  High-resolution inelastic x-ray scattering measurements were carried out on
molten NaI near the melting point at 680$^\circ$C at SPring-8. Small and damped
indications of longitudinal optic excitation modes were observed on the tails
of the longitudinal acoustic modes at small momentum transfers, $Q\sim5$
nm$^{-1}$. The measured spectra are in good agreement, in both frequency and
linewidth, with {\it ab initio} molecular dynamics (MD) simulations but not
classical MD simulations. The observation of these modes at small $Q$ and a
good agreement with the simulation permits clear identification of these as
collective optic modes with well defined phasing between different ionic
motions.
