Ab initio studies on complexes of ozone with diatomic molecules

Coupled cluster CCSD(T) calculations using the aug-cc-pVQZ basis set were performed on structures and energies of the complexes O3-HF, O3-HCl, O3-OH, O3-H2, O3-N2, O3-CO, O3-O2, O3-F2, O3-Cl2, and O3-ClF. Most complexes have Cs symmetry, with the symmetry plane being the plane of ozone (for hydrogen bonded O3-HF to O3-OH and for halogen bonded O3-Cl2 and O3-ClF) or the plane perpendicular to ozone (for most others). Dissociation energies De range from 718 to 1137 cm−1 for the hydrogen bonded O3-HCl to O3-HF complexes, from 540 to 872 cm−1 for the halogen bonded O3-Cl2 and O3-ClF complexes, and from to 200 to 433 cm−1 for complexes from O3-H2 to O3-CO. In hydrogen-bonded complexes calculated harmonic vibrational frequencies of the diatomic molecule are red shifted, by 164 cm−1 for O3-HF and by 52 cm−1 for O3-HCl, combined with blue shifts up to 29 cm−1 for the ozone frequencies. In halogen-bonded complexes, the halogen frequencies of O3-ClF are red shifted by up to 13 cm−1.


Introduction
The importance of ozone for our climate has been well documented [1][2][3][4]. Although occurring at very low concentration in the atmosphere, ozone absorbs most of the harmful UV radiation from the sun. Much work has been done to reverse ozone depletion [5,6].
It was recognized early that complexes of ozone with other gases in the atmosphere may play a role in ongoing chemical reactions [7]. Complexes of ozone with argon (1979) [8] and ethylene (1989) [9] were studied by microwave spectroscopy. Early theoretical work has been done on ozone-water [10] and ozone-acetylene complexes (1991) [11].
In this work structures and energetics of complexes of ozone with H 2 , N 2 , CO, O 2 , HF, HCl, OH, F 2 , Cl 2 , and ClF are studied. Further to diatomic molecules present in the atmosphere, hydrogen-bonded complexes of ozone with HF, HCl, and OH as well as halogen-bonded complexes of ozone with F 2 , Cl 2 , and ClF have been included due to their scientific interest.
It is the purpose of this work to present high-level theoretical results on structures, energies, and vibrational frequencies for the most stable complexes of each system.
Theoretical calculations performed at a similar level of theory are available only for the O 3 -N 2 system. In a recent publication by Kalugina et al. [12] coupled cluster fivedimensional potential energy surfaces were constructed for this complex. Using the CCSD(T)-F12a method with the aug-cc-pVTZ basis set a dissociation energy of 348.88 cm −1 was obtained for the global minimum. Six additional stable structures were identified.

Methods
Due to the ground state of ozone having multiconfigurational character [13][14][15], low-level computational methods cannot be used. Alcami et al. [16] found that ozone and complexes with ozone are not well described by RHF methods and by other methods lacking proper correlation. However, QCI, CASSCF, and in particular CCSD(T) methods appear to work well.
As Table 1 shows, the Møller-Plesset MP2 [17] method is not suitable for describing complexes with ozone. While 1 3 the geometry of ozone is well described by the MP2 method, and the ν 1 and ν 2 frequencies of ozone are also in good agreement with experimental values [18,19], the ν 3 vibrational frequency is in substantial error.
For the above reasons, all calculations were performed using the coupled cluster single, double, and perturbative triple CCSD(T) method [20,21], with augmented correlation consistent aug-cc-pVXZ (AVXZ) basis sets. Geometry optimizations were done at the CCSD(T)/AVQZ level, with the geometry of the monomers held fixed at their optimized monomer values. Dissociation energies D e were calculated as the difference between the energy of the complex and the sum of the monomer energies obtained by the same method.
Corrections for the basis set superposition error (BSSE) using the method of Boys and Bernardi [22] were applied to all dissociation energies. In several cases extrapolations to the complete basis set (CBS) limit were made. They are based on the exponential method proposed by Halkier et al. [23], using CCSD(T)/AVXZ energies with X = D, T, Q.
Harmonic vibrational frequencies were obtained by the CCSD(T)/AVDZ method, including full geometry optimizations. Structures having no imaginary frequencies are considered to be stable.
All calculations were performed using the Gaussian 16 [24] and MOLPRO [25,26] computer programs. Initially for each system a number of test calculations were carried out at lower levels of basis set (AVDZ and AVTZ), in C 1 and C s symmetries. Different starting orientations of the monomers were chosen, and all geometry parameters, including those of the monomers, were allowed to be optimized. The more stable structures were reoptimized by the CCSD(T)/AVQZ method.

