The lowest (2)Sigma (+) and (2)Pi electronic states of the HeBr molecule have been calculated by the ab initio coupled cluster approach in conjunction with a series of increasing size augmented correlation-consistent basis sets of double through quintuple zeta quality. Different extrapolation formulas to the complete basis set limit have been tested by comparing estimated and actual quintuple zeta quality counterpoise corrected interaction energies. Frozen-core approach is checked by performing calculations in which all electrons are correlated. The potential energy surfaces of the HeBr2 van der Waals complex have been obtained from the HeBr potentials by means of the diatomic-in-molecule approach. Finally, transport, scattering, and spectroscopic properties of HeBr and HeBr2(B) systems derived from ab initio data for different basis sets are examined. It is shown that their convergence closely follows the convergence of corresponding potential energy surfaces.