  Imaging of the structure of single proteins or other biomolecules with atomic
resolution would be enormously beneficial to structural biology. X-ray
free-electron lasers generate highly intense and ultrashort x-ray pulses,
providing a route towards imaging of single molecules with atomic resolution.
The information on molecular structure is encoded in the coherent x-ray
scattering signal. In contrast to crystallography there are no Bragg
reflections in single molecule imaging, which means the coherent scattering is
not enhanced. Consequently, a background signal from incoherent scattering
deteriorates the quality of the coherent scattering signal. This background
signal cannot be easily eliminated because the spectrum of incoherently
scattered photons cannot be resolved by usual scattering detectors. We present
an ab initio study of incoherent x-ray scattering from individual carbon atoms,
including the electronic radiation damage caused by a highly intense x-ray
pulse. We find that the coherent scattering pattern suffers from a significant
incoherent background signal at high resolution. For high x-ray fluence the
background signal becomes even dominating. Finally, based on the atomic
scattering patterns, we present an estimation for the average photon count in
single molecule imaging at high resolution. By varying the photon energy from
3.5 keV to 15 keV, we find that imaging at higher photon energies may improve
the coherent scattering signal quality.
