The capture rate coefficients of homonuclear diatomic molecules (H-2 and N-2) in the rotational state j=1 interacting with ions (Ar+ and He+) are calculated for low collision energies assuming a long-range anisotropic ion-induced dipole and ion-quadrupole interaction. A comparison of accurate quantum rates with quantum and state-specific classical adiabatic channel approximations shows that the former becomes inappropriate in the case when the cross section is dominated by few partial contributions, while the latter performs better. This unexpected result is related to the fact that the classical adiabatic channel approximation artificially simulates the quantum effects of tunneling and overbarrier reflection as well as the Coriolis coupling and it suppresses too high values of the centrifugal barriers predicted by a quantum adiabatic channel approach. For H-2(j=1)+Ar+ and N-2(j=1)+He+ capture, the rate constants at T-->0 K are about 3 and 6 times higher than the corresponding values for H-2(j=0)+Ar+ and N-2(j=0)+He+ capture. (C) 2004 American Institute of Physics.