The present work is concerned with the weak interactions between hydrogen and halogen molecules, i.e., the interactions of pairs H2–X2 with X = F, Cl, Br, which are dominated by dispersion and quadrupole-quadrupole forces. The global minimum of the four-dimensional (4D) coupled cluster with singles and doubles and perturbative triples (CCSD(T)) pair potentials is always a T shaped structure where H2 acts as the hat of the T, with well depths (De) of 1.3, 2.4, and 3.1 kJ/mol for F2, Cl2, and Br2, respectively. MP2/AVQZ results, in reasonable agreement with CCSD(T) results extrapolated to the basis set limit, are used for detailed scans of the potentials. Due to the large difference in the rotational constants of the monomers, in the adiabatic approximation, one can solve the rotational Schrödinger equation for H2 in the potential of the X2 molecule. This yields effective two-dimensional rotationally adiabatic potential energy surfaces where pH2 and oH2 are point-like particles. These potentials for the H2–X2 complexes have global and local minima for effective linear and T-shaped complexes, respectively, which are separated by 0.4-1.0 kJ/mol, where oH2 binds stronger than pH2 to X2, due to higher alignment to minima structures of the 4D-pair potential. Further, we provide fits of an analytical function to the rotationally adiabatic potentials.