The limited influence of the Debye–Waller factor on the intensities of high frequency molecular modes measured by neutron inelastic spectroscopy

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Abstract
Comparison of conventionally calculated vibrational spectra of a molecular crystal with neutron inelastic scattering spectra shows blatant differences which we relate to the very wide range of time scales now measurable. We have measured the complete vibrational spectrum of hexamethylenetetramine between 350 and 3600 cm−1 on beryllium filter spectrometers at several temperatures: 5, 80, and 300 K. We compare the experimental data with computed spectra derived from previously published normal coordinate analyses. At low temperature, we find a good agreement between the observed spectrum and the calculated one-phonon spectrum computed by Thomas and Ghosh. Combination peaks arising from the more intense bands are clearly identified. Numerical calculations of the Debye–Waller factor summed over all frequencies indicate that its value is so small at high energy transfers as to preclude any measurements of high frequency vibrations. However, we show that actual measurements of even C–H stretching frequencies are possible because the mean displacement of the intermolecular modes is zero on this time scale. For HMT (and most molecular crystals) at low temperature the influence of the Debye–Waller factor can be neglected in the comparison of the incoherent NIS spectrum with calculated one-phonon spectra.