An improved Lanczos eigenvalue analysis method has been developed to compute the bound ro-vibrational states for the DOCl system at a total angular momentum of J = 0 and J = 30. In this method, the error norm is used to identify all the true eigenvalues, using the Lanczos algorithm without re-orthogonalization. For ro-vibrational spectroscopy calculations, the comparisons among experimental results, the exact quantum mechanical calculations, and the widely used approximate adiabatic rotation method have been made for J = 30. For J = 0, the density of states (DOS) in both the bound and unimolecular dissociation regime have been computed, whereas for the J = 30 case, only the DOS in the lower portion of the bound spectrum has been reported, because of substantial computational tasks.