Quantum chemistry method, which can be used to deal with molecular system based on quantum mechanics, is employed widely to study different objects and yield many relevant methods. In this thesis, we investigate some currently attractive problems in large system such as fullerene, biomolecule and nanotubes, using the relevant methods in Quantum chemistry. The content is summarized as following:1. The symmetry of C_(20) cage is studied based on the intrinsical relationship among point groups. The structure of C_(20) cage with I_h symmetry is constructed, as are eight other structures with subgroup symmetry. A path from I_h symmetry to C_1 symmetry is obtained for closed-shell electronic state and the structure with D_(2h) symmetry is the most stable on this path. Using this D_(2h) structure the correlation energy correction is studied under the condition of restricted excitation space at the CCSD(T) level. We obtain the curves on the relation between the orbital number and the total energy at CCSD(T), CCSD and MP2 level, respectively. The results of these curves obtained from MP2 and CCSD(T) methods have the same tendency, while the results of CCSD gradually diverge with an increasing in orbital number. When the orbitals used in the calculation reach 460, the total energy is -759.644 hartree at MP2 level and is -759.721 hartree by CCSD(T) method, respectively. From the calculated