  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.
