Abstract
The symmetry of the C~20~ cage is studied based on the intrinsical relationship among point groups (Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry in Solids; Claredon Press: Oxford, 1972). The structure of the 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 the closedβshell electronic state, and the structure with D~2h~ symmetry is the most stable on this path. Using the D~2h~ structure the correlation energy correction is studied on the condition of restricted excitation space at the CCSD(T) level. We obtain curves on the relation between the orbital numbers and the total energy at the 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 increase in orbital numbers. When the orbitals used in the calculation reach 460, the total energy is β759.644 hartree at MP2 level and is β759.721 hartree by the CCSD(T) method. From the calculation results, we find that a large basis set can improve the reliability of the MP2 method, and to restrict excitation space is necessary when using the CCSD(T) method. Β© 2005 Wiley Periodicals, Inc. J Comput Chem 12: 1279β1283, 2005