Theoretical and computational methods are powerful in studying transition metal complexes. Our theoretical studies of C-H σ-bond activation of benzene by Pd(II)-formate complex and that of methane by Ti(IV)-imido complex successfully disclosed that these reactions are understood to undergo heterolytic σ-bond activation and the driving force is the formation of strong O-H and N-H bonds in the former and the latter, respectively. Orbital interactions are considerably different from those of σ-bond activation by oxidative addition. The transmetallation, which is a key process in the cross-coupling reaction, is understood to be heterolytic σ-bond activation. Our theoretical study clarifi ed how to accelerate this transmetallation. Also, we wish to discuss weak points in theoretical and computational studies of large systems including transition metal elements, such as the necessity to incorporate solvation effect and to present quantitatively correct numerical results. The importance of solvation effects is discussed in the oxidative addition of methyliodide to Pt(II) complex which occurs in a way similar to an S N 2 substitution. To apply the CCSD(T) (coupled cluster singles and doubles with perturbative triples correction) method, which is the gold standard of electronic structure theory, to large system, we need to reduce the size of the system by employing a small model. But, such modeling induces neglects of electronic and steric effects of substitutents which are replaced in the small model. Frontier-orbital-consistent quantum-capping potential (FOC-QCP) was recently proposed by our group to incorporate the electronic effects of the substituents neglected in the modeling. The CCSD(T) calculation with the FOC-QCP was successfully applied to large systems including transition metal elements.