particular electronic excited states, we now report the results of ab initio quantum-chemical calculations of the structure and vibrational frequencies of HOBr in its ground state together with vertical excitation energies and oscillator strengths for transitions to low-lying singlet and triplet states. II. Computational Method The equilibrium structure and vibrational frequencies of HOBr were computed using the GAUSSIAN 92 program12 with the 9s6p2d(d) basis of Binning and Curtiss13 for bromine and 6-311G(d,p) for oxygen and hydrogen. The methods employed were second-order Møller-Plesset perturbation theory (MP2) with all electrons correlated,14 configuration interaction theory X
Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(95)02978-9 CCC: $12.00
TABLE 1: Numbers of Configuration State Functions in MRCISD Calculations
HOBr
1A′ 1A′′ 3A′ 3
HOCl
A′′ A′ 1A′′ 3 A′ 3A′′ 1
reference space
contracted configurations
uncontracted configurations
106 90 100 110 106 90 100 110
76 152 75 213 95 757 96 091 99 954 98 721 123 225 123 637
2 060 970 1 888 116 3 459 519 3 335 158 2 942 146 2 708 838 4 943 515 4 792 126
in the space of single and double excitations (CISD),15 and coupled-cluster with single and double excitation and perturbative corrections for triple excitations [CCSD(T)].16 Calculations for excited states of HOBr were performed using the CIS method17 in GAUSSIAN 92, and for both HOBr and HOCl the MOLPRO program18 was employed for excited-state calculations using the complete-active-space self-consistent-field (CASSCF)19 method with state-averaged orbitals, in order to avoid bias in the excitation energies. A separate CASSCF calculation was necessary for electronic states of each symmetry species of each spin multiplicity, and in each case the stateaveraging involved only those states with vertical excitation energies less than about 7 eV. For the 1A′ states, the average of the ground and first excited states was taken; for the 1A′′ states, the average of the X ˜ 1A′ and the first three states was taken. This allowed calculation of the transition dipole moment, and hence the oscillator strength, between the ground and excited singlet states. For the triplet states of both A′ and A′′ symmetry, averages of the first two states were used. The molecular orbitals (MOs) obtained from these four CASSCF calculations were subsequently used in multireference configuration interaction (MRCISD) calculations20 for the ground and excited states. These were of the internally contracted type and used the projection method of Knowles and Werner.21 The Hartree-Fock electronic configuration for the X ˜ 1A′ 2 2 2 2 ground state of HOBr is (core) (14a′) (5a′′) (15a′) (16a′) (6a′′)2. Of the in-plane MOs, 14a′ and 15a′ are σ bonding and 16a′ is nonbonding, localized mainly on Br; the lowest two virtuals 17a′ and 18a′ are σ* antibonding orbitals. The out-of-plane MOs 5a′′ and 6a′′ are nonbonding and are localized on O and Br, respectively. An active space of 10 electrons in seven © 1996 American Chemical Society
Ab Initio Study of the Electronic Spectrum of HOBr
J. Phys. Chem., Vol. 100, No. 22, 1996 9251
TABLE 2: Optimized Geometry and Total Energiesb for Ground-State HOBr (X ˜ 1A′) 962(d)/6-311G(d,p) CISD CCSD(T)
MP2 HO OBr HOBr energy a
0.966 1.865 100.9 -2648.278 75
0.955 1.842 102.8 -2648.010 40
0.964 1.884 100.9 -2648.066 38
TZ2Pc CCSD(T)
0.966 1.897 100.1 -2647.916 41
0.964 1.853 102.3 -2648.220 65
exptd 0.961 1.834 102.3
Bond distances in angstroms and bond angles in degrees. b Energies in hartrees. c Reference 25. d Reference 19.
