Inelastic neutron scattering (INS) studies, electronic structure calculations, and molecular mechanics have been carried out on a series of molecular hydrogen complexes, M(CO)3(η2-H2)(PR3)2 (M = Mo, W, R = c-C6D11; M = W, R = i-C3D7), in order to determine relative electronic versus steric (ligand bulk) effects on the barrier to rotation of the H2 ligand. Low-lying vibrational excitations were identified with INS, and high-resolution spectrometers were used to measure the rotational tunneling splitting of the librational ground state on the solid complexes at 4 K. Replacement of the W by Mo changed the latter splitting by about a factor of 3, from 0.89 to 2.82 cm-1. Variation of the phosphine on the other hand changed the frequency by less than 20%. The torsional transitions observed in the range 300-400 cm-1 are consistent with the tunneling transitions for a simple double-minimum potential with one angular degree of freedom for the rotation. The barrier heights hindering the H2 rotation were determined from these measurements to be 2.4 kcal/mol (M = W, R = i-Pr), 2.2 kcal/mol (M = W, R = i-Pr), and 1.5-1.7 kcal/mol (M =Mo, R = Cy). Ab initio electronic structure calculations showed that the electronic component yields barriers of 1.4-1.8 kcal/mol for M = W and R = H, of 0.8 kcal/mol for M = W and R = Me, and of 0.6 kcal/mol for M = Mo and R = H. The present calculations show the simple double-minimum potential with the minima parallel to the P-M-P axis, which is indeed observed to be the equilibrium position for the H2 in the crystallographic studies. Molecular mechanics (MM2) calculations showed no direct steric effects arising from the bulky phosphine ligands on the H2 rotational barrier but did show an additional orientational preference (0.6-1.4 kcal/mol) for the H2 along the P-M-P axis. The sum of the calculated ab initio and MM2 barriers agreed remarkably well with the observed INS values.