The structural, thermodynamics, electronics and mechanical properties of Rhodium and Ruthenium transition metals are analyzed using the first principle calculations in this research. We adopted the DFT with the solution pf Kohn – Sham equation given and using the Xcryden package where the elemental structures were obtained and the PAW pseudo – potentials and GGA to treat the exchange – correlation function with the PBE functional. The results for the lattice parameters deviated from experimental and theoretical results with approximately 1.6% for Ru and 1.9% for Rh. The bulk moduli agree with other reported results reported in the literature. The outcome of this investigation shows that the examined elements are mechanically stable as they agreed excellently with the results discussed in the literature. The band three – fold, two – fold degenerate. And non – degenerate levels are represented by the parameters for Rh and Ru respectively are C44 is 2.0 and 221, C11 – C12 is 0.19 and 238, and 2C11 – 2C12 is 8.74 and 1376. The results also indicate that Ru exhibits anisotropic tendencies compared to Rh in terms of its elastic characteristics and more prone to modify its properties depending on the direction of its covalent bonding while Rh withstand breaking during experimental development compared to Ru because of its anisotropy’s greater deviation from unity, hence, this is accurately given that it’s also stiffer and tougher.

Bulk moduli, Rhodium, Ruthenium, DFT, GGA