Revisiting fundamental properties of TiO₂ nanoclusters as condensation seeds in astrophysical environments^★

¹ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
e-mail: janphilip.sindel@oeaw.ac.at
² Centre for Exoplanet Science, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK
³ SUPA, School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK
⁴ Institute for Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
⁵ Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigárden 4, 412 96 Gothenburg, Sweden
⁶ TU Graz, Fakultät für Mathematik, Physik und Geodäsie, Petersgasse 16, 8010 Graz, Austria

Received: 10 February 2022
Accepted: 24 June 2022

Abstract

Context. The formation of inorganic cloud particles takes place in several atmospheric environments, including those of warm, hot, rocky, and gaseous exoplanets, brown dwarfs, and asymptotic giant branch stars. The cloud particle formation needs to be triggered by the in situ formation of condensation seeds since it cannot be reasonably assumed that such condensation seeds preexist in these chemically complex gas-phase environments.

Aims. We aim to develop a method for calculating the thermochemical properties of clusters as key inputs for modelling the formation of condensation nuclei in gases of changing chemical composition. TiO₂ is used as benchmark species for cluster sizes N = 1–15.

Methods. We created a total of 90000 candidate (TiO₂)_N geometries for cluster sizes N = 3−15. We employed a hierarchical optimisation approach, consisting of a force-field description, density-functional based tight-binding, and all-electron density-functional theory (DFT) to obtain accurate zero-point energies and thermochemical properties for the clusters.

Results. In 129 combinations of functionals and basis sets, we find that B3LYP/cc-pVTZ, including Grimme’s empirical dispersion, performs most accurately with respect to experimentally derived thermochemical properties of the TiO₂ molecule. We present a hitherto unreported global minimum candidate for size N = 13. The DFT-derived thermochemical cluster data are used to evaluate the nucleation rates for a given temperature-pressure profile of a model hot-Jupiter atmosphere. We find that with the updated and refined cluster data, nucleation becomes unfeasible at slightly lower temperatures, raising the lower boundary for seed formation in the atmosphere.

Conclusions. The approach presented in this paper allows finding stable isomers for small (TiO₂)_N clusters. The choice of the functional and basis set for the all-electron DFT calculations has a measurable impact on the resulting surface tension and nucleation rate, and the updated thermochemical data are recommended for future considerations.