Tetrahydrofuran-containing clathrate hydrate is considered as a potential cold and very cold neutron moderator material. The fully deuterated form is more promising because of the lower neutron absorption cross section of deuterium. In this work we present theoretical calculations of neutron scattering cross sections for hydrogenated and deuterated clathrates at low temperature. The scattering cross sections are generated by using the crystalline structure and phonon density of states obtained from density functional theory calculations. The theoretical neutron scattering cross sections serve to compare against existing or future experimental data.