TABLE 3: Calculated and Observed Vibrational ˜ 1A′) Frequenciesa for Ground-State HOBr (X 962(d)/6-311G(d,p) TZ2P MP2 CISD CCSD(T) CCSD(T) ν1 HO stretch 3959 3991 ν2 HOBr bend 1138 1233 ν3 OBr stretch 616 653 d
MRCISD
3837 1180 573
3807 1197 608
expt 3590,b 3614.9c 1164,b 1162.6d 626,b 620.18d
a Expressed as wavenumbers (cm-1). b Reference 26. c Reference 28. Reference 27.
orbitals (14a′-18a′ and 5a′′-6a′′) was used for the CASSCF calculations, derived from the valence p-orbitals on Br and O and the 1s-orbital on H. The reference configurations in the MRCISD calculations were the full set of configurations generated in the CASSCF active space, as enumerated in Table 1. The total number of basis functions for HOBr was 66 (48 of a′ symmetry and 18 of a′′ symmetry). The Hartree-Fock electronic configuration for ground-state HOCl is qualitatively the same as for HOBr, and the (10 in 7) active space was chosen in the same way. The Dunning22 correlation-consistent polarized valence double-ζ (cc-pVDZ) basis set was used for Cl, and 6-311G(d,p) for O and H, as for HOBr. The total number of basis functions for HOCl was 65 (49 of a′ and 16 of a′′ symmetry). III. Results and Discussion A. Ground State Structure and Vibrational Frequencies. Optimized geometries for HOBr are listed in Table 2, together with experimental values from microwave spectroscopy.23 The UMP2, CCSD(T), and MRCISD methods overestimate the BrO bond length and underestimate the bond angle, whereas best agreement with experiment is obtained with the CISD method. Francisco and Sander24 found the CISD method to give geometries in close agreement with experiment for FOCl and Cl2O using a range of small to large basis sets. Lee25 has recently reported a CCSD(T) optimized geometry in closer agreement with experiment for HOBr than our present CCSD(T) result (although not as close as our CISD result); he has used a triple-ζ double-polarized (TZ2P) basis which is larger than the basis we have used here. This suggests that the geometry is affected both by the level of treatment of dynamical correlation and by the size of the basis set employed. The infrared spectrum of HOBr was first observed by Schwager and Arkell,26 who photolyzed an Ar/HBr/O3 mixture at 4° K. Fundamental frequencies for the ν2 (HOBr bending) and ν3 (OBr stretching) modes were reported at high resolution by McRae and Cohen,27 and for the ν1 (HO stretching) mode by Cohen and co-workers.28 These experimental fundamentals are presented together with our calculated harmonic vibrational frequencies in Table 3. The frequency calculated for ν1 is overestimated by each method, with CCSD(T) giving the best results, the closer agreement with experiment being obtained with the bigger TZ2P basis set; note that this mode is likely to show appreciable anharmonicity. The ν2 mode is underestimated by MP2 but overestimated by the other methods, with our present CCSD(T) result being the best. Only the CISD
method overestimates the frequency for the ν3 mode, the others all giving values too low. Overall, the root-mean-square deviations from the experimental results of Cohen and coworkers are 6.9% for MP2, 9.3% for CISD, 6.2% for CCSD(T) using our 962(d)/6-311G(d,p) basis, and 4.3% for CCSD(T)/ TZ2P. B. Electronic Excited States of HOBr. Vertical excitation energies and oscillator strengths calculated for HOBr with the CIS and MRCISD methods are shown in Table 4. Since the excited states are dissociative in character, excitation of the molecule from the ground state is accompanied by loss of zeropoint energy from the ν2 and ν3 modes; the ν1 mode is still quantized in the excited states and may be assumed to be unaffected, to a first approximation. It is appropriate, therefore, to correct