Calculation of the temperature dependence of the magnetic susceptibility of subnanosized titanium dioxide clusters
G.P. Mikhailov
Ufa University of Science and Technology
DOI: 10.26456/pcascnn/2025.17.284
Original article
Abstract: Subnanosized clusters containing paramagnetic titanium and oxygen ions can be considered as fragments of the surface of nanocrystalline titanium dioxide. The analysis of the temperature dependence of the magnetic susceptibility of titanium dioxide clusters makes it possible to study the manifestations of surface magnetic states and identify the type of magnetic ordering. Using the density functional theory method in the M06/6-31G(d, p) approximation, a quantum chemical calculation of the equilibrium geometry of (TiO2)n (n = 2-5, 13, and 15) clusters with a full or predominant proportion of surface atoms was performed. It is established that for all (TiO2)n clusters, the singlet electron configuration is the ground state. To assess the thermal stability of (TiO2)n cluster structures and study the effect of temperature in the range of 10-900 K in 50 K increments, calculations were performed using the ab initio method of molecular dynamics and the atom-centered density matrix propagation scheme. The length of each molecular dynamics trajectory was 1 ps with a time step of 1 fs. For each temperature, the magnetic susceptibility tensor was calculated using the coordinate invariant atomic orbitals (gauge including atomic orbitals) method in the approximation M06/6-31G(d, p). It is shown that the temperature dependence of the values of the isotropic magnetic susceptibility has a maximum at temperature Tmax. At T > Tmax, there is a decrease in the temperature dependence of the magnetic susceptibility of (TiO2)n clusters. It has been established that the main magnetic state of (TiO2)n clusters is an antiferromagnetic singlet. The importance of the anisotropy of magnetic susceptibility for the TiO2 molecule and clusters of (TiO2)n is shown.
Keywords: subnanosized cluster, titanium dioxide, density functional theory, ab initio molecular dynamics, magnetic susceptibility
- Gennady P. Mikhailov – Dr. Sc., Professor, Department of Materials Science and Physics of Metals, Ufa University of Science and Technology
For citation:
Mikhailov G.P. Raschet temperaturnoj zavisimosti magnitnoj vospriimchivosti subnanorazmernykh klasterov dioksida titana [Calculation of the temperature dependence of the magnetic susceptibility of subnanosized titanium dioxide clusters], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 284-292. DOI: 10.26456/pcascnn/2025.17.284. ⎘
Full article (in Russian): download PDF file
References:
1. Ermakov A.E., Uimin M.A., Korolev A.V. et al. [Anomalous magnetism of the nanocrystalline oxide TiO2 surface], Physics of the Solid State, 2017, vol. 59, issue 3, pp. 469-482. DOI: 10.1134/S1063783417030106.
2. Sui Y., Liu Q., Jiang T., Guo Y. Synthesis of nano-TiO2 photocatalysts with tunable Fe doping concentration from Ti-bearing
tailings, Applied Surface Science, 2018, vol. 428, pp. 1149-1158. DOI: 10.1016/j.apsusc.2017.09.197.
3. Kaleji B.K., Mirzaee S, Ghahramani S. et al. Sol–gel synthesis of Sn/Fe co-doped TiO2 nanoparticles: study of structural, optical and photocatalytic properties, Journal of Materials Science: Materials in Electronics, 2018, vol. 29, issue 14, pp. 12351-12359. DOI: 10.1007/s10854-018-9348-x.
4. Molochnikov L.S., Borodin K.I., Yermakov A.E. et al. Magnetism and temperature dependence of nano-TiO2: Fe EPR spectra, Materials Chemistry and Physics, 2022, vol. 276, art. no. 125327, 7 p. DOI: 10.1016/j.matchemphys.2021.125327.
5. Rana T.H., Sahota P.K., Solanki A.K. et al. Ab-initio study of free standing TiO2 clusters: Stability and magnetism, Journal of Applied Physics, 2013, vol. 113, pp. 17B526-1-17B526-3. DOI: 10.1063/1.4799616.
6. Qu Z.-w., Kroes G.-J. Theoretical study of stable, defect-free (TiO2)n nanoparticles with n=10-16, The Journal of Physical Chemistry C, 2007, vol. 111, issue 45, pp.16808-16817. DOI: 10.1021/jp073988t.
7. Mikhailov, G.P. Quantum chemical calculations of the magnetic susceptibility tensor of titanium dioxide clusters, Russian Journal of Physical Chemistry A: Focus on Chemistry, 2024, vol. 98, issue 8, pp. 1757-1762. DOI: 10.1134 /S003602442470081X.
8. Frisch M.J., Trucks G.M. et al. Gaussian 09 (Revision D.01). Wallingford, Gaussian Inc., 2013.
9. Schlegel H.B., Millam J.M., Iyengar S.S. et al. Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals, Journal of Chemical Physics, 2001, vol. 114, issue 22, pp. 9758-9763. DOI: 10.1063/1.1372182.
10. Ruud K., Helgaker T., Bak K.L et al.Hartree-Fock limit magnetizabilities from London orbitals / K. Ruud, T. Helgaker, K.L. Bak et al., Journal of Chemical Physics, 1993, vol. 99, issue 5, pp. 3847-3859. DOI: 10.1063/1.466131.
11. Chemcraft – graphical software for visualization of quantum chemistry computations. Version 1.6. Available at: www.chemcraftprog.com (accessed 1.09.2024).
12. Carlin R.L. Magnetochemistry. Berlin, Heidelberg, Springer-Verlag, 2011, XI, 328 p. DOI: 10.1007/978-3-642-70733-9.
13. Zhong X., Rungger I., Zapol P., Heinonen O. Electronic and magnetic properties of Ti4O7 predicted by self-interaction corrected density functional theory, Physical Review B, 2015, vol. 91, issue 11, pp. 115143-1-115143-8. DOI: 10.1103/PhysRevB.91.115143.
14. Yu X., Oganov A.R., Popov I.A., Qian G., oldyrev A.I. Antiferromagnetic stabilization in the Ti8O12 cluster, Angewandte Chemie, 2016, vol. 128, issue 5, pp. 1731-1735. DOI: 10.1002/ange.201508439.
15. Guo R., Uddin M.N., Price L.S., Price S.L. Calculation of diamagnetic susceptibility tensors of organic crystals: from coronene to pharmaceutical polymorphs, Journal of Physical Chemistry A, 2020, vol. 124, issue 7, pp. 1409-1420. DOI: 10.1021/acs.jpca.9b07104.