First principles investigations of vibrational properties of titania and zirconia clusters

Clusters are considered as ultrafine particles at microscopic scale and present the distinctive chemical and physical characteristics. In this paper, we described the structural and vibrational characteristics of titania and zirconia clusters calculated using density functional theory. The investigated clusters include monomers TiO2 and ZrO2, dimmers Ti2O4 and Zr2O4; and the hybrid TiZrO4 clusters. The hybrid cluster was prepared from two routes: first from titania and second from zirconia as starting material. The hybrid clusters are structural isomers of the same cluster and are named as trans − TiZrO4 and cis − TiZrO4, respectively. The geometries of the clusters were optimized at B3LYP level of theory and the structural properties including bond length, bond angle, and dipole moment, and Hirshfeld charges were studied. The vibrational properties of the clusters were predicted by calculating the Raman and infrared spectra. In case of monomers, the results indicated the presence of 3 Raman and 3 IR active modes. Whereas for dimmers, 12 modes of vibration were found which were simultaneously Raman and IR active. The hybrid clusters exhibited 12 Raman and IR active modes which are described in details. The formation of the trans − TiZrO4 is energetically cheaper than that of cis − TiZrO4 by an amount of 0.25 eV. The various parameters such as intensities, linear depolarization factors, and vibrations in route for preparation of the hybrid clusters are discussed. The studied Raman and IR properties shed light on the characteristics of the clusters which will be helpful to explore the applications of the materials. The calculated thermodynamic properties of the clusters are also given and discussed in detail.