We report results of non-relativistic and two-component relativistic single-reference coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] treatments for the 4p-block dimers Ga2 to Br2, the 5p-block dimers In2 to I2, and their atoms. Extended basis sets up to pentuple zeta are employed and energies extrapolated to the complete basis-set limit. Relativistic and non-relativistic results for the dissociation energy De are in close agreement with each other and previously published data, provided non-relativistic or scalar-relativistic results are corrected for spin–orbit contributions taken from the literature. An exception is Te2 where theoretical results scatter by 0.085 eV. By virtue of this agreement it is unexpected that comparison with the experimental D0 or De dissociation energies (zero-point vibrational effects are negligible in this context) reveal errors larger than 0.1 eV for Ga2, Ge2, and Sb2. Only relativistic treatments are presented for the 6p-block cases Tl2 to At2. Sufficient agreement with experimental data is found only for Pb2 and Bi2, the deviation of the computed and experimental D0 values for Po2 is again larger than 0.1 eV. Deviations of 0.1 eV between the computed and experimental D0 values are a major reason for concern and call for additional investigations in both fields to clarify the situation.