We have theoretically studied the structures of molecules and the profiles of chemical reactions using quantum chemical computational methods such as the ab initio (non-empirical) molecular orbital method and the density functional theory method. These first-principles calculations would give information on the electronic as well as geometric structures, which are expected to be useful in designing molecules and chemical reactions. With the theoretical calculations we could clarify the nature of transient species and transition states, which are difficult to study experimentally, and recognize the factors controlling chemical reactions. We are investigating with such calculations mechanisms of elementary organometallic reactions and a whole catalytic cycle constructed by combining elementary reactions.