# Ozone Activation on TiO\({}_{2}\) Studied by IR Spectroscopy and Quantum Chemistry
## 3 Results
### Results of Calculations
As expected for the localized vibration, the substitution of the second or third oxygen atoms resulted in almost equal large (about 30 cm\({}^{-1}\)) shifts of the band of \(\
u_{1}\) vibration, while the effect of replacement of the first O atom did not exceed 1 cm\({}^{-1}\) (Figure 4). As a result, the structure of the split \(\
u_{1}\) band is typical of an isotopically mixed diatomic: a triplet with the central band twice as intense as the others for a 50:50% mixture. The frequency of \(\
u_{3}\) vibration is sensitive to substitution of the first and second atoms, but the shifts in this case are different, at about 19 and 30 cm\({}^{-1}\), respectively. The effect of the third atom is much weaker (about 4 cm\({}^{-1}\)). A strong bulk absorption of TiO\({}_{2}\) below 1000 cm\({}^{-1}\) precludes the observation of a better spectrum than that shown in Figure 3b with the resolved peaks of different isotopomers. Nevertheless, the computed frequencies of the \(\
u_{1+3}\) combination vibrations shown in Figure 1 are in perfect agreement with the observed spectrum. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Isotopomer** & \multicolumn{2}{c}{\(\
u_{1}\)**, cm\({}^{-1}\)**} & \multicolumn{2}{c}{\(\
u_{3}\)**, cm\({}^{-1}\)**} & \multicolumn{2}{c}{\(\
u_{1+3}\)**, cm\({}^{-1}\)**} \\ \cline{2-6}  & **Calc. 1** & **Exp.** & **Calc. 2** & **Exp.** & **Calc. 3** & **Exp.** \\ \hline
16 16 16 & 1147.2 & 1145 & 993.0 & 993 & 2135.4 & 2136 \\
18 16 16 & 1147.0 & 1145 & 973.7 & - & 2118.8 & 2115 \\
16 16 18 & 1117.2 & 1118 & 1001.2 & - & 2103.6 & 2103 \\
18 16 18 & 1116.5 & 1118 & 979.7 & - & 2087.1 & 2084 \\
16 18 16 & 1114.9 & 1115 & 962.4 & - & 2070.8 & 2073 \\
18 18 16 & 1114.4 & 1115 & 943.4 & - & 2052.1 & 2051 \\
16 18 18 & 1083.8 & 1084 & 958.9 & - & 2034.2 & 2038 \\
18 18 18 & 1082.8 & 1084 & 939.7 & - & 2017.5 & 2019 \\ \hline \end{tabular}  
* scaling factor 0.9183. 2 scaling factor 1.0892. 3 scaling factor 0.9826.  
\end{table} 
Table 2: Experimental and calculated frequencies of different isotopomers of monodentate ozone complex with cluster TiO\({}_{2}\). As a more complex model, we chose the Ti\({}_{20}\)O\({}_{40}\) cluster (Figure 5), which simulates the predominant (101) anatase crystal face. The geometry of this cluster was optimized for the relaxation of Ti-O bonds. There are 16 four-coordinated and 4 five-coordinated Ti\({}^{4+}\) ions in this cluster after relaxation. As for oxygen, there are 8 three-coordinated, 28 two-coordinated, and 4 one-coordinated O\({}^{2}\) ions in this model cluster. The presence of the latter in the model in order to save stoichiometry should not create a problem. The structure allows us to model the monodentate and bidentate complexes with ozone on different surface centers. The optimized geometries of monodentate and bidentate ozone complexes with four-coordinated and five-coordinated Ti\({}^{4+}\) ions of the Ti\({}_{20}\)O\({}_{40}\) anatase cluster are shown in Figure 6. The calculated values on the geometry and energies are given above in Table 1 together with those for the TiO\({}_{2}\) cluster. According to the calculations, monodentates are the most stable ozone complexes for all the sites. In the order of adsorption energy decrease, the monodentate complex with four-coordinated titanium I is followed by monodentate complex III with the five-coordinated Ti\({}^{4+}\) ion, then the bidentate complex IV, and finally the bidentate complex II. Figure 4: Experimental spectrum of isotopically mixed ozone with 50% \({}^{18}\)O content (solid curve) and the calculated frequencies (vertical lines) of \({}^{18}\)O-containing ozone complexes with a TiO\({}_{2}\) cluster in the regions of \(\
u_{1}\) (**a**) and \(\
u_{3}\) (**b**) vibrations. Masses of oxygen atoms number 1–3 are shown from bottom to top. Figure 5: Geometry of the initial and relaxed anatase Ti\({}_{20}\)O\({}_{40}\) cluster (symmetry C\({}_{2h}\)).