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, $Qsim5$ 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.
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