Results for structures and dissociation energies
Most structures listed in the following tables have C s symmetry. There are two different planes of symmetry. One is the plane of O 3 , to be named Cs-A, the other the plane perpendicular to the O 3 plane, named Cs-B.
Structures for the hydrogen-bonded complexes of O 3 with HF, HCl, and OH have all atoms lying in the Cs-A plane, with the diatomic molecule in cis (Cs-A-cis) or trans (Cs-Atrans) orientation relative to O 3 .
Complexes of O 3 with H 2 , N 2 , O 2 , and CO have the diatomic molecule placed in the Cs-B plane (Cs-B-inpl) or perpendicular to that plane (Cs-B-ppd). Complexes with structures located in the Cs-A plane, in both cis and trans orientations, have dissociation energies much lower than Cs-B complexes.
Halogen-bonded complexes of O 3 with F 2 , Cl 2 , and ClF have linear planar Cs-A-C2v structures of similar or higher dissociation energy than corresponding Cs-B-inpl structures.

O 3 -HF, O 3 -HCl, and O 3 -OH complexes
BSSE-corrected CCSD(T)/AVQZ dissociation energies for complexes of HF, HCl, and OH with ozone are given in Table 2.
IR spectra by Andrews et al. [27] showed that the terminal oxygens of ozone in the O 3 -HF complex are not equivalent, implying that HF is attached to one of the terminal oxygens. At a low level of basis set, several starting structures in C 1 symmetry were tested. They all ended in Cs-A planar structures. There is a cis form with the diatomic molecule located inside O 3 ( Fig. 1a for O 3 -HF), and a trans form with H located outside O 3 (Fig. 1b for O 3 -HF).
A very large D e of 1137 cm −1 was found for cis O 3 -HF, and a slightly smaller one, 1080 cm −1 , for trans O 3 -HF. The CBS dissociation energy for the C s -A-cis structure of O 3 -HF is 1142 cm −1 , very close to the BSSE adjusted value. The  U s i n g Q C I S D ( T ) / 6 -3 1 1 + + G ( d , p ) / / QCISD/6-311 + G(d) methods, Tachikawa et al. [28] obtained for O 3 -HF a dissociation energy of 1190 cm −1 for the cis structure, close to the present result, and 1260 cm −1 for the trans structure, exceeding the present value.
Lower dissociation energies, with 718 cm −1 for cis and 647 cm −1 for trans, were obtained for the O 3 -HCl complex. Bulanin et al. [29] performed IR spectroscopic studies on the O 3 -HCl molecular complex in liquid argon. They also reported calculated dissociation energies. Using the QCISD/6-311 + + G(2d,2p) method they obtained for the cis structure a D e of 6.3 kJ/mol or 526 cm −1 , compared to 718 cm −1 from the present calculations.
Calculated dissociation energies for the O 3 -OH complex are 753 cm −1 for the cis and 575 cm −1 for the trans structure. Mansergas and Anglada [30] studied theoretically the reaction between O 3 and OH, obtaining with the CCSD(T)/ AVTZ//QCISD/6-311 + G(2df,2p) method a dissociation energy of 2.57 kcal/mol or 899 cm −1 for the cis O 3 -OH complex, a value much higher than found in this work, probably due to differences in theoretical methods used.

O 3 -H 2 , O 3 -N 2 , O 3 -O 2 , and O 3 -CO complexes
In Table 3 Gadzhiev et al. [31] performed CCSD and CCSD(T) calculations on van der Waals complexes of O n for n ≤ 6. For triplet O 3 -O 2 only Cs-A planar structures were considered. Using the CCSD/cc-pVTZ method dissociation energies of 0.7 and 1.1 kJ/mol (59 and 92 cm −1 ) were reported for the cis and trans structures, respectively.
As for the previous complexes, the Cs-B-inpl structure of O 3 -CO is found to be stable. It has a higher dissociation

