Density functional theory calculations have been carried out to observe the role of hydrogen bonding in hydrolysis and the coordination mechanism of three amino acid residues (histidine, cysteine, and alanine) with Ru-bis-DMSO complex via which the complex tends to interact with the HSA protein receptor. The interaction mechanism shows that ruthenium complexes prefer to bind protein receptor through cysteine and histidine residues rather than through alanine, which has been confirmed by DFT evaluated H-bonding and g-tensor analysis. The number of H-bonds plays a major role in stabilizing the intermediates and transition states involved in the Ru-bis-DMSO and amino acid residue interactions. Our theoretical g-tensor values are in good agreement with the available experimental results. Further QM/MM calculation on the Ru-bis-DMSO-HSA adducts reveals that the adduct is more stable when Ru gets coordinated with histidine imidazole rather than cysteine. These investigations helped us in understanding the type of amino acid residue responsible for binding the metal complex Ru-bis-DMSO with the carrier protein HSA.