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

Abstract

Orbital hybridization ͑mixing of electron configurations of opposite parities͒ 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 5f 3 and 5f 2 6d configurations for the wave functions of open-shell electrons in the U 3+ ion. This method provides a fundamental understanding and quantitative analysis of the crystal-field induced 5f-6d mixing in U 3+ : LaCl 3 and U 3+ : CeCl 3 . The odd terms of the crystal-field interaction ͓B 3 3 ͑fd͒ and B 3 5 ͑fd͒ in C 3h site symmetry͔ selectively couple the states of the 5f 3 and 5f 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 ͑ECM͒ of crystal-field theory is used to calculate the crystal-field parameters of the 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 U 3+ energy levels to the experimental absorption spectra. The configuration-mixed eigenfunctions of the U 3+ states are directly used to calculate the electric dipole transition intensities and simulate the absorption spectra where the 5f 3 and 5f 2 6d configurations overlap and the Judd-Ofelt theory fails because of significant configuration mixing.

Characterization of berkelium(III) dipicolinate and borate compounds in solution and the solid state

“…However, starting from 21,000 cm −1 in the blue and ultraviolet (UV) region, a broad band lacking 5f characteristics appears in the absorption and excitation spectra. The 6d levels of Bk(III) are much lower in energy than those of Am(III) or Cf(III) with the same ligands (8,11,12,32), and we attribute this transition in the Bk(III) spectra to 5f 8 to 5f 7 6d transitions. The narrow and intense peak at 21,350 cm −1 in the excitation spectrum has an energy and bandwidth consistent with the scheme of the 5f 8 states but an intensity on the same scale as the parity allowed 5f-6d transitions.…”

Advances in the theoretical understanding of photon upconversion in rare-earth activated nanophosphors

“…1 intensities. 42 In this case, transition intensities can be calculated directly with the 4f-5d mixed wave functions. Other systems in which Judd-Ofelt theory failed in predicting transition intensities include Er 3+ in YAlO 3 at C s site symmetry.…”

“…This explains why the upconversion luminescence is much stronger in the hexagonal NaYF 4 than in the cubic NaYF 4 . For evaluation of crystal-field induced intensity enhancement in crystals of C 3h symmetry, Wang et al 42 derived a theoretical method for calculating the f N -f NÀ1 d configuration coupling. Using the standard irreducible tensor operator technique, 43,44 the matrix elements of 4f N -4f NÀ1 5d crystal field coupling can be expressed in a general form as 42…”

“…Wang et al demonstrated that in LaCl 3 with C 3h symmetry the crystal-field induces strong mixing the 5f 3 and 5f 2 6d states of U 3+ , and Judd-Ofelt theory failed to predict transitions intensities. 42 In this case, transition intensities can be calculated directly with the 4f-5d mixed wave functions. Other systems in which Judd-Ofelt theory failed in predicting transition intensities include Er 3+ in YAlO 3 at C s site symmetry.…”

Perplexing EPR Signals from 5f36d1 U(II) Complexes

“…The Coulomb repulsion parameters (Slater F parameter) for the 5f and 6d electrons are ∼20,000 cm −1 . 87 Consequently, 5f and 6d electrons in the excited 5f 2 6d 1 excited state U(III) in LaCl 3 are strongly coupled. While Coulomb repulsion will be weaker in divalent uranium complexes, it should still be sufficiently strong to couple the 5f 3 and 6d 1 electrons, so no EPR spectrum would be expected for [K(crypt)][Cp tet 3 U] in perpendicular mode, which does not match the observed results in Figures 1 and 2.…”