Theory of the generalized dynamic structure factor of polyatomic molecular fluids measured by inelastic x-ray scattering

We describe a theory for the calculation of the generalized dynamic structure factor S(k,omega) as measured by an inelastic x-ray scattering (IXS) experiment on single-component Molecular or polyatomic molecular fluids. IXS spectrum of a simple fluid is proportional to the dynamic structure factor of a single species or atom. In the case of a molecular fluid, however, IXS spectrum is a weighted sum of partial dynamic structure factors of pairs of atomic species. The weighting factors are products of the atomic form factors of the pairs. We call this weighted average dynamic structure factor the generalized dynamic structure factor. We extend the formalism of a three effective eigenmode theory (TEE) developed previously for simple fluids to derive an approximate evolution equation for the generalized dynamic structure factor, which can be considered as, a generalized hydrodynamic equation for molecular fluids. As examples, we first study the contributions or the partial dynamic structure factor to the generalized dynamic structure factor Computed from Molecular dynamics simulation of SPC/E model water. We found that the generalized dynamic structure factor of water measured by IXS can be well approximated by the center of mass or the oxygen atom dynamic structure factors. The generalized TEE model was then employed to analyze IXS spectra of nearly fully hydrated dilauroylphosphatidylcholine. The theory is able to fit all of the spectra in the k range from 5 to 32 nm(-1) quantitatively and gives their deconvoluted generalized dynamic structure factors.