This work applies a recently developed first-principles scheme for calculat
ing core excited states in solids to non-resonant inelastic x-ray scatterin
g. The model explicitly includes the interaction between the excited electr
on and the core hole. The calculated results are compared with recent exper
imental results on inelastic x-ray scattering from K shells of Li, Be and C
in lithium fluoride, beryllium oxide and diamond, respectively. The overal
l agreement between experimental and theoretical spectra is found to be goo
d in all cases, even for the near-edge structure.