the calculated vertical excitation energies by subtraction from the electronic potential energy difference of the ground-state zero-point energy for the OBr stretching and HOBr bending modes; the excitation energies given in Table 4 have been corrected in this way. All of the excited states considered here arise from excitation of an electron into the antibonding σ*BrO MO 17a′, and all are dissociative in nature; the states differ only in regard to the identity of the MO out of which the electron is excited. For ˜ 1A′, and C ˜ 1A′′ excitation occurs the singlet states A ˜ 1A′′, B from the nonbonding nBr 6a′′, nonbonding nBr 16a′, and nonbonding nO 5a′′ MOs, respectively. In the triplet manifold, the states a˜ 3A′′, b 3A′, and c 3A′′ arise from electronic excitation from exactly the same three MOs, respectively, with spin inversion. In the absence of any treatment of spin-orbit coupling effects in our calculations, the oscillator strengths are all formally zero for triplet r singlet transitions. However, the presence of the heavy bromine atom in HOBr may be expected to facilitate such transitions. Before returning to a discussion of the vertical transition energies for HOBr, it is useful first to consider the HOCl molecule. Table 5 contains zero-point-energy-corrected vertical transition energies and oscillator strengths calculated with the MRCISD method for singlet excited states of HOCl. The experimental absorption spectrum29 shows a shoulder at about 300 nm (∼4.13 eV) and a peak at about 250 nm (∼4.96 eV). Nambu et al.30,31 performed MRCI calculations of two types to obtain vertical excitation energies for the lowest two singlet excited states. The first, which was biased toward the ground state, yielded (uncorrected) energies of 4.87 and 6.83 eV. Better agreement was claimed for the second set of calculations, which yielded (uncorrected) energies of 4.13 and 5.35 eV. Significantly though, these authors were able to reproduce the experimental spectrum satisfactorily both in shape and in intensity. Our corrected MRCISD results for HOCl (following subtraction of 0.12 eV for the ground-state zero-point energy of the HOCl bend and OCl stretch) give vertical excitation energies at the experimental geometry of 4.51 and 5.68 eV for the lowest two singlet states (corresponding to 275 and 218 nm, respectively), in good agreement with the calculations of Bruna et al.32 and in fair accord with experiment. The essential point of our calculations for HOCl is to establish the reasonableness
9252 J. Phys. Chem., Vol. 100, No. 22, 1996
Francisco et al.
TABLE 4: Vertical Excitation Energiesa (E/eV) and Oscillator Strengths (f) for Singlet and Triplet States of HOBr MRCISD method
CIS method exptl geom
MRCISD geom
CCSD(T) geom
exptl geom
state
E
f
E
f
E
f
E
f
A 1A′′ B 1A′ C 1A′′ a 3A′′ b 3A′ c 3A′′
4.16 5.08 7.89 2.95 3.72 5.97
0.6 × 10-3 5.5 × 10-3 8.9 × 10-3
3.29 4.24 5.57 2.48 3.44 5.17
1.8 × 10-6 1.0 × 10-3 3.7 × 10-3
3.39 4.35 5.77 2.57 3.53 5.35
1.0 × 10-7 1.2 × 10-3 4.1 × 10-3
3.66 4.69 6.38 2.84 3.80 5.95
1.0 × 10-5 1.6 × 10-3 5.9 × 10-3
a Corrected by subtraction of zero-point energy (0.11 eV, based on experimental frequencies) for ground-state HOBr bending and OBr stretching modes.
TABLE 5: MRCISD Vertical Excitation Energiesa (E/eV) and Oscillator Strengths (f) for Singlet and Triplet States of HOClb state 1A′′
A B 1A′ C 1A′′ a 3A′′ b 3A′ c 3A′′
E
f
4.51 5.68 7.75 3.47 4.68 7.09
1.9 × 10-5 1.7 × 10-3 6.2 × 10-3
a
Corrected by subtraction of zero-point energy (0.12 eV, based on MP2/6-311G(d,p) frequencies) for ground-state HOCl bending and OCl stretching modes. b At experimental geometry: O-H ) 0.960 Å, Cl-O ) 1.689 Å, H-O-Cl ) 102.5°; total energy for X 1A′ ground state ) -535.240 83 hartrees.
