Excited States of Dibromine Monoxide (Br2O): MRCI, Coupled Cluster

Apr 26, 2010 - Department of Chemistry and Centre for Laser, Atomic and Molecular Sciences, University of New Brunswick, PO Box 4400, Fredericton, N.B...
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J. Phys. Chem. A 2010, 114, 6157–6163

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Excited States of Dibromine Monoxide (Br2O): MRCI, Coupled Cluster, and Density Functional Studies Friedrich Grein* Department of Chemistry and Centre for Laser, Atomic and Molecular Sciences, UniVersity of New Brunswick, PO Box 4400, Fredericton, N.B. E3B5A3 Canada ReceiVed: March 10, 2010; ReVised Manuscript ReceiVed: April 8, 2010

Vertical excitation energies up to about 9 eV, and related oscillator strengths, were calculated by multireference configuration interaction (MRCI) methods for singlet and triplet states of BrOBr in C2V symmetry, including the low-lying s- and p-Rydberg states. Observed maxima in the visible/UV spectra were identified as excitations to 13B1 (665 nm, 1.86 eV), 11B1 (520 nm, 2.38 eV), 11B2 (355 nm, 3.49 eV), 21A1 (314 nm, 3.94 eV), and 31B2 (∼200 nm, ∼6.20 eV). The calculated vertical excitation energies lie within 0.1 eV of the observed values. Many more singlet and weaker triplet excitations are predicted. Although most excited states have small oscillator strengths, that of 31B2 is very large. Vertical excitation energies were also calculated at the 11A′ ground state geometry of the BrBrO isomer. Using DFT/B3LYP and CCSD(T) (CC) methods with the 6-311+G(3df) basis set, geometries were optimized for about 12 excited singlet and triplet states of BrOBr in C2V symmetry. Frequency analysis showed that many states, including 11B1, 11B2, 13B1, and 13B2, are not stable. Cs structures corresponding to 11B1, 13B1, and 13B2 were optimized. In addition, geometry optimizations were performed for the lowest singlet and triplet A′ and A′′ states of BrBrO. This isomer lies 0.61 (CC) to 0.66 eV (MRCI) above BrOBr. Comparison was made with the lowest excited states of Cl2O and F2O. Introduction Halogen compounds are known to play a crucial role in ozone depletion. Chlorine-containing species have been extensively studied over many years. Much less is known about bromine compounds. Although bromine is not as abundant in the atmosphere as chlorine, it is known to be potentially more damaging to the ozone layer.1 Bromine oxides are difficult to characterize since many are unstable.2 Dibromine monoxide Br2O is found to have a very short lifetime. Br2O together with H2O is in equilibrium with HOBr, which is considered to be a reservoir of Br compounds in the atmosphere.3 The lowest energy isomer of Br2O has a symmetric BrOBr structure with C2V symmetry. The BrBrO isomer (Cs) has also been observed.4 Tevault et al.4 as well as Campbell et al.5 determined the structure of BrOBr by IR spectroscopy, whereas Levason et al.6 used IR and EXAFS spectroscopy. Using rotational spectroscopy, Mueller et al.2,7 obtained the experimental values re ) 1.83786 Å and Re ) 112.249°. The UV-visible spectrum of BrOBr was taken by several groups. Maxima near 200 nm and at 314 nm have been reported by Orlando and Burkholder.8 Deters et al.,3 measuring from 205 to 450 nm, found a maximum at 315 nm, with a shoulder at 355 nm. Rattigan et al.9 determined the absorption spectrum over the wavelength range 230-750 nm, finding maxima at 314, 350, 520, and 665 nm. The photoionization efficiency spectrum has been reported by Thorn et al.10 Photoelectron spectra were measured by Chau et al.,11 as well as Qiao et al.12 The reversible photoisomerization BrOBr T BrBrO was measured by Koelm et al.13 Fourier transform IR spectra of BrOBr in gas phase were taken by Chu and Li.14 By passing a mixture of Br2, O2, and Ar through a microwave discharge, Galvez et al.15 observed several bromine oxide species, among them BrBrO, but not BrOBr. * E-mail: [email protected].

Theoretical results for the ground state geometries and energies of BrOBr and BrBrO were reported in a number of papers.10-21 CCSD(T) (coupled cluster single and double substitutions with noniterative triple excitations), CASSCF (complete active space self-consistent field), and DFT (density functional theory) methods predicted the ground state geometry of BrOBr in good agreement with the experimental values. Theoretical data for the geometry of the 11A′ ground state of BrBrO are 2.51 Å (Br-Br), 1.69 Å (Br-O), 113.1° (Br-Br-O) (CCSD(T)),17 and 2.45-2.58 Å, 1.64-1.72 Å, 112.8-114.3°, depending on method.13 Its energy was calculated to be 0.70 eV17 and 0.67-0.80 eV13 above that of BrOBr. Vertical excitation energies (VEE) of singlet and triplet states of BrOBr and BrBrO were calculated by Koelm et al.13 using CASSCF and MCQDPT2 (multiconfiguration quasidegenerate secondorder perturbation) methods, in connection with their photoisomerization studies. The lowest excited singlet states 11B1, 11B2, and 11A2 (notation B1, B2 exchanged to conform with present convention, molecule in the yz plane) of BrOBr were reported to have MCQDPT2 VEE energies of 2.16, 3.11, and 3.34 eV, respectively. Chau et al.11 calculated the geometries and energies of low-lying triplet states of BrOBr in combination with their photoelectron spectra. In this work, a theoretical study of excited states of BrOBr and BrBrO was undertaken. At the optimized geometry for the ground state, vertical excitation energies were calculated by MRCI (multireference configuration interaction) methods. Geometries and adiabatic excitation energies of excited states were obtained using standard (spin-unrestricted) CC (coupled cluster) and DFT methods, by performing electron promotions appropriate for the particular excited state. Such methods were restricted to symmetric molecules, and cannot be applied to all excited states. Although single-determinant methods were not designed to handle excited states, and the additional problem of spin contamination is encountered for open-shell systems, they have

