The energy dependence of the capture cross section and the temperature dependence of the capture rate constants for inverse power attractive potentials VϰϪR Ϫn is considered in the regime where the quantum character of the relative motion of colliding partners is important. For practically interesting cases nϭ4 and nϭ6, a simple formula for the cross section is suggested which interpolates between the classical and the quantum Bethe limits. We have shown that the classical approximation for the capture cross section performs well far below the simple estimations of the onset the quantum regime. This seemingly ''classical'' feature of the cross section and the rate constant is due to the large quantum effects of the waves in transmission through and reflection above the centrifugal potential barriers.

Cross sections and rate coefficients for capture of low-energy electrons with polar and polarizable target molecules are calculated in the framework of Fabrikant and Hotop's extended version of the Vogt-Wannier model and an extension of this approach is given in the present article. Analytical approximations are derived in order to facilitate the application to experiments. A comparison with a selection of experimental electron attachment rate coefficients provides insight into the competition between anion formation through electron capture and scattering processes which do not follow this pathway.

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 (H2, HD, and D2) 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 H2 in collisions with hydrogen-containing ions at low temperatures is discussed.