of the procedures employed for the study of HOBr. That we obtain results consistent with the accepted spectroscopic assignments for HOCl lends support to our predictions for HOBr. The UV/visible absorption spectrum observed for gas-phase HOBr shows two peaks (350 and 280 nm) with intensities in the ratio of about 1:4. Initial inspection of the calculated results in Table 4 might lead to the conclusion that these peaks correspond to transitions from the ground state to the B and C states, respectively, since these transitions have calculated oscillator strengths in the ratio roughly of 1:4 also. However, it is doubtful whether these calculated oscillator strengths should be trusted in any quantitative fashion, and the calculated ˜ 1A′ and C ˜ 1A′′ r X ˜ 1A′ are transition energies for B ˜ 1A′ r X much too high to account for the observed absorptions, which correspond to energies of about 3.54 and 4.43 eV. Just as for HOCl, so for HOBr there is reasonable agreement with the energies (3.66 and 4.69 eV) calculated for transitions to the lowest two singlet states at the experimental geometry for the ground state. It should be noted that these transition energies are rather sensitive to the choice of geometry. Although there would be internal consistency in taking the geometry optimized with the same method as used to evaluate to transition energies, there is no guarantee that the MRCISD method, with the particular basis set employed in this work, correctly predicts the displacements of the repulsive excited-state potential energy curves relative to the ground state. Perhaps fortuitously, use of the experimental ground-state geometry leads to the smallest error in the energies for vertical transitions to the A ˜ and B states. In passing, it may be noted that the critical dependence of the excitation energies upon geometry may explain why our results for HOBr are in apparently better agreement with experiment than are those for HOCl. Barnes et al.33 have recently observed an absorption band at about 440 nm which they claim to be due to HOBr. Since it has been argued above that the shoulder at about 300 nm should be attributed to the A ˜ 1A′′ state, any absorption at longer
Figure 1. Schematic representation of the a˜ 3A′′ r X 1A′ excitation leading to dissociation: HOBr f HO + Br. Excitation of a single electron with spin inversion from the out-of-plane nBr nonbonding MO to the in-plane σOBr* antibonding MO occurs, leading to a singly occupied in-plane MO on the hydroxyl radical fragment and a singly occupied out-of-plane AO on the atomic bromine fragment. Along with this, polarization of the in-plane σOBr bonding MO occurs, leading to a doubly occupied in-plane AO on the atomic bromine fragment. The electronic state of the hydroxyl radical may therefore be considered as 2A′.
wavelength clearly could not arise from a transition to a singlet excited state. Inspection of Table 4 reveals a calculated vertical excitation energy of 2.85 eV (437 nm) for the a˜ 3A′′ r X ˜ 1A′ transition. Lock et al.34 have inferred that the transition is of A′ symmetry, which appears to be inconsistent with our suggestion that this absorption involves a transition to the a˜ 3A′′ state. Assuming the interpretation of the experiments to be correct, we would simply note that spin-orbit coupling between the a˜ 3A′′ state and a remote singlet state of A′ symmetry may possibly account for the observed intensity and symmetry of the transition through borrowing. Such behavior has previously been noted35 for NOCl: MRCISD calculations attributed a longwavelength band in the spectrum of this molecule to the a˜ 3A′′ r X ˜ 1A′ transition, for which measurements of the recoil anisotropy and rotational alignment indicated A′ symmetry. It was proposed that mixing between the a˜ 3A′′ state and higher 1A′ states was responsible for the oscillator strength, thus determining the values of the β and A(2) 0 parameters, and that only a small percentage of the appropriate singlet wave function was required to yield the experimentally observed intensity; the a˜ state was still predominantly 3A′′ in character, and Λ-doublet
