We present the first examples of ab initio calculations of electron transition current density (TCD) for vibrational transitions in molecules, The non-Born-Oppenheimer (non-BO) theoretical expressions for TCD, derived in the first paper in this series, are implemented at the nb initio level for the 6 vibrational transitions of formaldehyde and the 12 vibrational transitions of ethylene. Vector field calculations of the TCD were carried out with 6-31G(d) and larger basis sets and displayed with the AVS visualization software program package. TCDs for vibrational transitions arise from the non-BO correlation of electron current density to nuclear velocities, The formalism used to express this correlation is the complete adiabatic approximation in which the electronic wave function carries an explicit dependence on the nuclear velocities as well as the usual dependence on positions. Vibrational TCDs provide a unique, unambiguous visualization of electronic motion in molecules that accompanies the vibrational nuclear motion. Patterns of calculated TCD in formaldehyde and ethylene are analyzed in terms of their group theoretical properties and allowed multipole transitions. Two principal classes of TCD motion are observed. One is motion that reflects linear, laminar current densities that lead to changes in electron probability density in response to nuclear displacements. A second is circulatory motion of TCD about atomic centers that appears be associated primarily with the lateral motion of two adjacent atomic centers. The latter motion does not lend to changes in electron probability density, but gives rise to magnetic dipole moments, and is likely important in the generation of vibrational circular dichroism intensity.