Spin-orbit interactions play an essential part in elucidating the magnetic structures which are measured by the polarized neutron diffraction technique. This work extends our previous Hartree-Fock theory, with a one-electron spin-orbit term limitation, to incorporate both one- and two-electron terms exactly. This new theory, which is based on the current density, has been applied to calculate the low-temperature magnetic structure factors of the Cs3CoCl5 crystal. The crystal is assumed to be assembled from noninteracting molecular fragments. The calculated structure factors were compared directly with those observed from experiment. The agreement between these theoretical results and the experimental data shows great improvement compared with those from the usual unrestricted Hartree-Fock theory and with those from the previous generalized Hartree-Fock theory including one-electron terms. To examine the electron correlation effects, we use ab initio wave-function-based correlation methods, unrestricted second-order Moller-Plesset perturbation (UMP2) and quadratic configuration interaction including single and double excitations (QCISD), and also density functional theoretical methods, X-alpha, local-spin density approximation, generalized gradient approximation, Becke's three-parameter hybrid methods, and modified half-and-half hybrid methods, to calculate magnetic structure factors. Results indicate that the effects of spin-orbit interactions are comparable to those of electron correlation, and both must be included in reproducing the experimental data. To consider both these effects simultaneously we employed a simple model. With only three parameters, this model reproduced the observed data almost exactly as reflected by a chi (2) goodness of fit close to unity. (C) 2001 American Institute of Physics.