State-selected rate coefficients for the capture of ground and rotationally excited homonuclear molecules by ions are calculated, for low temperatures, within the adiabatic channel classical (ACCl) approximation, and, for zero temperature, via an approximate calculation of the Bethe limit. In the intermediate temperature range, the accurate quantal rate coefficients are calculated for j=0 and j=1 states of hydrogen isotopes (H-2, HD, and D-2) colliding with hydrogen-containing ions, and simple analytical expressions are suggested to approximate the rate coefficients. For the ground rotational state of diatoms, the accurate quantal rate coefficients are higher compared to their ACCl counterparts, while for the first excited rotational state the reverse is true. The physical significance of quantum effects for low-temperature capture and the applicability of the statistical description of capture are considered. Particular emphasis is given to the role of Coriolis interaction. The relevance of the present capture calculations for rates of ortho-para conversion of H-2 in collisions with hydrogen-containing ions at low temperatures is discussed. (c) 2005 American Institute of Physics.