10.1021/jp102170h  2010 American Chemical Society Published on Web 04/26/2010

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nevertheless been applied to such purpose in many theoretical studies. Systematic investigations into the usefulness and performance of such methods have been undertaken by this author. Results for the dioxides TiO2,22 CrO2,23 FeO2,24 NO2,25 SeO2,26 on ozone,27 and on the tetroxides ClO428 and BrO4,29 have been published. It was found that energies usually lie within 0.5 eV of exact energies (CC values are usually better than DFT results) and that geometries compare reasonably well with the few available data known from experiments or high-level theoretical methods. However, there are exceptions that cannot easily be foreseen or explained, such as the energy and geometry of the 11B2 state of ozone. It has been suggested27 to take CC and DFT calculated Vertical excitation energies as a guide. If they lie close to MRCI values, the optimized CC and DFT energies and geometries may be considered to be trustworthy. In many instances, CC and DFT predicted energies have been confirmed by experiments (for example, ref 30). The present studies on Br2O have been designed to further the knowledge on the performance of CC and DFT methods for excited states. Following this outline, in the first step MRCI VEEs are obtained. For states that qualify, CC and DFT VEEs are calculated and compared with MRCI values. As a matter of interest, VEEs will also be obtained by TDDFT (time-dependent DFT). Next, geometries and adiabatic excitation energies of excited states will be calculated by CC and DFT methods. The results are to be compared with experimental and other theoretical data. Comparison with the related dihalogen monoxides Cl2O and F2O will also be made.

Grein TABLE 1: MRCI (MR), TDDFT (TD), CCSD(T) (CC), and DFT VEEs (eV) for Singlet States of BrOBr and MRCI Oscillator Strengths (Osc.) state 1

X A1 1 1B 1 1 1B 2 1 1A 2 21A1 2 1A 2 31A1 3 1A 2 4 1A 1 2 1B 1 31B1 21B2 3 1B 2 4 1B 1 5 1A 1 6 1A 1 4 1A 2 5 1B 1

MRCI config. a

a,b

GS 6b1f16a1 13b2 f 16a1 5a2 f 16a1* 15a1 f 16a1 6b1 f 14b2* 6b12 f 16a12 6b113b2 f 16a12 13b2 f 14b2 15a16b1 f 16a12* 5a2 f 14b2* 5a26b1 f 16a12 + 6b12 f 16a114b2 15a1 f 14b2 5b1 f 16a1 + 5a2 f 14b2 13b22 f 16a12 + 15a12 f 16a12 5a26b1 f 16a114b2 15a16b1 f 16a114b2* 6b1 f 17a1c

MR

TD

CC

DFT

0.00 2.49 3.57 3.74 3.96 4.47 4.83 5.43 5.45 5.50 5.68 6.17

0.00 2.11 3.28 3.46 3.50 3.96

0.00 2.30 3.29 3.67

0.00 1.75 2.88 3.21

4.08 3.71 5.37

3.53 4.79 4.94

4.74 5.93 6.27 5.22

5.10 5.66 6.14 4.93

6.81

5.62

7.52

0.015 44

7.15 7.25 7.32

6.87

7.02

0.000 00 0 0.010 01

6.21 6.42

5.11 5.44 5.60 6.11

Osc. 0.000 02 0.007 74 0 0.000 29 0 0.000 01 0 0.001 02 0.001 86 0.002 42 0.000 53 0.130 37 0.002 49

a Excitations with respect to ground state configuration (GS) ...15a125a226b1213b22. b An asterisk indicates strong mixing with other configurations. Listing of two configurations indicates nearly equal contributions from each one. c Lowest singlet Rydberg state.

Methods DFT and CCSD(T) calculations were performed with the Gaussian03 programs.31 For DFT the B3LYP functional (Becke hybrid functional B332 combined with the Lee, Yang, and Parr correlation functional33) was used. In both DFT and CCSD(T), the standard basis set is 6-311+G(3df). Other functionals and basis sets were applied for testing purposes. The ground state of Br2O has the electron configuration ...15a125a226b1213b22. MRCI calculations were carried out using the GrimmeWaletzke programs,34,35 employing the TZVPP basis set.36 For BrOBr (but not for BrBrO), Rydberg s and p orbitals on O (s: 0.032, p: 0.028) were added.37 Integrals were produced by the Turbomole package, utilizing the RI (resolution of identity) approach.38,39 Orbitals for the closed-shell ground state were used. No excitations were performed out of the core orbitals (1s of the O’s; 1s, 2s, 2p, 3s, 3p of Br), leaving 40 electrons available for excitations. MRCI calculations were performed for 8 roots of each irreducible representation (irrep) of the C2V or Cs symmetry groups. All configurations with c2 >0.001 in the final CI were chosen as reference configurations. On average, there were about 90 reference configurations per irrep. The final configuration selection threshold was 0.1 µh for VEEs. At this threshold, the number of configurations selected for diagonalization was about 1.3 × 106 per irrep, out of 18 × 106 interacting configurations for BrOBr, and 1.5 × 106 per irrep out of 28 × 106 interacting configurations for BrBrO. The final “estimated full CI” energies, as given in the tables, were obtained by adding to the diagonalized CI energies the sum of the multireference Møller-Plesset2 energy contributions of the omitted configurations to account for the inclusion of previously neglected single and double excitations, and by applying a Davidson-type correction to account for higher excitations.40,41 A higher selection threshold of 0.2 µh was chosen for the potential curves.

