The main focus of the work is to establish the energy positions of 4f and 5d levels of lanthanide ions, the values of energy gaps and to analyze luminescence mechanisms in the series of crystals CeX3 (X = F, Cl, Br, I) and LaF3:Ln (Ln = Ce-Lu). In this work, computer models of crystal cells were created, provided calculations of partial density of states, total density of states and energy band structure using projector augmented wave method (PAW) within density functional theory (DFT) framework for two groups of crystal series: CeX3 (X=F, Cl, Br, I) and LaF3:Ln (Ln=Ce-Lu). In particular, it has been demonstrated the effectiveness of using the PBE0 exchange-correlation hybrid functional in the case of CeX3 (X=F, Cl, Br, I) and it has been obtained sufficiently accurate positions of the 4f and 5d levels of lanthanide ions, thanks to the inclusion of Hubbard corrections (DFT+U) in the calculations for LaF3:Ln crystals (Ln=Ce-Lu). Single crystals LaF3:Ce, CeF3 and CaF3:Ce have been grown in an inert atmosphere and a series of experimental studies of the spectral-kinetic properties of the luminescent characteristics have been performed for the purpose of comparative analysis and confirmation of the theoretical calculations correctness. It is shown that the valence band of CeX3 crystals (X = F, Cl, Br, I) is formed by np halogen states (n = 2, 3, 4, 5), and 4f states form a narrow band, which is located above the valence band. The conduction bands in CeF3, CeCl3, and CeBr3 crystals are formed by 5d cerium states which have a feature in the form of energetically separated subbands 5d1 and 5d2 with different effective electron masses. In the case of CeI3 these subbands overlap, what makes the occurrence of luminescence 5d→4f at room temperature complicated. By comparing the obtained experimental and theoretical data, easy to confirm the concept that the energy structure of CeX3 is a result of the superimposition of the energy structures of LaX3 and cerium impurity states in the LaX3:Ce systems, which allowed compare the calculated energy parameters of the 4f and 5d levels in CeX3 with the energy of these states in LaX3:Ce. It has been demonstrated that the calculated energy band structure of CeX3 (X=F, Cl, Br, I) crystals corresponds to the expectation that the energy structure of CeX3 is the result of the energy states superposition of the electron in the field of holes 4f 0 and np X0. It was found that in the case of CeF3 the effective masses of 5d1 and 5d2 subbands are m*5d1 = 4.9m0 and m*5d2 = 0.9m0, respectively. Such values of effective masses assume the presence of localized states of electrons in the 5d1 subband and delocalized states in the 5d2. From this point of view, the 4f→5d1 transitions may correspond to the internal transitions in the Ce3+ ion, which promotes the formation of Frenkel excitons, and the 4f → 5d2 transitions may be associated with the ionization of cerium ions. The energy gap between subbands 5d2 and 5d1 occurs as a gap in the excitation spectra of exciton luminescence at 7.1 eV, or as a luminescence maximum with a peak at 340 nm in the excitation spectrum at 7.1 eV. The mechanism of energy transfer from cerium Frenkel excitons to the luminescent centers, which are responsible for bands at 340 nm, is radiative. The anionic exciton corresponding to the 2p F→5d2 transition is associated with a peak band at 10.8 eV in the cerium luminescence excitation spectrum. It was stated that in CeCl3 and CeBr3 crystals conduction states form a 5d1 subband with a relatively large value of the effective mass of charge carriers (3.6m0 and 2.3m0, respectively). As in the case of CeF3, such effective masses contribute to the barrier-free autolocalization of electrons, which agrees well with the model of self-trapped Frenkel excitons in these compounds. This effect is a prerequisite for the existence of typical 5d→4f Ce luminescent transitions in CeCl3 and CeBr3 crystals. Free charge carriers in the conduction band exist due to the transitions from the valence band np X- to the band 5d2 Ce3+ with effective masses 0.5m0 and 0.1m0 for CeCl3 and CeBr3, respectively. Calculated energies for np X-→5d2 Ce3+ transitions are 6.9 eV, 5.7 eV and 2.4 eV, what is in good agreement with the experimental values of the energy band gap in LaCl3, LaBr3 and LaI3 crystals (7.0 eV, 5.9 eV and 3.8 eV, respectively). In the case of LaF3:Ln crystals, it was demonstrated that 2p states of fluorine form the top of the valence band, the bottom of the conduction band is formed by 5d lanthanum levels, and narrow 4f lanthanide band is characterized by high intensity of state densities and are mostly located within the forbidden band. There are 5 peaks 5d of Ln3+ states slightly below the bottom of the conduction band (from 8 eV to 10 eV), as it was expected due to the symmetry of P3c1, where the Ln3+ ion is in the coordination environment of 9 fluorine ions.
