A method is presented to calculate the natural circular dichroism rece
ntly discovered in the Xray range (XNCD). The basic formula represents
XNCD as an odd second-rank tensor and leads to a sum rule that relate
s XNCD to the mixing of odd and even orbitals in the ground state. A m
ultiple-scattering theory of XNCD is presented, and calculated spectra
for the L-edges of iodine in LiIO3 compare favorably with the experim
ents.