# Ozone Activation on TiO\({}_{2}\) Studied by IR Spectroscopy and Quantum Chemistry
## 3 Results
### Results of Calculations  
As the simplest model of the interaction of ozone with the uttermost coordinately unsaturated titanium ion, we considered the O\({}_{3}\) complex with the TiO\({}_{2}\) molecule. Geometry optimization led to two stable structures, the monodentate (a) and bidentate (b) ozone complexes, as shown in Figure 3.  
The calculated interatomic distances, angles, and adsorption energies of ozone complexes with TiO\({}_{2}\) clusters are given in Table 1. One can see that the angle does not change much on adsorption, slightly decreasing by less than 1.5\({}^{\circ}\). Interatomic distances in bidentate complex with two-coordinated Ti increased by 0.06 A, and the adsorption energy due to simultaneous interaction by two oxygen atoms with coordinately unsaturated titanium was rather high. However, such sites or spectral features of adsorbed ozone have nothing to do with the experimental data, indicating the nonequivalence of terminal oxygen atoms, and we shall consider this case only for comparison. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Model**} & \multicolumn{1}{c}{**E, kJ/mol**} & \multicolumn{1}{c}{**Angle \(\alpha\)\({}^{\circ}\)**} & \multicolumn{1}{c}{**R(O1-O2)**, Å} & \multicolumn{1}{c}{**R(O2-O3)**, Å} & \multicolumn{1}{c}{**R(Ti-O1)**, Å} & \multicolumn{1}{c}{\(\mathbf{\
u_{1}-\
u_{3}\), cm\({}^{-1}\)}} \\ \hline \multicolumn{2}{c}{Free O\({}_{3}\), calc.} & - & 118.46 & 1.256 & 1.256 & - & 65.5 \\ \hline TiO\({}_{2}\) cluster & Monodentate & \(-\)92.69 & 115.49 & 1.325 & 1.239 & 2.103 & 337.6 \\
2-coord. Ti\({}^{4+}\) & Bidentate & \(-\)138.89 & 117.80 & 1.315 & 1.315 & 2.184 & 64.2 \\ \multicolumn{2}{c}{Mnoodentate} & \multicolumn{1}{c}{\(-\)66.59} & 116.89 & 1.285 & 1.231 & 2.306 & 230.2 \\
4-coord. Ti\({}^{4+}\) & Bidentate (II) & \(-\)59.49 & 117.73 & 1.282 & 1.237 & 2.277 & 168.2 \\ \multicolumn{2}{c}{Mnoodentate} & \multicolumn{1}{c}{\(-\)64.74} & 116.94 & 1.290 & 1.227 & 2.354 & 258.9 \\
5-coord. Ti\({}^{4+}\) & Bidentate & \(-\)61.58 & 118.45 & 1.285 & 1.234 & 2.342 & 193.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adsorption energy (E), geometry, and the difference in fundamental frequencies (\(\
u_{1}-\
u_{3}\)) of O\({}_{3}\) molecule bound to TiO\({}_{2}\) model clusters. Figure 3: Optimized geometry of (**a**) monodentate (symmetry C\({}_{s}\)) and (**b**) bidentate (symmetry C\({}_{2\
u}\)) ozone complexes with TiO\({}_{2}\). In the monodentate ozone complex with the TiO\({}_{2}\), the molecule adsorption energy and the short distance between the molecule and Ti\({}^{4+}\) atom provide evidence of a very strong interaction with the cluster, which results in a serious deformation of the molecule: the O-O bond adjacent to the titanium atom becomes longer, while another is shortened. This means that the force constants become quite different, leading to an increase in the difference between the frequencies of \(\
u_{1}\) and \(\
u_{3}\) vibrations shown in the right column of Table 1. The two vibrations, which for the free molecules were the symmetric and antisymmetric stretching modes, become now localized at different bonds, O\({}^{1}\)-O\({}^{2}\) and O\({}^{2}\)-O\({}^{3}\), respectively, if we numerate the oxygen atoms from that nearest the Ti atom. For the monodentate ozone complex with TiO\({}_{2}\) we calculated the frequencies of all the combinations of ozone isotopic mixtures; the results are presented in Table 2. Regarding how the calculated frequencies were shifted with respect to those observed experimentally, to compare the isotopic splitting of the bands the calculated values were multiplied by scaling factors chosen for each vibrational mode by minimizing the mean square deviation. The factor values are presented in the bottom line of the table. As seen from the table, even this oversimplified model reproduces the experimental frequencies assigned to the calculated isotopic configurations.