We study the origin of the resonant x-ray signal in manganites and generali
ze the resonant cross section to the band-structure framework. With nb init
io LSDA and LSDA + U calculations we determine the resonant x-ray spectrum
of LaMnO3. The calculated spectrum and azimuthal angle dependence at the Mn
K edge reproduce the measured data without adjustable parameters. The inte
nsity of this signal is directly related to the orthorhombicity of the latt
ice. We also predict a resonant x-ray signal at the La L edge, caused by th
e tilting of the MnO6 octahedra. This shows that the resonant x-ray signal
in the hard x-ray regime can be understood in terms of the band structure o
f a material and is sensitive to the fine details of crystal structure.