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Orbital hybridization (mixing of electron configurations of opposite parities) is analyzed in the framework of crystal-field theory with a complete diagonalization of the crystal-field Hamiltonian, including both even and odd terms of crystal-field potential, and with all basis sets of the $5{f}^{3}$ and $5{f}^{2}6d$ configurations for the wave functions of open-shell electrons in the ${\text{U}}^{3+}$ ion. This method provides a fundamental understanding and quantitative analysis of the crystal-field induced $5f\text{\ensuremath{-}}6d$ mixing in ${\text{U}}^{3+}:{\text{LaCl}}_{3}$ and ${\text{U}}^{3+}:{\text{CeCl}}_{3}$. The odd terms of the crystal-field interaction [${B}_{3}^{3}(fd)$ and ${B}_{3}^{5}(fd)$ in ${\text{C}}_{3\text{h}}$ site symmetry] selectively couple the states of the $5{f}^{3}$ and $5{f}^{2}6d$ configurations, inducing a shift of the energy levels and allow electric dipole transitions between the configuration-mixed states. The mixture of the $5f$ and $6d$ configurations is evaluated by introducing an index of configuration mixing. The exchange charge model (ECM) of crystal-field theory is used to calculate the crystal-field parameters of the ${\text{U}}^{3+}$ $5f$ and $6d$ electrons in terms of point-charge electrostatic interaction and orbital overlapping and covalent effect. The initial ECM estimations of the crystal-field parameters were optimized along with free-ion parameters of the Hamiltonian in nonlinear least-squares fitting of the calculated ${\text{U}}^{3+}$ energy levels to the experimental absorption spectra. The configuration-mixed eigenfunctions of the ${\text{U}}^{3+}$ states are directly used to calculate the electric dipole transition intensities and simulate the absorption spectra where the $5{f}^{3}$ and $5{f}^{2}6d$ configurations overlap and the Judd-Ofelt theory fails because of significant configuration mixing.

physical review b

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>5</mml:mn><mml:mi>f</mml:mi><mml:mtext>−</mml:mtext><mml:mn>6</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math>orbital hybridization of trivalent uranium in crystals of hexagonal symmetry: Effects on electronic energy levels and transition intensities

5f−6dorbital hybridization of trivalent uranium in crystals of hexagonal symmetry: Effects on electronic energy levels and transition intensities