The structures of different neutral and cationic isomers of Nb3O, Nb3S and Nb3Se were optimized within the framework of Kohn-Sham density functional theory. For Nb3O, neutral and cationic, the lowest minimum is a planar C-2v structure with an edge-bound oxygen atom. The binding energy of the oxygen to the Nb-3 cluster is 184.9 kcal/mol, 185.4 kcal/mol for the cationic system. For Nb3S and Nb3Se, neutral and cationic, the lowest minima are three-dimensional structures. The corresponding binding energies are 137.9, 138.1, 131.8 and 132.3 kcal/mol for Nb3S, Nb3S+, Nb3Se and Nb3Se+, respectively. In order to explain the different ground state structures of Nb3O, on the one hand, and Nb3S and Nb3Se, on the other, in terms of the nature of the bonding in each of them a topological analysis of the molecular electrostatic potential was performed. The different relative stabilities of two- and three-dimensional structures can be explained on the basis of bond critical points in the molecular electrostatic potential.