Rotationally resolved mid-infrared spectra of the Cl-35(-)-H-2 and Cl-35(-)-D-2 anion complexes are measured in the regions associated with the H-2 and D-2 stretch vibrations. The Cl-35(-)-H-2 spectrum contains a single Sigma-Sigma transition assigned to the more abundant ortho H-2 containing species. The corresponding Cl-35(-)-D-2 spectrum consists of two overlapping Sigma-Sigma transitions whose origins are separated by 0.24 cm(-1), and which are due to absorptions by complexes containing para and ortho D-2. The spectra are consistent with linear equilibrium structures for Cl--H-2 and Cl--D-2, although zero-point bending vibrational excursions are expected to be substantial. Ground state vibrationally averaged intermolecular separations between Cl- and the diatomic center-of-mass are deduced to be 3.195 +/-0.003 Angstrom (Cl-35(-)-H-2) and 3.159 +/-0.002 Angstrom (Cl-35(-)-D-2). Vibrational excitation of the diatomic core profoundly affects the intermolecular interaction and leads to contractions of 0.118 Angstrom (Cl-35(-)-H-2) and 0.078 Angstrom (Cl-35(-)-D-2) in the vibrationally averaged intermolecular separations. Effective one-dimensional radial potential energy curves are developed. Their form near the equilibrium separation is determined by Rydberg-Klein-Rees inversion of the spectroscopic data, and at longer ranges by averaging the dominant long range electrostatic and induction potentials over the angular motion of the atom-diatomic system. On the basis of these potentials the dissociation energies for Cl-35(-)-H-2(o), Cl-35(-)-D-2(p), and Cl-35(-)-D-2(o) are estimated as 488, 499, and 559 cm(-1).