NiO - from first principles
  We have calculated from first-principles the octupolar interactions of the Ni2+ ion in NiO, which gives the theoretical basis for the ionic description of properties of NiO with fully localized strongly-correlated eight d electrons. A failure of the up-now first principles ionic calculations for NiO was largely due to too small values taken for the octupolar moment of the transition-metal atom, largely generated by too small value for <r_d^4>. Our many-electron crystal-field based approach enables successful calculations of the electronic structure and magnetic properties both in the paramagnetic and in magnetically-ordered state as well as zero-temperature properties and thermodynamics. 
R. J. Radwanski, Z. Ropka