Cluster Geometry
A cluster size of 15 Ir atoms was chosen by analyzing the cohesive energy and spin density of Irn clusters (n=10, 15, 20, 25, 30) shown in Figure 1. Each Ir atom has nine valence electrons spread amongst its 5d and 6s orbitals. An initial estimate for the number of unpaired electrons in our modeled catalyst was determined using Kua and Goddard’s Interstitial Electron Model.35Their model estimates the unpaired electrons for the (111) surface and hypothesizes that the surface has s1d8 configuration. This methodology was used to describe the (100) surface as well, as an initial guess. The number of unpaired electrons in the ground state and the energies of each cluster are calculated and presented in Table 1. Cluster energies were calculated for two multiplicities above and below the ground state multiplicity to evaluate convergence to a minimum. Clusters larger than 20 atoms did not converge using B3LYP or B3LYP-D3. Only the (100) surface of B97-D3 converged for clusters larger than 25. As shown in Table 1, the larger the cluster, the closer the cohesive energy comes to approaching the experimental bulk cohesive energy of iridium, 670 kJ/mol.36,37 (111) surfaces are more tightly packed and thus approach the bulk cohesive energy quicker than (100) surfaces. A cluster size of 15 atoms is ultimately chosen over a size of 20 atoms because the spin densities across the 15-atom cluster are closer to the number of unpaired electrons per atom in the ground state d-orbital i.e. two (see Figure 2).
The 15-atom cluster is chosen for both the (111) and (100) surfaces; they are pictured in Figure 1c and 1d respectively. They are both two-layer clusters with enough surface area that all principal adsorption sites on the surface are distanced from the catalyst’s edge, reducing “edge effects.”