Comparison between correlation crystal field calculations using extended basis sets and two-electron operators

There are two established methods for extending the crystal-field model for 4fN configurations. One is to add two-electron correlation crystal-field operators, the other is to extend the basis set to include more configurations. We consider the case of Pr3+ ions in LiYF4 and show, by projecting the configuration-interaction Hamiltonian into the 4f2 configuration, that in this case the two approaches give very similar results.