We describe the calculations of the 4fn4fn energy levels, reduced matrix elements for 4fn4fn-4fn4fn transitions and the simulation of absorption and emission spectra. A complete 4fn4fn energy level diagram is calculated for all trivalent lanthanide ions in LaF3LaF3. The calculated energy levels are compared with experimentally obtained energies. For Ce, Pr, Nd, Eu, Gd, Ho, Er, Tm and Yb many, and in some cases all, energy levels have been observed. This work provides a starting point for future investigation of as yet unobserved VUV energy levels.