The geometries and the relative energies of two $Cl_2O$, three $Cl_2O_2$ isomers and various $Cl_2O_3$ isomers in the ground state have been calculated using DFT(density functional theory) methods. The DFT relative energies using extended basis sets are in good agreement with CCSD(T) results. The vibration frequencies of two $Cl_2O$ isomers, ClOCl and ClClO, are also calculated and compared with experimental data. The present study suggests that the DFT method could be an economical means for investigating relative energies of chlorine oxide in their ground state for which large basis sets are essential even for the modest accuracy.