The vibrational spectra of three isotopomers of tetramethyl ammonium borohydride (TMAB) as well as of tetramethylammonium borofluoride were measured at 15 K by inelastic neutron scattering (INS). Direct analysis of the measured spectra was accomplished using classical molecular dynamics (MD) simulations and ab initio electronic structure theory for the crystalline solid. Comparison of observed and computed INS spectra revealed that the periodic electronic structure calculations for the crystalline solid provide a good description of the experimental INS spectrum and clearly demonstrates the power of this combined experimental/theoretical approach.