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We aim to understand the formation of cloud condensation nuclei inoxygen-rich substellar atmospheres by calculating fundamental properties of theenergetically most favorable vanadium oxide molecules and clusters. Ahierarchical optimization approach is applied in order to find the mostfavorable structures for clusters of (VO)$_{N}$ and (VO$_2$)$_{N}$ for N=1-10,and (V$_2$O$_5$)$_{N}$ for N=1-4 and to calculate their thermodynamicalpotentials. The candidate geometries are initially optimized applying classicalinteratomic potentials and then refined at the B3LYP/cc-pVTZ level of theory toobtain accurate zero-point energies and thermochemical quantities. We presentpreviously unreported vanadium oxide cluster structures as lowest-energyisomers. We report revised cluster energies and their thermochemicalproperties. Chemical equilibrium calculations are used to asses the impact ofthe updated and newly derived thermodynamic potentials on the gas-phaseabundances of vanadium-bearing species. In chemical equilibrium, largerclusters from different stoichiometric families are found to be the mostabundant vanadium-bearing species for temperatures below ~1000 K, whilemolecular VO is the most abundant between ~1000 K and ~2000 K. We determine thenucleation rates of each stoichiometric family for a given (T$_{gas}$,p$_{gas}$) profile of a brown dwarf using classical and non-classicalnucleation theory. Small differences in the revised Gibbs free energies of theclusters have a large impact on the abundances of vanadium bearing species inchemical equilibrium at temperatures below ~1000 K, which subsequently has animpact on the nucleation rates of each stoichiometric family. We find that withthe revised and more accurate cluster data non-classical nucleation rates areup to 15 orders of magnitude higher than classical nucleation rates.

Vanadium oxide clusters in substellar atmospheres: A quantum chemical study