O 3 -F 2 , O 3 -Cl 2 , and O 3 -ClF complexes
Møller-Plesset results on complexes of F 2 , Cl 2 , and ClF with HF, H 2 O, and NH 3 were reported by Alkorta et al. [33] and coupled cluster results on complexes of these halogens with NH 3 were obtained by Karpfen [34]. Dissociation energies were found to increase strongly in the order F 2 , Cl 2 , and ClF. For the C 3v structures of NH 3 -AB Karpfen obtained D e values of 409 cm −1 for F 2 , 1546 cm −1 for Cl 2 , and 3281 cm −1 for ClF. In both investigations linear X-A-B (X = F, O, N) structures were chosen.
In a first step, Cs-B-inpl structures (non-linear X-A-B, not halogen bonded) were examined for complexes of ozone with F 2 , Cl 2 , and ClF. These structures were previously seen as being most stable for complexes of ozone with H 2 , N 2 , O 2 , and CO. Dissociation energies obtained for Cs-B-inpl structures with F 2 , Cl 2 , and ClF will be used as benchmarks for comparison with halogen bonding.
As halogen bonding is known to be associated with linear or near-linear X-A-B arrangements, Cs-A structures with C 2v symmetry (Cs-A-C2v, linear) were considered. For the C 2v structure of O 3 -F 2 the dissociation energy is slightly below the Cs-B-inpl value, but for O 3 -Cl 2 it is 40 cm −1 above and for O 3 -ClF almost 300 cm −1 above the Cs-B-inpl dissociation energies (Table 4). However, in all three cases an imaginary frequency was found for the C 2v structure. Therefore, inplane distortions of the halogen molecules were examined. The resulting Cs-A-cis structures now have dissociation energies higher by 12 cm −1 for the F 2 , 23 cm −1 for the Cl 2 (Fig. 4), and 142 cm −1 for the ClF (Fig. 5) complex compared to Cs-A-C2v values. There are no imaginary frequencies for the C s -A-cis structures.
Overall, the dissociation energy for the C s -A-cis structure of O 3 -F 2 is very close to the Cs-B-inpl value, but for O 3

Results for geometries O 3 -HF, O 3 -HCl, and O 3 -OH complexes
In Table 5

O 3 -H 2 , O 3 -N 2 , O 3 -O 2 , O 3 -CO, O 3 -F 2 , O 3 -Cl 2 , and O 3 -ClF complexes in Cs-B-inpl and Cs-B-ppd configurations
In Tables 6 and 7, geometrical parameters are given for complexes relating to the Cs-B plane, with the inplane structures in Table 6, and the perpendicular structures in Table 7.
For the inplane structures the O1-A distance and the shortest distances as well as the X1-O1-A and O1-A-B angles are shown. X1 lies on the C 2v symmetry axis of O 3 above the central oxygen. The distances are close to 3 Å, except for the distance in O 3 -Cl 2 , which is about 3.4 Å. The X1-O1-A angles of the inplane complexes are about 120°

O 3 -F 2 , O 3 -Cl 2 , and O 3 -ClF complexes in Cs-A-C2v and Cs-A-cis configurations
In Table 8, geometrical parameters are listed for halogenbonded O 3 -F 2 , O 3 -Cl 2 , and O 3 -ClF systems. As seen, the more stable Cs-A-cis conformers are slightly distorted from C 2v symmetry, with X1-O1-A angles differing by 13° to 17° from 180°. The advantage of distortion from C 2v symmetry is for one halogen atom to have a shorter distance to one of the terminal oxygens of O 3 , thereby lowering the energy of the complex.

Changes in harmonic vibrational frequencies
It is well known that the HF vibrational frequency is red shifted in HF complexes due to lengthening of the H-F bond. For example, Kolenbrander and Lisy [36] observed a red shift of 43 cm −1 for the HF frequency in HF-N 2 . IR spectra for O 3 -HF in solid argon were reported by Andrews et al. [27]. They found for isolated HF a frequency of 3919 cm −1 . Compared to 3803 cm −1 in the O 3 -HF complex, this corresponds to a red shift of 116 cm −1 .
The theoretical result for the HF frequency of O 3 -HF cis obtained in this work is 3948 cm −1 . With a calculated frequency of 4081 cm −1 for the HF monomer, the red shifts are 133 cm −1 for cis O 3 -HF, close to the experimental value, and 164 cm −1 for trans O 3 -HF. In both complexes, the calculated HF distances increased by about 0.006 Å. The ozone frequencies for O 3 -HF change by smaller amounts. In the order ν 1 , ν 2 , and ν 3 (see Table 1) they change by +10, −5, and +15 cm −1 for the cis structure, and by +11, −15, and +29 cm −1 for the trans structure. As seen, most are blue shifted.
Results obtained by Tachikawa et al. [28] for harmonic frequencies and IR intensities of O 3 -HF differ from the present results due to differences in method and basis set (QCISD/6-31G* used).
Smaller frequency shifts are expected for the O 3 -HCl complex. Here the calculated frequencies are 2942 cm −1 for HCl in O 3 -HCl cis and 2919 cm −1 for HCl in O 3 -HCl trans. With a calculated vibrational frequency of 2971 cm −1 for isolated HCl, the red shifts are 29 cm −1 for the cis and   52 cm −1 for the trans complex. A blue shift of 9 cm −1 was obtained for the ν 1 frequency of ozone in the trans complex. Bulanin et al. [29] performed IR spectroscopic studies of the O 3 -HCl molecular complex in liquid argon. The complex showed a new feature at 2840 cm −1 , ascribed to the HCl stretching frequency in the complex. With an experimental frequency of 2921 cm −1 for HCl, the red shift amounts to 81 cm −1 , larger than calculated values.
The calculated OH frequencies for the O 3 -OH complex are 3674 cm −1 for the cis and 3662 cm −1 for the trans complex. Compared to the OH monomer value of 3686 cm −1 the red shifts are 8 cm −1 for the cis and 24 cm −1 for the trans complex.
The calculated blue shift for the vibrational frequency for CO in the O3-CO complex is 6 cm −1 (2129 cm −1 in complex, 2123 cm −1 for CO). Experimentally [32] a blue shift of 2 cm −1 was found (2140 cm −1 in complex).
For complexes of O 3 with the homonuclear diatomic molecules H 2 , N 2 , and O 2 changes in frequency are small (for example, − 2 cm −1 for N 2 in O 3 -N 2 ).
For other complexes included in this paper shifts in frequency are small.