Ab Initio Study of the Electronic Spectrum of HOBr populations reflected the symmetry of the excited-state MO as predicted by the calculations.35 All of the excited states considered in our theoretical study of HOBr involve promotion of an electron into the in-plane σ*BrO antibonding MO. Dissociation of the molecule along the OBr coordinate in each of the excited states therefore gives rise to a hydroxy radical fragment with its unpaired electron in the plane of symmetry of the molecule. In the case of the a˜ 3A′′ rX ˜ 1A′ transition, the promoted electron comes from the outof-plane nonbonding nBr MO, and the electron left behind in this orbital is the unpaired electron on the atomic bromine fragment of the dissociating molecule (Figure 1). Finally, it may be noted that the lowest triplet excited state of HOCl is predicted to lie at 3.47 eV, which would correspond to an absorption at about 357 nm, which might be observable if spin-orbital coupling were sufficient to give some intensity ˜ 1A′ transition in this to the formally forbidden a 3A′′ r X molecule. Acknowledgment. We thank A. Sinha for bringing to our attention this problem and for helpful discussions. Support for the computing research was provided by the JPL Supercomputing Project. The JPL Supercomputing Project is sponsored by JPL and the NASA Office of Space Science and Application. I.H.W. thanks the NERC Atmospheric Chemistry Initiative for support of this research. References and Notes (1) Poulet, G.; Pirre, M.; Maguin, F.; Romaroson, R.; Le Brag, G. Geophys. Res. Lett. 1992, 19, 2305. (2) Bridler, I.; Veyret, B.; Lesclaux, R. Chem. Phys. Lett. 1993, 201, 563. (3) Fan, S. M.; Jacob, D. J. Nature 1992, 359, 522. (4) Finlayson-Pitts, B. J.; Livingston, F. E.; Berko, H. N. Nature 1990, 343, 622. (5) Hanson, D. J.; Ravishankara, A. R. NATO ASI Ser. 1993, 17, 281. (6) Atkinson, R.; Bauleh, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Troe, J. J. Phys. Chem. Ref. Data 1992, 21, 1125. (7) De More, 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
J. Phys. Chem., Vol. 100, No. 22, 1996 9253 Modeling; Evaluation No. 10; NASA JPL Publ. 1992. (8) Monks, P. S.; Nesbitt, F. L.; Scanlon, M.; Stief, L. J. J. Phys. Chem. 1993, 97, 11699. (9) Yang, Y. L.; Pinto, J. P.; Watson, R. J.; Sander, S. P. J. Atmos. Sci. 1980, 37, 379. (10) Garcia, R. R.; Solomon, S. J. Geophys. Res. 1994, 99, 12937. (11) Orlando, J. J.; Burkholder, J. B. J. Phys. Chem. 1995, 99, 1143. (12) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, 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. GAUSSIAN92, Revision A; Gaussian, Inc.: Pittsburgh, PA 1992. (13) Binning, R. C.; Curtiss, L. A. J. Comput. Chem. 1990, 11, 1206. (14) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J. Quantum Chem. Symp. 1976, 10, 1. (15) Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8, 61. (16) Lee, T. J.; Rendell, A. P. J. Chem. Phys. 1991, 94, 6219. (17) Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. J. Phys. Chem. 1992, 96, 135. (18) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. (19) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. (20) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 145, 514. (21) Knowles, P. J.; Werner, H.-J. Theor. Chim. Acta 1988, 84, 95. (22) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007. Woon, D. E.; Dunning, T. H. J. Chem. Phys. 1993, 98, 1358. (23) Koga, Y.; Takeo, H.; Kondo, S.; Sugie, M.; Matsumura, C.; McRae, G. A.; Cohen, E. A. J. Mol. Spectrosc. 1989, 138, 467. (24) Francisco, J. S.; Sander, S. P. Chem. Phys. Lett. 1994, 223, 439. (25) Lee, T. J. J. Phys. Chem. 1995, 99, 15074. (26) Schwager, I.; Arkell, A. J. Am. Chem. Soc. 1967, 89, 6006. (27) Mc Rae, G. A.; Cohen, E. A. J. Mol. Spectrosc. 1990, 139, 369. (28) Cohen, E. A.; McRae, G. A.; Tan, T. L.; Friedl, R. R.; Johns, J. W. C.; Noel, M. J. Mol. Spectrosc. 1995, 173, 55. (29) Molina, L. T.; Molina, M. J. J. Phys. Chem. 1978, 82, 2410. Mishalanie, E. A.; Rutkowski, C. J.; Hutte, R. S.; Birks, J. W. J. Phys. Chem. 1986, 90, 5578. (30) Nambu, S.; Nakata, K.; Iwata, S. Chem. Phys. 1989, 135, 75. (31) Nambu, S.; Iwata, S. J. Phys. Chem. 1992, 96, 2102. (32) Bruna, P. J.; Hirsch, G.; Peyerimhoff, S. D.; Buenker, R. J. Can. J. Chem. 1979, 57, 1839. (33) Barnes, R. J.; Lock, M.; Coleman, J.; Sinha, A. J. Phys. Chem. 1996, 100, 453. (34) Lock, M.; Barnes, R. J.; Sinha, A. J. Phys. Chem., submitted. (35) Bai, Y. Y.; Qian, C. X. W.; Iwata, L.; Segal, G. A.; Reisler, H. J. Chem. Phys. 1989, 90, 3903.
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