Thermal rate constants for capture of permanent and induced dipoles by ions are calculated by the statistical adiabatic channel model (SACM) using analytical representations of adiabatic channel eigenvalues. Linear, symmetric, and asymmetric top dipoles with closed and open electronic shells are considered. Analytical representations of the capture rate constants over broad temperature ranges are presented for all systems. Numbers of open channels W(E,J) are also investigated. The present analytical SACM treatment provides an economical, transparent, and accurate approach to the considered type of capture processes. At the same time, the implementation to ion fragmentation processes is elucidated.