1-[2-(2-hydroxy-3-methoxy-5-(4-methoxyphenylazo)benzaldeneamino)ethyl]-3-methyl-3H-imidazole (HMY) and 1-[2-(2-hydroxy-3-methoxy-5-(4-methylphenylazo)benzaldene amino)ethyl]-3-methyl-3H-imidazole (HMM) were synthesized and characterized using spectral analysis. Conformational analysis has been achieved using potential energy scan for different rotable bonds for obtaining the lowest energy conformer. Conformer with minimum energy is obtained along the dihedral angle N30-C31-C34-N37. QTAIM analysis gives nature and strength of hydrogen bonding interactions. UV-Vis, electrostatic potential and chemical descriptors are analyzed. Interaction of HMY and HMM with graphene is analyzed in terms of SERS activity. Chemical reactivity descriptors were investigated for graphene-drug systems. NLO activity of parent drugs and its graphene complexes show good activity. The wavenumber downshift of different modes is noted. Title molecules exhibit inhibitory activity against cytochrome C peroxidase. Interactions with graphene sheets are theoretically predicted for the title compounds.