Results Vertical Excitation Energies for Singlet and Triplet States of BrOBr. MRCI and CCSD(T) VEEs were obtained at the CCSD(T) optimized ground state geometry, and TDDFT and DFT values at the B3LYP optimized geometry, always using the 6-311+G(3df) basis set (see later). Table 1 lists VEEs and leading MRCI configurations. The lowest excited state, 11B1, lies at 2.49 eV, followed by 11B2 at 3.57 eV and 11A2 at 3.74 eV. Many excited states result from double excitations. An asterisk following the leading configuration indicates strong contributions from other configurations. If two leading configurations are listed, they have nearly the same weight. The MRCI energies will serve as reference for comparison with results obtained by other methods. TDDFT states have been matched with MRCI states that have the same leading configuration. The TDDFT method fails for states arising from double excitations. The TDDFT energies lie 0.2-0.6 eV below the corresponding MRCI values. Both CC and DFT calculations cannot be performed for states where the orbital promotion occurs within the same irrep. Among the lower states, these are 21A1 (15a1 f 16a1), 41A1 (13b2 f 14b2), and 21B1 (15a16b1 f 16a12). However, contrary to the TDDFT method, CC and DFT methods are well suited to describe states with double excitations. With several exceptions, the CC energies lie 0.1-0.4 eV below the MRCI values, whereas the DFT energies lie 0.1-0.7 eV below the reference values. In cases of two leading MRCI configurations of almost equal weight, CC and DFT calculations were performed for one or the other configuration, as indicated. This obviously does not allow for any mixing of configurations, and the resulting VEEs are not expected to emulate the MRCI value. The lowest Rydberg state is 51B1 at 7.32 eV, due mostly to 6b1 f 17a1, where 17a1 is the lowest diffuse a1 orbital (of s-type). Low-lying states with an oscillator strength f larger than 10-4 are 11B2 (3.57 eV, 347 nm, f ) 0.0077) and 21A1 (3.96

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TABLE 2: MRCI (MR), TDDFT (TD), DFT, and CCSD(T) (CC) VEEs (eV) for Triplet States of BrOBr state 3

1 B1 13B2 13A2 13 A 1 23A2 23 A 1 23B1 23 B 2 33A2 33B2 33B1 43B2 43B1 53B1 33 A 1 43A2 63B1 53 B 2 43A1 53A2 53A1 73B1

MRCI config.

a,b

6b1 f 16a1 13b2 f 16a1 5a2 f 16a1 + 6b1 f 14b2 15a1 f 16a1 6b1 f 14b2 + 5a2 f 16a1 13b2 f 14b2 6b1 f 16a1 + 5a2 f 14b2 15a1 f 14b2 6b113b2 f 16a12 5a26b1 f 16a12 15a16b1 f 16a12 6b12 f 16a114b2 6b113b2 f 16a114b2 6b113b2 f 16a114b2 + 5a2 f 14b2 + 5b1 f 16a1 14a1 f 16a1 15a16b1 f 16a114b2 6b113b2 f 16a114b2 + 5a213b2 f 16a12 15a113b2 f 16a12 5a26b1 f 16a114b2 15a16b1 f 16a114b2 5a26b1 f 16a114b2 6b1 f 17a1

MR

TD

CC

DFT

1.85 2.91 2.96 3.13 4.24 4.98 5.05 5.14 5.22 5.27 5.29 5.82 5.95 6.41 6.42 6.46 6.49 6.59 6.62 6.75 7.06 7.08

1.35 2.46 2.62 2.56 3.57 4.47 4.72 4.55

1.99 2.99 3.42d 3.28 3.71d 4.78 4.36e 4.80 5.29 5.42

1.53 2.66 3.08d 2.81 3.31d 4.60 4.94e 4.62 4.86 5.02

5.86

5.51

5.64c 5.73 7.02f 6.74

6.39

6.73

a Excitations with respect to ground state configuration (GS) ...15a125a226b1213b22. b Listing of two configurations indicates nearly equal contributions. c TDDFT has the 5b1 f 16a1 configuration. d DFT and CC calculation for first MRCI configuration. e DFT and CC calculation for 5a2 f 14b2. f DFT calculation for second MRCI configuration.

