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.”