All DFT local energy minimizations were carried out using the Vienna ab initio Simulation Package (VASP) with the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation exchangecorrelation functional. We used the projector-augmented wave method, with the potentials listed in Table in the SI. The convergence criterion for electronic self-consistency was set to 10 -5 eV per cluster. Structures were optimized using the conjugate gradient approximation as implemented in VASP until all the atomic forces were less than 0.15 eV/Å. All calculations were run at the gamma point with spin polarization. Methfessel Paxton smearing with s= 0.001 eV was used to achieve high accuracy when calculating final energies. To accelerate convergence for some clusters, a two-step minimizations scheme was adopted with smearing of 0.1 eV in the initial step for faster convergence and a smaller value of 0.001 eV for the final step. Symmetry was turned off for all DFT calculations to increase the likelihood that the calculation completed successfully.