Stability-driven analysis of rhodium and ruthenium doping in titanium clusters: DFT study

Research studies on doped titanium clusters have not received significant attention in both theoretical and experimental fields. This is attributed to the complexity of almost empty d orbital for titanium metal, which results in its unique bonding properties. Thus, bimetallic systems offer a new degree of freedom to extend the titanium nanoclusters' properties by doping with other transition metal elements. In this study, the density functional theory (DFT) approach was employed with the PBEsol exchange-correlation functional to investigate the structural and electronic properties of Ti_NM (N = 1 - 19, M = Ru, Rh) nanoclusters. The investigation revealed that Rh mostly favours to be placed on the edge and surface, whereas the Ru impurity mostly favours the apex of the nanoclusters. Rhodium and ruthenium dopants are observed to enhance the binding energy of pure Ti nanoclusters, with Ru dopant revealing the least binding energies. The relative stability showed that the doping of Rh and Ru converted the N = 13 cluster into the magic cluster, whereas the dissociation energy showed reduction in stability strength for N = 7 and enhanced stability for N = 13. Notably, the local maxima of the HOMO-LUMO gap for Rh, Ru doped Ti clusters occur at N = 13, suggesting relatively stable cluster. VIP, VEA, η, S, electronegativity, chemical potential, electrophilicity, and wavelength suggested that the results have strong quantum size effects at small N and progressive quasi-metallic stabilisation at larger sizes, with Rh inducing stronger oscillatory and localised reactivity while Ru promotes smoother electronic evolution. The density of states (DOS) for both Rh and Ru impurities stabilise the Ti₁₃ cluster electronically, with rhodium emerging as the more favourable dopant.