The experimentally interesting ${\mathrm{Nb}}_3$ and ${\mathrm{Nb}}_4$ clusters and their cations have been studied in great detail using density-functional methodology in conjunction with relativistic effective core potentials. Close attention has been paid to full optimization along the flat potential energy surfaces and numerous minima and several transition states have been characterized. The ${\mathrm{Nb}}_3$ cation is predicted to have a ${}^3{A}_1^{\prime }$ ground state with an equilibrium geometry of $D_{3h}$ symmetry. The ground state of the neutral is predicted to be a ${}^2{B}_1$ state of $C_{2v}$ symmetry with two shorter bonds and one longer. The transition state for pseudorotation or “peak” atom interchange, however, lies only 0.01 kcal/mol higher in energy, implying a fluxional structure for the neutral species. The global minimum of the ${\mathrm{Nb}}_4$ cationic cluster is a $C_{2v}$ structure, Jahn-Teller distorted from the $T_d$ global minimum of the singlet neutral. Numerous other energetically low-lying stationary points are characterized for each species. We discuss the bonding features of these minima and relate our predictions to the existing experimental data.

• Received 12 January 1999

DOI:https://doi.org/10.1103/PhysRevA.60.3058