TABLE 3: MRCI VEEs (eV) of Higher Singlet and Triplet States, Including Oscillator Strengths (Osc) for Singlet States statea 1

6 B1 71B1 51A2 4 1B 2 71A1 5 1B 2 61A2# 71A2 61B2# 71B2

configurationb,c 6b113b2 f 16a114b2* 6b113b2 f 16a114b2* 15a16b1 f 16a114b2* 5a213b2 f 16a12* 14a1 f 16a1* 15a113b2 f 16a12* 6b1 f 15b2* 6b113b2 f 14b22* 13b2 f 17a1* 14a1 f 14b2*

VEE 7.43 7.47 7.52 7.66 7.77 7.96 8.09 8.28 8.51 8.56

statea

Osc 0.069 21 0.005 13 0 0.011 65 0.038 68 0.003 87 0 0 0.000 66 0.096 21

3

6 A2 6 3B 2 7 3A 2 6 3A 1 73B2# 73A1#

configurationb,c 2

5a215a1 f 16a1 * 12b2 f 16a1* 5b1 f 14b2 5a26b1 f 16a114b2* 13b2 f 17a1 6b1 f 7b1

VEE 7.11 7.16 7.46 7.64 7.97 8.24

a States marked with a number sign are diffuse, as indicated by their calculated 〈r2〉. b Excitations with respect to ground state configuration (GS) ...15a125a226b1213b22. Rydberg orbitals are 17a1 (sR), 18a1 (pzR), 15b2 (pyR), and 7b1 (pxR). c An asterisk indicates strong mixing with other configurations.

eV, 313 nm, f ) 0.0003). Larger oscillator strengths were found for states lying above 5.45 eV (228 nm). The 31B2 state, calculated at 6.21 eV (200 nm), has a high f value of 0.1304. Due to spin-orbit interaction from the heavy element Br, transitions from the ground state to triplet states are to be expected. Vertical excitation energies for triplet states are shown in Table 2. The lowest triplet state, 13B1, lies vertically 1.85 eV above the ground state. Its configuration is the same as that of the lowest excited singlet state 11B1, vertically at 2.49 eV. The last state listed in Table 2, 73B1, has Rydberg character, again with an excitation to 17a1. TDDFT energies of states having the same leading configuration are lower than corresponding MRCI values, with differences up to 0.7 eV. Overall, the CC and DFT energies lie closer to MRCI than the TDDFT values. The singlet and triplet VEEs obtained by Koelm et al.13 are 0.3-0.5 eV lower than the present MRCI results. In Table 3, MRCI VEEs of higher singlet and triplet states, as well as oscillator strengths of singlet states, are given. TDDFT, DFT, or CCSD(T) energies for these states have not been calculated. Diffuse states have been marked by the number sign.

DFT and CC Optimized Geometries and Adiabatic Excitation Energies for BrOBr. Geometries for ground and excited states of BrOBr, together with adiabatic excitation energies, have been calculated by the DFT (B3LYP) method using the 6-311+G(3df) basis set. The state numbering corresponds to the sequence of states in MRCI, as listed in Tables 1 and 2. The configurations chosen for DFT are identical to the leading configurations in MRCI. In cases of two MRCI configurations of nearly equal weight, the one chosen for DFT is indicated. Frequency calculations show that many excited states are not stable in C2V symmetry and will distort to Cs. Optimized geometries and adiabatic excitation energies of singlet and triplet states that are stable in C2V symmetry are listed in Table 4. Also included are 11B1, 13B1, and 13B2, which are not stable in C2V, for comparison with their Cs geometries and energies to be given later. Optimized geometries of the remaining unstable states are listed in Table S1 (Supporting Information). CCSD(T) geometry optimizations, with the same basis set, were performed for the ground state and the lowest 1B1, 1B2, 1 A2, 3B1, 3B2, 3A2, and 3A1 states. CCSD(T) results are shown in Tables 4 and S1. The known experimental geometry of the

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TABLE 4: B3LYP (DFT) and CCSD(T) (CC) Optimized Geometriesa, Adiabatic Excitation Energies (Te, eV), and Harmonic Frequenciese for Singlet and Triplet States of BrOBr in C2W Symmetry state

configurationb

R

r

Te

ν1 (a1)

ν2 (a1)

ν3 (b2)

1

1 A1 DFT 11A1 CC 11A1c theor. 11A1d expt. 11B1 DFT 11B1 CC 21A2 DFT 31A2 DFT 21B2 DFT 31B2 DFT 13B1 DFT 13B1 CC 13B2 DFT 13B2 CC 23A2 DFT 23A1 DFT 23B2 DFT 43B2 DFT

GS 1.8520 115.01 0.00 529 179 603 GS 1.8507 113.27 0.00 GS 1.865 112.9 0.00 GS 1.8379 112.25 0.00 6b1 f 16a1 1.9574 137.72 1.34 6b1 f 16a1 1.9501 135.63 1.93 6b1 f 14b2 2.0775 104.58 2.82 409 146 816 6b113b2 f 16a12 2.1439 180.00 2.97 158 173 382 5a26b1 f 16a12 2.1707 180.00 3.13 348 139 323 15a1 f 14b2 2.1511 107.43 4.04 160 167 867 6b1 f 16a1 1.9573 136.79 1.12 6b1 f 16a1 1.9589 133.73 1.63 13b2 f 16a1 2.0318 88.25 2.16 13b2 f 16a1 2.0147 86.32 2.47 6b1 f 14b2 2.0711 104.99 1.58 434 150 701 13b2 f 14b2 2.1409 81.59 2.82 470 179 1039 15a1 f 14b2 2.1311 110.18 3.76 352 136 296 6b12 f 16a114b2 2.3691 110.14 3.53 248 69 468 ´ angle R (Br-O-Br) in degrees. b Excitations relative to the ground state (GS) configuration ...15a 25a 213b 26b 2. a Distance r (Br-O) in Å, 1 2 2 1 c Reference 17. d Reference 7. e Underlined frequencies have higher infrared intensity. ν1, symmetric stretch; ν2, bend; ν3, antisymmetric stretch.

