Computational spectroscopic analysis of orbital hybridization and crystal field interaction for trivalent uranium ion in crystals of hexagonal symmetry

In the framework of crystal field theory, the absorption spectra in the Vis (blue)-UV region of trivalent uranium ion doped into LaCl3 and CeCl3 single crystals are directly predicted and simulated. A new computational method for modeling the orbital hybridization (mixing of electron configurations of opposite parities) is developed with a modified crystal field approach. The developed method is based on the complete diagonalization of the modified crystal field Hamiltonian (which includes both even and odd terms of the crystal field) defined in the basis set spanned by all 5f 3 and 5f26d wave functions (1274 states in total) for the open shell electrons of U3+ ion. The method provides a fundamental understanding and quantitative analysis of the crystal-field induced 5f-6d mixing in U3+:LaCl3 and U3+:CeCl 3 (C3h site symmetry at the U3+ position). The odd terms of the crystal field interaction (B33(f-d) and B5 3(f-d) in the C3h symmetry) selectively couple the states of the 5f3 and 5f26d configurations, producing a shift of the energy levels and allow electric dipole transitions between the configuration-mixed states. The mixture of the 5f and 6d configurations was described by introducing an index of configuration mixing, which varies from 0 (no mixing) to 1.0 (maximum mixing of electron configurations). For the first time, the exchange charge model (ECM) of crystal field theory has been used to calculate the parameters of crystal field acting on the 5f and 6d electrons of U3+. The calculated crystal field parameter values based on ECM are further optimized along with free-ion parameters of the Hamiltonian in non-linear least squares fitting of the calculated U3+ energy levels to the experimental absorption spectra. The eigenfunctions of the U3+ energy levels (with configuration mixing) can be directly used to calculate the electric dipole transition intensities and simulate the absorption spectra in the spectral region where 5f3 and 5f26d configurations overlap. Intensities of electronic transitions are calculated based on electric dipole coupling between the configuration-mixed eigenfunctions, which reproduce the experimental spectra very well. Good agreement between the calculated and observed energy levels and transition intensities prove the general validity and applicability of the developed approach, which can be further extended to other systems in a straightforward way.;Two computer programs, Felectron and CFPC, are developed with the C language to carry out the calculations with the new computational method of crystal field analysis. These two programs are designed to calculate the wavefunctions of open shell electrons in trivalent uranium ion doped into the lattice of LaCl3 and CeCl3 crystals. With a simple modification of the input profiles, these two programs can serve as a platform to investigate the electronic states of open shell electrons of entire lanthanide (4fn, 4fn-15d) and actinide (5fn, 5fn-16d) series in other host lattices. The high performance computational packages, PETSC and TAO, are included in Felectron to improve the efficiency of the developed program and the accuracy of the calculated results.