New multireference, configuration-interaction potential energy surfaces are reported for the interaction of Ar with the BH radical in its ground (X (1) Sigma(+)) and first excited (A (1) Pi) electronic states. These potential energy surfaces are then used with an adiabatic bender model for the calculation of the vibrational energy levels of the ArBH van der Waals complex in its ground and first excited singlet electronic states. Comparison of vibrational energies calculated using this adiabatic bender model with computed exact vibrational energies indicates that the former provides a very useful description of the bound levels of the ArBH complex. A qualitative discussion of the expected features in the A (1) Pi-X (1) Sigma(+) electronic spectrum of ArBH is also presented, to facilitate comparison with the experimental ArBH spectrum reported in the following paper [E. Hwang and P. J. Dagdigian, following paper, J. Chem. Phys. 101, 2903 (1994)]. The most strongly bound ArBH(A) levels, with Ar-BH separations less than in the ground state ArBH(X) complex, correspond to motion described primarily by the more attractive V-A" potential energy surface and to a helicopterlike internal motion of the BH moiety. For the more weakly bound states supported by higher bender curves, the vibrational motion cannot be described as occurring on either the V-A" or V-A’ potential energy surfaces separately.