TABLE 5: B3LYP (DFT) and CCSD(T) (CC) Optimized Geometriesa, Adiabatic Excitation Energies (Te, eV), and Harmonic Frequenciesf for Singlet and Triplet States of BrOBr in Cs Symmetry state 1

1

1 A′′ (1 B1) DFT 11A′′ (11B1) CCd 13A′′ (13B1) DFT 13A′′ (13B1) CCd 13A′ (13B2) DFT 13A′ (13B2) CC

configurationb

r1

r2

R

Tec

ν1

ν2

ν3

11a′′ f 29a′ 11a′′ f 29a′ 11a′′ f 29a′ 11a′′ f 29a′ 28a′ f 29a′ 28a′ f 29a′

1.7262 1.7113 1.7517 1.7258 1.7257 1.7254

2.5591 3.0283 2.3235 2.6977 2.9642 3.1998

120.36 110.32 122.69 113.33 176.78e 180.0

1.13 1.32 0.98 1.27 1.25 1.35

57

118

731

94

202

656

36

55

742

´ angle R (BrOBr) in degrees. b The ground state configuration in C symmetry is ...28a′2 11a′′2. a Distance r1 (Br1O) and r2 (Br2O) in Å, s Energy relative to X1A1. d CC not fully converged. e Linear structure, at 180°, has slightly higher energy, and one imaginary frequency. f Underlined frequencies have higher infrared intensity. c

ground state is included in Table 4. DFT and CC geometries of the ground state are in good agreement with experimental values. Using the correlation-consistent basis sets cc-pVDZ to cc-pVQZ with CCSD(T), and cc-pVDZ to cc-pV5Z42 with B3LYP, a best geometry of 1.8399 Å and 112.06° was obtained with CCSD(T)/ cc-pVQZ, differing from the experimental geometry by only 0.002 Å and 0.02° (Table S2 in Supporting Information). It should be noted that cc-pVnZ basis sets have not been modified to include core-valence or 3d correlation effects. In addition, scalar relativistic effects have been ignored. Experimental geometries for excited states are not known. On the basis of experience from previous studies, DFT and CC optimized geometries are considered to be reliable provided the VEEs calculated by these methods compare reasonably well with MRCI values. As discussed above, such is the case for most of the excited states covered in this study. The lowest triplet state has a Te value of 1.12 eV in DFT, and 1.63 eV in CC. DFT and CC geometries are similar, whereas the CC Te values are usually 0.4-0.6 eV higher than the DFT values, resembling the trend observed for the vertical excitation energies. As mentioned above, the stability of singlet and triplet states has been checked by vibrational frequency calculations. Only five singlet and four triplet states have no imaginary frequencies, and can therefore be considered to be stable in C2V geometry. For all unstable states the imaginary frequency has b2 character, which indicates distortion to Cs symmetry. Geometry optimizations in Cs symmetry have been performed for the lowest singlet and triplet A′ and A′′ states, as shown in Table 5. 11A′′ correlates with 11B1. The adiabatic energy has lowered from 1.93 eV for

11B1 to 1.32 eV for 11A′′ in CC. The CC energy of 13A′′ moved from 1.63 (13B1) to 1.27 eV. 13A′′ is therefore adiabatically the lowest excited of BrOBr. However, the CC energy of 11A′′ is only 0.05 eV higher. The adiabatic excitation energy of 13A′, corresponding to 13B2, lowers by a large amount, from 2.47 to 1.35 eV in CC. The long BrO distances of the Cs structures seen in Table 5 indicate near-dissociation of BrOBr to BrO + Br. Such is confirmed by the short BrO distance around 1.72 Å, close to the optimized bond distance of 1.7275 Å in the BrO radical. The stabilization energy of the Cs structures of BrOBr relative to BrO + Br ranges from 0.04 to 0.16 eV in DFT, and from 0.07 to 0.15 eV in CCSD(T), where 13A′ has the lowest and 13A′′ the highest value. MRCI calculations for singlet and triplet states were performed at fixed r1 ) 1.7275 Å and R )150°, allowing r2 to vary from 2.0 to 4.0 Å in intervals of 0.5 Å. Shallow minima were found around 3 Å for 11A′′, 21A′, 21A′′, 13A′, and 23A′′, and around 2.5 Å for 13A′′ and 23A′. Other states, such as 11A′ (the ground state), and several of the higher states, do not show such minima. These MRCI results confirm that the optimized states of Table 5, all having long r2 distances and are indeed van der Waals-like complexes of type BrO · · Br, rather than being completely dissociated. For such complexes, an accurate optimization of the long bond distance and of the bond angle is difficult, as seen by the differences between DFT and CCSD(T) optimized values. Harmonic frequencies calculated for the stable states are included in Tables 4 and 5. Koelm et al.12 reported absorption frequencies of 525.3 and 622.2 cm-1 for BrOBr in an Ar matrix,

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Figure 1. Potential energy curves as function of bond angle for singlet states of BrOBr. The Br-O distance is 1.8507 Å.

