The magnetic properties of the octahedral cluster NpCl diluted in Cs2ZrCl6 crystal have been calculated using a first principle method, SO-CASPT2. The spin Hamiltonian parameters modeling the fourfold degenerate ground state are extracted from calculations according to a first principle procedure. The agreement with the model parameters issued from experimental EPR data is good. The spin and orbital contributions to the model parameters are evaluated. Calculations are compared to crystal field theory at the different steps of calculations: while this theory is a very good framework to explain the main magnetic behavior, it is shown that it is not able to render precisely all the small effects.