Hydrogen storage and fuel cell catalysis are the corner stones of a green and sustainable economy. In the first part of the thesis, material design from first principles for hydrogen storage at ambient conditions was discussed with a specific emphasis on Kubas interaction in transition metal paddlewheel framework (TM-PWF) and transition-metal-incorporated defective graphene. In TM-PWF, orbital polarization arises due to the covalent metallic bonding between exposed metal sites. While the resulting anti-bonding dd$\sigma$* in general can have very favorable overlap with $H_2 \sigma$ , noticeable adsorption energies are only observed in late transition metals as gap between aforementioned orbitals are reduced. A simple 2D framework built from Co-PWF was also proposed with binding energy suitable for ambient storage application. Transition metal can also be stabilized against potential cohesion with strong covalent interaction with defective graphene. Especially for early TM such as Sc, Ti and V, the out-of- plane protrusion introduces addition $s-p_z$ polarization that plays in important role in stabilizing multiple $H_2$ adsorptions via Kubas mechanism. The degree of protrusion can be further tuned without compromising kinetics stability by taking advantage of covalent metal-metal bond exists in the TM dimer. Thus, TM-dimer embedded in di-vacancy defective graphene is a suitable design for high capacity $H_2$ storage. The second part of the thesis aims to provide understanding of the oxygen reduction reaction (ORR) mechanism in biomimetic $FeN_4$ embedded in nanostructure, which has recently been realized. Using state-or-the art free energy calculation, the interplay between four-electron pathway and two-electron pathway was investigated to reconcile the discrepancy between experiment and theoretical predictions.