The applicability of the Born-Oppenheimer approximation for the description of the coupled nuclear and electronic tunneling dynamics in anionic dimers of hydrogen fluoride and water is studied. These complex molecules are modeled by a simpler system, with only one nuclear coordinate, which can be solved easily with arbitrary accuracy. Although the Born-Oppenheimer approximation is not applicable in a strict sense in the tunneling region where the electron becomes unbound, quite accurate values for the binding energy can be obtained when working with a discrete electronic basis. Employing a basis which is diabatic with respect to the angular coordinates, but adiabatic with respect to the radial coordinate, the convergence of a nonadiabatic perturbation expansion is also studied. Inclusion of the lowest-order nonadiabatic corrections reduces the error in the binding energy already by a factor of 10-20, while for the correct prediction of the tunneling splitting, it proves necessary to take into account higher-order corrections. With increasing number. of diffuse functions included in the electronic basis, the nonadiabatic effects increase and the perturbation series converges more slowly. (C) 2004 American Institute of Physics.