A theory of resonant elastic x-ray scattering (REXS) by free molecules
is presented. Different scattering channels and their interference on
the formation of the spectral profile are identified. It is shown tha
t atomiclike contributions to the cross section are totally eliminated
Tor orthogonal orientations of the polarization vectors of the incide
nt and scattered x-ray photons. A strong deviation from a Lorentzian p
rofile of the spectral bands for REXS resonances is predicted. Numeric
al applications for the C K and O K spectra of carbon monoxide demonst
rate the strong dependence of the spectral profile on the excitation e
nergy and the spectral distribution of the incident radiation. Two qua
litatively different contributions to the spectral shape are identifie
d in the limit of narrow-band excitation: the first follows the excita
tion energy, while the second is determined by the absorption resonanc
es. The vibrational progressions are very frequency dependent, and at
large detuning frequencies the REXS cross Section collapses to a singl
e resonance with the width equal to the width of the photon function.
This result is shown to hold for resonant as well as for nonresonant c
ontributions to the REXS cross section.