The rotationally resolved infrared spectrum of the B-D 2 ion-neutral complex is recorded in the D-D stretch vibration region (2805-2875 cm -1) by detecting B photofragments. Analysis of the spectrum confirms a T-shaped equilibrium geometry for the B-D 2 complex with a vibrationally averaged intermolecular bond length of 2.247 Å, around 0.02 Å shorter than for the previously characterised B-H 2 complex [V. Dryza, B. L. J. Poad, and E. J. Bieske, J. Am. Chem. Soc. 130, 12986 (2008)10.1021/ja8018302]. The D-D stretch band centre occurs at 2839.76 ± 0.10 cm -1, representing a -153.8 cm -1 shift from the Q 1(0) transition of the free D 2 molecule. A new three dimensional ab initio potential energy surface for the BH 2 interaction is calculated using the coupled cluster RCCSD(T) method and is used in variational calculations for the rovibrational energies of B-H 2 and B-D 2. The calculations predict dissociation energies of 1254 cm -1 for B-H 2 with respect to the BH 2 (j = 0) limit, and 1313 cm -1 for B-D 2 with respect to the BD 2 (j = 0) limit. The theoretical approach reproduces the rotational and centrifugal constants of the B-H 2 and B-D 2 complexes to within 3, and the magnitude of the contraction of the intermolecular bond accompanying excitation of the H 2 or D 2 sub-unit, but underestimates the H-H and D-D vibrational band shifts by 7-8. Combining the theoretical and experimental results allows a new, more accurate estimation for the B-H 2 band origin (3939.64 ± 0.10 cm -1).