Density functional theory calculations are employed to investigate the electronic, adsorption, and catalytic properties of Bi-, Sb-, and As-nanoclusters. The stability of these clusters are confirmed by the obtained positive binding energies, the change in the free energy, and frequencies, also they can be grown on different substrates such as graphene and hexagonal boron nitride. They have energy gaps ranging from 2.1 to 3 eV that can be controlled by adsorption of different gases or molecules, for instance, adsorption of C2 decreases the gap in Sb18-a cluster from 2.7 eV to 0.8 eV. These clusters show also interesting adsorption properties where some gases are physically adsorbed (like, N2 and CH4) while others are chemically adsorbed (O2 and SO2). In the first case, the linear N2 molecule has a strong triple bond, from the sp-hybridization, that can't be broken through the interaction with the clusters, the same occurs also for the sp3-hybridized CH4 with the strong sigma bonds. For the sp2-hybridized O2 molecule, one of the relatively weaker double bond can be broken through the interaction to form another with the cluster. The oxygen evolution reaction (OER) on the edges of these clusters requires lower overpotential than their surfaces due to the moderate adsorption of O by one edge atom with respect to the strong adsorption by two surface atoms. Nanoclusters and quantum dots of Sb provide the best values for the overpotential due to moderate bonding that Sb atoms form with all intermediates not only O, namely overpotentials equal 0.31 and 0.39 V for the nanocluster and the quantum dots, respectively. This significant enhancement of the OER activity makes such clusters strong applicants for water oxidation catalysts.