TABLE 6: B3LYP/6-311+G(3df) and CCSD(T)/ 6-311+G(3df) Optimized Geometriesa, and Adiabatic Excitation Energies (Te, eV), for Singlet and Triplet States of BrBrO in Cs Symmetry state

configurationb

r1

11A′ DFT 11A′ CC 11A′′ DFT 13A′′ DFT 13A′′ CCd 13A′ DFT 13A′′-lin DFT 13A′′-lin CC

GS GS 11a′′ f 29a′ 11a′′ f 29a′ 11a′′ f 29a′ 28a′ f 29a′ 11a′′ f 29a′ 11a′′ f 29a′

2.4249 2.4197 2.7152 2.6278 2.6769 2.8281 2.5940 2.5371

r2

R

Tec

1.6726 111.20 0.51 1.6739 111.18 0.61 1.7162 144.02 0.99 1.7198 149.42 0.83 1.7178 141.80 1.30 2.3079 100.54 1.72 1.7243 180.00 0.97 1.7416 180.00 1.43 ´ angle R (BrBrO) a Distances r1 (Br1-Br2) and r2 (Br2-O) in Å, in degrees. b The ground state configuration is ...28a′2 11a′′2. c Energy relative to X1A1.

whereas Chu and Li,14 from FTIR, reported frequencies of 532.9 and 629.0 cm-1 in the gas phase. The DFT results are 529 and 603 cm-1, respectively. Potential Energy Curves for Singlet States. Keeping the Br-O distance fixed at 1.8507 Å, MRCI energies for singlet states were calculated at angles from 90 to 180°, in intervals of 15°. The potential curves for the lowest 10 states as a function of the bond angle are shown in Figure 1. Despite the lack of distance optimization, the potential minima are seen to be close to the DFT and CC calculated angles, as given in Tables 4 and S1. A linear geometry is predicted for 21A1, 31A1, 21B1, and 21B2. Potential curves for the variation of the Br-O distance from 1.8 to 2.2 Å, at a fixed angle of 113.27°, were also produced (not shown). In agreement with calculated values, all excited states are seen to have minima at distances around and above 2.0 Å. Vertical and Adiabatic Excitation Energies and Geometries of BrBrO. DFT and CCSD(T) optimized geometries and energies for the lowest singlet and triplet states of BrBrO are shown in Table 6. There is nearly perfect agreement between the DFT and CC geometries of the 11A′ ground state. The Br-Br distance is 2.4197 Å, shorter than that reported by Lee17 (2.51 Å) and Koelm et al.13 (2.45 to 2.58 Å), but very similar

to that of Galvez et al.,15 whereas the Br-O distance lies in the range of values obtained by Lee,17 Koelm et al.,13 and Galvez et al.15 The energy difference relative to the ground state of BrOBr is 0.51 eV in DFT and 0.61 eV in CC, compared with 0.70 eV by Lee, and 0.67 to 0.80 eV by Koelm et al. The lowest triplet state 13A′′ lies at 0.83 eV (DFT) and 1.30 eV (CC; not fully converged). The higher-lying 11A′′ and 13A′ states have DFT energies of 0.99 and 1.72 eV, respectively. Dyke et al.19 found the lowest triplet state of BrBrO to be 3 Σ , followed closely by 13A′′. In this work, the DFT energy of the lowest linear triplet state is 0.14 eV higher than that of 13A′′, and one of the frequencies is imaginary. The CC energy of the linear state is 0.13 eV higher than 13A′′. Data for linear BrBrO are included in Table 6. Chau et al.11 obtained by QCISD a very long Br-Br distance of 3.20 Å for the 13A′′ state of BrBrO, compared with the DFT value of 2.63 Å and the CC value of 2.68 Å. Tevault et al.4 measured BrBrO vibrational frequencies of 235.8 and 804 cm-1, Koelm et al.13 obtained 804.6 cm-1. This compares with our calculated values of 257 and 826 cm-1. Frequencies of 215 and 793 cm-1 were reported by Lee,17 and 163-242, 711-1056 cm-1 by Koelm et al.13 MRCI vertical excitation energies, both for singlet and triplet states, calculated at the CC geometry of the BrBrO ground state, are displayed in Table 7. The MRCI energy difference between the ground states of BrOBr and BrBrO is 0.66 eV. The lowest excited singlet states 11A′′, 21A′′, and 21A′ lie at 1.43, 3.12, and 3.24, respectively. The VEE values given by Koelm et al.13 are lower by 0.3-0.9 eV. Of the states listed in Table 7, only 41A′ has a high oscillator strength, comparable to that of 31B2. Discussion Singlet and triplet excited valence states of BrOBr are characterized by excitations into 16a1 (located mainly on O), 14b2 (a Br-Br σ*-type orbital), as well as double excitations into 16a12, 14b22, and 16a114b2. The excited singlet states of BrOBr have a surprising similarity to those of the diatomic molecules Br2 and Cl2.43 Low-lying excited states of Br2 result from excitations πg f LUMO, πu f LUMO, πg2 f LUMO2 (∆ state), and σg f LUMO.44 The four highest occupied orbitals of BrOBrs5a2, 15a1, 13b2, 6b1sare fully or mostly localized on the Br atoms, and correspond to πg (13b2, 5a2) and πu (6b1, 15a1) of Br2. This situation is illustrated in Figure 2. As seen in Table 1, the four lowest excited states of BrOBrs11B1 (6b1 f 16a1), 11B2 (13b2 f 16a1), 11A2 (5a2 f 16a1) and 21A1 (15a1 f 16a1)shave excitations of type π f LUMO (16a1), just like Br2. Furthermore, 31A1 (6b12 f 16a12) and 31A2 (6b113b2 f 16a12), with double excitations of type π2 f LUMO2, correspond to the ∆g state πg2 f LUMO2 of Br2. However, the character of the LUMO differs. In Br2, it is a σu orbital, whereas in BrOBr the 16a1 LUMO is localized on oxygen. The LUMO + 1 molecular orbital of Br2O, 14b2, corresponds to σu of Br2. Excitations from the four π-equivalent orbitals of BrOBr to 14b2 start with 21A2. It is interesting that 31B2 (15a1 f 14b2), outstanding for its large oscillator strength, has some similarity to 11Σu+ (σg f σu), the lowest state of Br2 having a large f. This state of Br2 owes its large oscillator strength to being a charge-transfer state, dissociating to the ions Br+ + Br-. Contrary to the repulsive character of the lower states of Br2 and Cl2, their charge-transfer states are stable. In the same way, the 31B2 state of BrOBr has no imaginary vibrational frequencies and is structurally stable. The structures of excited states of Cl2O45 are very similar to those of Br2O, and one would expect the high-intensity state 21B2 of Cl2O to relate to 11Σu+ of Cl2, although this situation has not yet been explored.

