Low energy phonons in single crystal ZrW$_{2}$O$_{8}$
ZrW$_{2}$O$_{8}$ is the prototypical example of a material exhibiting negative thermal expansion (NTE). It is now widely accepted that in ZrW$_{2}$O$_{8}$, and in many other framework materials exhibiting NTE, a collection of low energy phonon modes, as opposed to just one or two, are responsible for the anomalous thermal properties. However, quantitative verification and analysis of the density functional theory (DFT) calculations which underpin this proposal are still lacking. In particular, probing the low energy phonons directly throughout reciprocal space using inelastic neutron scattering, as opposed to other techniques which only probe the Brillouin zone center, is technically challenging and hence rarely done. Here we report inelastic neutron scattering measurements in a large number of Brillouin zones over a 400 K temperature range. We find excellent agreement between DFT calculations and experimental data at low temperature. However, the shifts in phonon modes predicted by DFT due to the reduction in lattice parameter (warming) are not observed. This is most likely due to counteractive anharmonic effects, which we verified using finite temperature molecular dynamics (MD) calculations. Notwithstanding, both DFT and MD results are consistent with NTE in ZrW$_{2}$O$_{8}$ arising from the tension effect, and by extension this explanation is supported by the neutron scattering results.