In the case of Rh₆, a thorough search of likely structures was enough to identify two possible structural isomers. We optimized (using density functional theory, DFT) five likely structures (some of which were taken from results of basin-hopping simulations using the Sutton-Chen potential for Rhodium) as a function of spin states ranging from the singlet to the octet (neutral case) and the doublet ranging to the septet (cation case).

Our results indicate two likely structures: the octahedron and the trigonal prism. We have taken these two structures and performed reactivity calculations with respect to adsorption of both NO (nitric oxide) and N₂O (nitrous oxide). This was done in order to aid interpretation of current experiments performed in Warwick that have observed evidence of structural isomerism for Rh₆⁺ with respect to reaction with NO, and an unusual accelerating rate with respect to reaction with N₂O.

Below is an example of the kind of reaction we are investigating. On the left, we have the pre-dissociative minimum, in the centre, the transition state (the transition vector is shown), and on the left the dissociated product is shown. These three critical points on the potential energy surface were found using eigenvector following to follow the reaction pathway down from the transition state.