Computational chemistry is a branch of modern chemistry that utilizes the computers to solve chemical problems. The fundamental of computational chemistry is Schrödinger equation. To solve the equation, researchers developed many methods based on BornOppenheimer Approximation, such as Hartree-Fock method and DFT method, etc. Computational chemistry is now widely used on reaction mechanism study and new chemical designing. In the first project described in Chapter 3, we designed phosphine oxide modified Ag3, Au3 and Cu3 nanocluster catalysts with DFT method. We found that these catalysts were able to catalyze the activation of H2 by cleaving the H-H bond asymmetrically. The activated catalyst-2H complex can be further used as reducing agent to hydrogenate CO molecule to afford HCHO. The mechanism study of these catalysts showed that the electron transfer from electron-rich metal clusters to O atom on the phosphine oxide ligand is the major driving force for H2 activation. In addition, different substituent groups on phosphine oxide ligand were tested. Both H affinity of metal and the substituent groups on ligand can both affect the activation energy. Another project described in Chapter 4 is the modelling of catalyst with DFT. We chose borane/NHC frustrated Lewis pair (FLP) catalyzed methane activation reaction as example to establish a relationship between activation energy and catalysts’ physical properties. After performing simulation, we further proved the well-accepted theory that the electron transfer is the main driving force of catalysis. Furthermore, we were able to establish a linear relationship for each borane between activation energy and the geometrical mean value of HOMO/LUMO energy gap (ΔEMO). Based on that, we introduced the formation energy of borane/NHC complex (ΔEF) and successfully established a generalized relationship between Ea and geometrical mean value of ΔEMO and ΔEF. This model can be used to predict reactivity of catalysts.