2024A&A...690A..34L

Context. As a refractory material, vanadia (solid V₂O₅) is likely to be found as a condensate in the atmospheres of substellar objects such as exoplanets and brown dwarfs. However, the nature of the nanometer-sized vanadium oxide clusters that partake in the nucleation process is not well understood.
Aims. We aim to understand the formation of cloud condensation nuclei in oxygen-rich substellar atmospheres by calculating the relevant fundamental properties of the energetically most favorable vanadium oxide molecules and clusters and, investigate how they contribute to the formation of condensation seeds.
Methods. We applied a hierarchical optimization approach in order to find the most favourable structures for clusters of (VO)_N and (VO₂)_N for N = 1-10, and of (V₂O₅)_N for N = 1-4, and to calculate their thermodynamical potentials. The candidate geometries are initially optimized by applying classical interatomic potentials; these are then refined at the B3LYP/cc-pVTZ level of theory to obtain accurate zero-point energies and thermochemical quantities.
Results. We present previously unreported vanadium oxide cluster structures as the lowest-energy isomers. Moreover, we report revised cluster energies and their thermochemical properties. Chemical equilibrium calculations are used to assess the impact of the updated and newly derived thermodynamic potentials on the gas-phase abundances of vanadium-bearing species. In chemical equilibrium, larger clusters from different stoichiometric families are found to be the most abundant vanadium-bearing species for temperatures below ∼1000 K, while molecular VO is the most abundant between ∼1000 K and ∼2000 K. We determine the nucleation rates of each stoichiometric family for a given (T_gas, p_gas) profile of a brown dwarf using both classical and non-classical nucleation theory.
Conclusions. Small differences in the revised Gibbs free energies of the clusters have a large impact on the abundances of vanadium-bearing species in chemical equilibrium at temperatures below ∼1000 K. These abundance changes subsequently have an impact on the nucleation rates of each stoichiometric family. We find that with the revised and more accurate cluster data, non-classical nucleation rates are up to 15 orders of magnitude higher than classical nucleation rates.