For the prototypical diatomic-molecule diatomic-molecule interactions H-2-HX and H-2-X-2, where X = F, Cl, Br, quantum-chemical ab initio calculations are carried out on grids of the configuration space, which permit a spherical-harmonics representation of the potential energy surfaces (PESs). Dimer geometries are considered for sets of representative leading configurations, and the PESs are analyzed in terms of isotropic and anisotropic contributions. The leading configurations are individuated by selecting a minimal set of mutual orientations of molecules needed to build the spherical-harmonic expansion on geometrical and symmetry grounds. The terms of the PESs corresponding to repulsive and bonding dimer geometries and the averaged isotropic term, for each pair of interacting molecules, are compared with representations in terms of a potential function proposed by Pirani et al. (see Chem. Phys. Lett. 2004, 394, 37-44 and references therein). Connections of the involved parameters with molecular properties provide insight into the nature of the interactions.