In this research the validity of various computational techniques has been determined and applied the appropriate techniques to investigate and propose a good catalytic system for C-H bond activation and functionalization. Methane being least reactive and major component of natural gas, its activation and conversion to functionalized products is of great scientific and economic interest in pure and applied chemistry. Thus C-H activation followed by C-C/C-X functionalization became crux of the synthesis. DFT (density functional theory) methods are well suited to determine the thermodynamic as well as kinetic factors of a reaction. The obtained results are helpful to industrial catalysis and experimental chemistry with additional information: since C-X (X = halogens) bond cleavage is important in many metal catalyzed organic syntheses, the results obtained in this research helps in determining the selectivity (kinetic or thermodynamic) advantage. When C-P bond activation is considered, results from chapter 3 indicated that C-X activation barrier is lower than C-H activation barrier. The results obtained from DFT calculations not only gave a good support to the experimental results and verified the experimentally demonstrated Ni-atom transfer mechanism from Ni=E (E = CH2, NH, PH) activating complex to ethylene to form three-membered ring products but also validated the application of late transition metal complexes in respective process. Results obtained supported the argument that increase in metal coordination and electronic spin state increases catalytic activity of FeIII-imido complexes. These results not only encouraged the fact that DFT and multi-layer ONIOM methods are good to determine geometry and thermodynamics of meta-stable chemical complexes, but also gave a great support to spectroscopic calculations like NMR and Mossbauer calculations.