The scope of work in this dissertation has comprised several major investigations on applications and theoretical studies of ab initio quantum mechanics and density functional theory where those techniques were applied to the following: (i) investigation of the performance of density functionals for the computations of molecular properties of 3d transition metal containing systems; (ii) guidance for experimental groups for rational design of macrometallocyclic multinuclear complexes with superior π-acidity and π-basicity that are most suitable for p- and n-type semiconductors of metal-organic molecules and nanomaterials; (iii) investigation of the metallo-aromaticity of multi-nuclear metal complexes; (iv) investigation of the kinetics and thermodynamics of copper-mediated nitrene insertion into C-H and H-H bond; and (v) accurate computations of dissociation energies of hydrogen-bonded DNA duplex moieties utilizing the resolution of identity correlation consistent composite approach (RI-ccCA).