The theory of Inelastic Neutron Scattering (INS) Spectroscopy is outlined, and the spectrometers employed in the study of low frequency (< 1500cm(^-1)) vibrations of hydrogen-containing molecules described. Square planar platinum-ethylene complexes of the general form trans-PtCl(_2)(C(_2)H(_4)).L and cis-PtCl(_2)C(_2)H(_4)).L (where L is a Ligand) have been investigated by INS spectroscopy, and assignments made of their spectra below 850cm(^-1). In all cases, a frequency was found representing the torsion of the ethylene group about an axis projected from the platinum atom through the centre of the C=C band, and the barrier to this rotation calculated. INS active modes of Co(_2)(CO)(_6).C(_2)H(_2) (O-1450cm(_1)) have been tentatively, identified, and a value for the barrier to the rotation of the acetylene molecule about an axis running through the mid-points of the Co-Co and C=C bonds derived. INS spectra of C(_2)H(_4) and C(_2)D(_4), adsorbed at two overpressures onto silver exchanged type A (Ag(_12)A) zeolite have been measured. On this basis of deuteration shifts and relative intensities, all three torsional modesand two of the three translational modes expected for the ethylene moleculerelative to a silver ion have been assigned. In addition, several weak spectroscopic features appeared to indicate the presence of a secondless populated adsorption site. C(_2)H(_2) and C(_2)D(_2) adsorbed onto Ag(_12)A zeolite at one overpressure have been studied by INS spectroscopy. All six predicted acetylene-surface modes were observed, the presence of the torsional vibration of the acetylene molecule about an axis running parallel to the C=C bond indicating the adsorbed molecule to be non-linear. Finally , INS spectra of the complexes Cr(C(_6)H(_6))(_2), Cr(C(_6)H(_6)(_2)I, C(_6)H)(_6)Cr(CO)(_3) and C(_6)H(_6)Mn(CO)(_3) Br have been recorded in the region 0-900(^1). Assignments have been attempted and, wherever possible, the barrier to the rotation of the benzene ligand (s) about the six - fold axis calculated.