A few open-shell molecules are taken as examples in order to examine the performance of the open-shell perturbation theory for electron correlation(J Chem Theory Comput,2009,5:931–936).The convergence of the perturbation series is shown to be stable for the doublet state of NH2 at both the equilibrium and stretched geometries.The equilibrium bond lengths,and harmonic and anharmonic vibrational frequencies are calculated for NO(X2),OH(X2),CH(X2)and NH(X2)with different second-order perturbation theories at the cc-pVDZ,cc-pVTZ and cc-pVQZ levels.The ground state energies of BeF(X2+), MgH(X2+)and the HCCl triplet state have also been computed with various perturbation theories and compared with configuration interaction with single and double excitations(CISD)and CISD+Davidson correction.The energy difference between the formaldehyde(H2CO + )and hydroxymethylene(HCOH+)radical cations has been computed.Our perturbation theory predicts correctly that H2CO + is more stable than HCOH+.However,calculations using UMP2,CASPT2,the Z-averaged perturbation theory and restricted Mφller–Plesset theory fail even to produce the correct sign of the energy difference. A few open-shell molecules are taken as examples in order to examine the performance of the open-shell perturbation theory for electron correlation (J Chem Theory Comput, 2009, 5: 931-936). The convergence of the perturbation series is shown to be stable for the doublet state of NH2 at both the equilibrium and stretched geometries. The equilibrium bond lengths, and harmonic and anharmonic vibrational frequencies are calculated for NO (X2), OH (X2), CH (X2) and NH (X2) with different second-order perturbation theories at the cc-pVDZ, cc-pVTZ and cc-pVQZ levels. The ground state energies of BeF (X2 +), MgH (X2 +) and the HCCl triplet state have also been computed with various perturbations theories and than with configuration interaction with single and double excitations (CISD) and CISD + Davidson correction. energy difference between the formaldehyde (H2CO +) and hydroxymethylene (HCOH +) radical cations has been computed. Our perturbation theory predicts correctly that H2CO + is more stable than HCOH + .Howev er, calculations using UMP2, CASPT2, the Z-averaged perturbation theory and restricted Mφller-Plesset theory fail even to produce the correct sign of the energy difference.