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Grein

TABLE 7: MRCI VEEs (eV) for Singlet and Triplet States of BrBrO and MRCI Oscillator Strengths (Osc.) for Singlet States state 1

1 A′ 11A′′ 21A′′ 2 1A ’ 31A′ 41A′ 31A′′ 41A′′ 51A′ 51A′′ a

configurationa GS 11a′′ f 29a′ 10a′′ f 29a′ 28a′ f 29a′ 11a′′2 f 29a′2 27a′ f 29a′ 11a′′ f 30a′ 28a′11a′′ f 29a′2 28a′ f 30a′ 27a′11a′′ f 29a′2

VEE 0.00 1.43 3.12 3.24 3.55 3.92 3.99 4.09 5.42 5.47

Osc.

state 3

0.000 04 0.000 02 0.000 61 0.000 27 0.147 85 0.000 03 0.000 05 0.004 75 0.000 50

1 A′′ 13A′ 23A′′ 23A′ 33A′′ 33A′ 43A′′ 43A′ 53A′′ 63A′′

configurationa

VEE

11a′′ f 29a′ 28a′ f 29a′ 10a′′ f 29a′ 27a′ f 29a′ 11a′′ f 30a′ 10a′′11a′′ f 29a′2 28a′11a′′ f 29a′2 28a′ f 30a′ 9a′′ f 29a′ 27a′11a′′ f 29a′2

1.15 2.15 2.88 2.99 3.19 3.97 4.00 4.75 4.99 5.07

Excitations relative to the ground state configuration (GS) ...28a′2 11a′′2

Figure 2. The four highest occupied orbitals of BrOBr, resembling the in-plane and out-of-plane components of the πg and πu orbitals of Br2.

The basis set used in this work allows for the description of low-lying Rydberg states, characterized by excitations into the diffuse orbitals 17a1 (sR), 18a1 (pzR), 15b2 (pyR), and 7b1 (pxR) (Rydberg orbitals are oxygen-based). The lowest Rydberg states, both singlet and triplet, result from 6b1 f 17a1, at energies of 7.32 and 7.08 eV, respectively (Tables 1 and 2). Table 3, listing higher states not covered in Tables 1 and 2, shows two additional singlet, and two additional triplet states of Rydberg character. The singlet (but not triplet) Rydberg states show strong mixing of Rydberg with valence configurations. As outlined in the Introduction, maxima in the UV-visible spectrum were observed at 665 nm (1.86 eV), 520 nm (2.38 eV), 350 nm (3.54 eV), at 314 nm (3.94 eV), and near 200 nm (6.20 eV). According to Tables 1 and 2, matching states are 13B1 (1.85 eV), 11B1 (2.49 eV, f ) 0.00002), 11B2 (3.57 eV, f ) 0.00774), 21A1 (3.96 eV, f ) 0.00029), and several possible states in the vicinity of 6.2 eV. The 31B2 state, calculated at 6.21 eV (200 nm), has an unusually high f of 0.13, and can therefore be assumed to make the major contribution to observed bands in the 200 nm region. Weak transitions in the range of 2.9-3.1 eV are expected from the triplet states 13B2, 13A2, and 13A1, and around 3.7 eV from 11A2. Several triplet states lie in the 5.0-5.3 eV range, and four singlet states, most with a significant oscillator strength, are located in the 5.4-5.7 eV region. Many more observable states are predicted in the VUV region below 200 nm. The observed excitation at 665 nm is due to the lowest triplet state 13B1. The UV spectrum of Cl2O also shows a peak due to this state.45 As a consequence of spin-orbit interactions being higher for bromine than for chlorine compounds, more intense excitations to triplet states are expected in Br2O than in Cl2O.

