The complex linear response function is extended to mixed electric-dipole-magnetic-dipole properties using London atomic orbitals which ensures gauge-origin independent properties. The optical rotation is determined by mixed electric-dipole-magnetic-dipole polarizability. The anomalous optical rotatory dispersion (ORD) spectra of chiral molecules is calculated using first-principle quantum-chemical methods when absorption is considered. This methodology of ORD is applied to hydrogen peroxide, 3R-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)-ferrocenophan-2-on, and D2 isomer of C 84 fullerene.