Discussion
The diatomic molecules forming complexes with ozone included in this work can be divided into three categories: (a) the hydrides HCl, HF, and OH, forming hydrogen bonds with ozone; (b) the halogens F 2 , Cl 2 , and ClF, forming halogen bonds with ozone; and (c) the diatomic molecules H 2 , N 2 , O 2 , and CO forming no particular types of bonding. One expects the hydrogen-bonded complexes to be most stable, followed by the halogen-bonded complexes, and last by complexes of ozone with the remaining diatomics.
The hydrogen-bonded complexes O 3 -HF, O 3 -HCl, and O 3 -OH have stable cis and trans structures lying in the Cs-A plane, the plane of O 3 , with the cis structures being more stable than the trans structures. In the complex the hydrogen of HF, HCl, and OH is closest to one of the terminal oxygens of O 3 .
For complexes of ozone with the halogens F 2 , Cl 2 , and ClF linear and near-linear structures were investigated, representing halogen bonding. It was found that for Cl 2 and in particular for ClF, halogen-bonded near-linear structures have much higher dissociation energies than their corresponding Cs-B-inpl structures. For the O 3 -F 2 complex the halogen-bonded structure is about equally stable as Cs-B-inpl.
Complexes of ozone with H 2 , N 2 , O 2 , and CO have stable structures with the diatomic molecule lying in the Cs-B plane (Cs-B-inpl), the plane perpendicular to the O 3 plane. They also have C s structures (C 1 structure for CO) of lower dissociation energy, with the diatomic molecules lying perpendicular to the Cs-B plane (Cs-B-ppd).
The highest dissociation energy of 1137 cm −1 was found for the hydrogen-bonded O 3 -HF complex. This is followed by the halogen-bonded O 3  Significant shifts in vibrational frequencies have been calculated for the hydrogen-bonded O 3 -HF complex, with a red shift of 133 cm −1 for the HF frequency (116 cm −1 found experimentally) and blue shifts up to 29 cm −1 for the O 3 frequencies. For the halogen-bonded complexes red shifts of 5 cm −1 for Cl 2 in O 3 -Cl 2 and 13 cm −1 for ClF in O 3 -ClF were found.
Extrapolations to the complete basis set limit done for O 3 -HF and O 3 -N 2 resulted in dissociation energies almost equal to the BSSE adjusted values (within 7 cm −1 ). The fact that BSSE corrections are very close to CBS corrections indicates a very high level of method.

Conclusion
Structures, energies, and vibrational spectra of ozone complexes have been calculated using high-level computational methods. Small diatomic molecules, some of atmospheric interest, have been chosen for the monomers. It is seen that ozone forms rather strong intermolecular bonds, especially with the hydrogen-bonded molecules HF and HCl as well as with the halogen-bonded molecules Cl 2 and ClF, but also with molecules like CO and N 2 . Large vibrational frequency shifts for hydrogen-bonded complexes, and smaller ones for halogen-bonded complexes, were obtained.
For five of ten complexes dealt with in this work no theoretical results on structures, energies, and vibrational spectra (but several experimental investigations) were available in the literature. For the other complexes, except for O 3 -N 2 , literature results obtained at a lower level of theory could be improved.
Work is in progress on complexes of ozone with triatomic and larger molecules.