However, if the Cl2O spectrum is any guide, excitations to higher triplet states may not be identifiable due to underlying strong singlet transitions. According to Koelm et al.,13 the photoisomerization BrOBr f BrBrO requires light in the wavelength range from 350 to 400 nm. Their best fit is the 1B2 state calculated at 3.11 eV, 399 nm, with f ) 0.007 (1B1 in ref 13). In this work, the vertical excitation energy of 11B2 is calculated at 3.59 eV, or 349 cm-1, with f ) 0.0077 (Table 1). As outlined above, vertical transition to this state is observed at 355 nm. The photoisomerization BrOBr f BrBrO may be assisted by the fact that 11B2 is not stable in C2V symmetry, and will distort to Cs. Back isomerization of BrBrO to BrOBr has been achieved with light of wavelengths smaller than 340 nm. For this step, Koelm et al. assigned the BrBrO state calculated at 3.77 eV, 330 nm, with f ) 0.079, whereas the best fit from the present work is 41A′ at 3.92 eV, 316 nm, with a rather high f ) 0.15 (Table 7). Vertical and adiabatic excitation energies of the lowest excited states of BrOBr may be compared with those of the isovalent molecules ClOCl and FOF. MRCI values for the VEE of 11B1 change from 2.49 eV for BrOBr to 3.11 eV for ClOCl45 and 4.67 eV for FOF, and VEE of 11B2 goes from 3.57 eV to 4.5945 and 7.42 eV (this work). MRCI values of FOF calculated by Tomasello et al.46 are about 0.7 eV higher. The adiabatic energies of 11B1, calculated here by CCSD(T)/6-311+G(3df), are 1.93, 2.21, and 2.37 eV, respectively. Summary and Conclusion Vertical excitation energies were calculated by MRCI methods for singlet and triplet states of BrOBr in C2V symmetry, with energies up to about 9 eV, including the lowest s- and p-Rydberg states. Low-lying excited states are similar in structure to those of Br2. Most states have small oscillator strengths. An exception is 31B2, which may be compared with the 11Σu+ charge-transfer state of Br2. Observed maxima in the VUV spectra were identified as excitations to 13B1 (665 nm, 1.86 eV), 11B1 (520 nm, 2.38 eV), 11B2 (350 nm, 3.54 eV), 21A1 (314 nm, 3.94 eV), and 31B2 (∼200 nm, ∼6.20 eV). The calculated vertical excitation energies lie within 0.1 eV of the observed values. Many more singlet excitations at energies higher than 3.94 eV are predicted. Due to the expected strong spin-orbit interaction, many triplet excitations should also be observable. Vertical excitation to 11B2 (oscillator strength of 0.0077) is responsible for the observed photoisomerization BrOBr f BrBrO. Vertical excitation energies were also calculated at the 11A′ ground state geometry of the BrBrO isomer. An especially high oscillator strength of 0.15 was found for 41A′. This state is proposed to be involved in the observed reverse photoisomerization BrBrO f BrOBr. UsingDFT/B3LYPandCCSD(T)methodswiththe6-311+G(3df) basis set, geometries were optimized for about 12 excited singlet

Excited States of Dibromine Monoxide and triplet states of BrOBr in C2V symmetry. Frequency analysis showed that many states, including 13B1, 11B1, 11B2, and 13B2, are not stable in C2V symmetry and will distort to a Cs structure. Cs geometries corresponding to 13B1, 11B1, and 13B2 were optimized. Geometry optimizations were also performed for the lowest singlet and triplet A′ and A′′ states of BrBrO. The 11A′ ground state of BrBrO lies 0.61 eV (CC) and 0.66 eV (MRCI) above the ground state of BrOBr. Comparison was made with the lowest excitation energies of Cl2O and F2O. The VUV spectrum of Cl2O has been well studied, both experimentally and theoretically. In contrast, not much is known about F2O, and more work is to be done on this molecule. Also, more studies on ionization potentials and electron affinities of Br2O are warranted. The surprising similarity of excited states of BrOBr with those of the diatomic Br2 molecule, and the relationship of the XOX and XXO (X ) F, Cl, Br, I) states, which have a high oscillator strength, with corresponding charge-transfer states of X2 is to be investigated in more detail. Acknowledgment. Financial support by NSERC (Canada) is gratefully acknowledged. Thanks to Dr. Pablo J. Bruna for reading the manuscript and for making valuable comments. Provision of computer time by the ACEnet computer network has been essential to this work. Supporting Information Available: Table S1 on geometries and energies of BrOBr states with imaginary frequencies; Table S2 on geometries and energies for X1A1 and 11B1 states of BrOBr, using correlation-consistent basis sets. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Barrie, L. A.; Bottenheim, J. W.; Schnell, R. C.; Crutzen, P. J.; Rasmussen, R. A. Nature (London) 1988, 334, 138. (2) Mueller, H. S. P.; Miller, C. E.; Cohen, E. A. Angew. Chem., Int. Ed. Engl. 1996, 35, 2129. (3) Deters, B.; Burrows, J. P.; Himmelmann, S.; Blindauer, C. Ann. Geophys. 1996, 14, 468. (4) Tevault, D. E.; Walker, N.; Smardzewski, R. R.; Fox, W. B. J. Phys. Chem. 1978, 82, 2728. (5) Campbell, C.; Jones, J. P. M.; Turner, J. J. Chem. Commun. 1968, No. 15, 888. (6) Levason, W.; Ogden, J. S.; Spicer, M. D.; Young, N. A. J. Am. Chem. Soc. 1990, 112, 1019. (7) Muller, H. S. P.; Cohen, E. A. J. Chem. Phys. 1997, 106, 8344. (8) Orlando, J. J.; Burkholder, J. B. J. Phys. Chem. 1995, 99, 1143. (9) Rattigan, O. V.; Lary, D. J.; Jones, R. L.; Cox, R. A. J. Geophys. Res. [Atmos.] 1996, 101, 23021. (10) Thorn, R. P., Jr.; Monks, P. S.; Stief, L. J.; Kuo, S.; Zhang, Z.; Klemm, R. B. J. Phys. Chem. 1996, 100, 12199. (11) Chau, F. -T.; Lee, E. P. -F.; Mok, D. K. -W.; Wang, D. -C.; Dyke, J. M. J. Electron Spectrosc. Relat. Phenom. 2000, 108, 75. (12) Qiao, Z.; Sun, S.; Sun, Q.; Zhao, J.; Wang, D. J. Chem. Phys. 2003, 119, 7111.

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