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Modeling the Temperature Dependence of the Energy Gap of a Subnanocluster of Titanium Dioxide

G.P. Mikhailov, Yu.G. Voronova

Ufa University of Science and Technology

DOI: 10.26456/pcascnn/2026.18.XXX

Original article

Abstract: Using quantum-chemical modeling methods, the temperature dependence of the energy gap of the (TiO2)15 subnanocluster was studied in the range from 10 to 900 K. Within the framework of density functional theory (M06/6-31G(d,p) approximation), it was found that the (TiO2)15 subnanocluster has a quasi-spherical shape (C2h symmetry, diameter of 0,9 nm), and its inner core exhibits the atomic order of rutile. Thermostable structures (TiO2)15 were obtained by the non-empirical molecular dynamics method using the Atom-Centered Density Matrix Propagation scheme. For each temperature, the energy gap Egap between the lowest vacant and highest occupied molecular orbitals was calculated using the M06/6-31G(d,p) approximation. The obtained data were analyzed using the Eg(T) model dependencies developed for crystalline solids. The qualitative similarity of the temperature dependencies of Eg(T) for the (TiO2)15 cluster and bulk semiconductors has been established, namely, a non-linear monotonic decrease of the Eg with increasing temperature. As the temperature increases, significant anharmonicity of the (TiO2)15 cluster vibrations is observed, and the temperature sensitivity of the O 2p (highest occupied molecular orbital) and Ti 3d (lowest unoccupied molecular orbital) molecular orbitals is different, with the titanium orbitals showing a weak dependence. The most adequate and physically interpretable results are obtained using the O’Donnell-Chen model, which takes into account the quantum nature of the subnanocluster vibrations and allows us to determine the average energy of the vibrational modes that determine the temperature dependence of the energy gap.

Keywords: nanocluster, titanium dioxide, density functional theory, energy gap

  • Gennady P. Mikhailov – Dr.Sc., Professor, Department of Materials Science and Physics of Metals, Ufa University of Science and Technology
  • Yulia G. Voronova, Ufa University of Science and Technology

For citation:

Mikhailov G.P., Voronova Yu.G. Modelirovanie temperaturnoj zavisimosti energeticheskogo zazora subnanoklastera dioksida titana [Modeling the Temperature Dependence of the Energy Gap of a Subnanocluster of Titanium Dioxide], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2026, issue 18, pp. __-__. DOI: 10.26456/pcascnn/2026.18.XXX. ⎘

Full article (in Russian): download PDF file

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