The dependence of the U = 0 + 1 vibrational excitation of diatomic molecules in their ground state by ion projectiles as a function of scattering angle is described using a potential model represented by multipolar and exponential interactions and assuming pure electronically elastic scattering. The linearly forced harmonic oscillator model is assumed in the calculation of the corresponding vibrational energy transfer. This treatment lends itself to solutions in closed analytical form and enables one to investigate the dependence of the vibrational energy transfer upon the molecule orientation. It is applied to He++ N, and CO collisions; overall agreement with experiment is found whenever electronic transition processes may be neglected.