DescriptionNowadays, catalysis is of critical importance in chemical and pharmaceutical industry, and understanding the underlying mechanism of small molecule activation boosts development in the fields of organometallics and catalysis. In this Dissertation, we discuss DFT studies of several catalytic systems explored in our research lab. Headlines in the works are: (1) For pincer PCP iridium complexes catalyzed olefin hydroaryloxylation reaction, an organometallic mechanism via olefin insertion into an iridium−alkoxide bond, followed by rate-determining C−H reductive elimination, is proposed against a hidden Brønsted acid pathway common to previously developed transition-metal-based catalysts. (2) For a newly prepared carbazolide-based pincer PNP iridium complexes catalyzed olefin hydrogenation reaction, C2H4 and H2 assisted pathways are discovered. Especially, the more efficient H2 assisted pathway is found undergoing an Ir(III)/Ir(V)/Ir(III) cycle, in contrast to the Ir(III)/Ir(V)/Ir(III) cycle proceeded by isoelectronic (PCP)Ir systems. (3) For carbazolide-based pincer PNP rhodium complexes catalyzed hydrogenation /dehydrogenation reactions, the forming/ opening of a β-H agostic intermediate is found to be the rate determining step. (4) For the olefin insertion reaction and alkane hydrogenolysis reaction on (Phebox)Ir acetate complexes, Na+ is found to catalyze the reactions through bonding to the terminal acetate O atom on key intermediates and rate determining states, thus stabilizing these states.