4f N − 1 5d energy levels of lanthanides: a quasi-angular-momentum approach and its application to Cs 2 NaYF 6 :Er 3+ (original) (raw)
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Spectroscopy of High-Energy States of Lanthanide Ions
European Journal of Inorganic Chemistry, 2010
We discuss recent progress and future prospects for the analysis of the 4f N −1 5d excited states of lanthanide ions in host materials. We demonstrate how ab-initio calculations for Ce 3+ in LiYF 4 may be used to estimate crystal-field and spin-orbit parameters for the 4f 1 and 5d 1 configurations. We show how excited-state absorption may be used to probe the electronic and geometric structure of the 4f N −1 5d excited states in more detail and we illustrate the possibilities with calculations for Yb 2+ ions in SrCl 2 .
Spectroscopy and Calculations for 4f N → 4f N –1 5d Transitions of Lanthanide Ions in K 3 YF 6
The Journal of Physical Chemistry A, 2012
In the present work, we report on the combined experimental and theoretical studies of the 4f−5d spectra of Ce 3+ , Pr 3+ , Nd 3+ , Eu 3+ , Gd 3+ , Tb 3+ , Dy 3+ , and Er 3+ ions in a newly synthesized K 3 YF 6 matrix. The low temperature experimental 4f−5d excitation spectra have been analyzed and compared with the results of the energy-level and intensity calculations. For this theoretical analysis, the extended phenomenological crystal-field model for the 4f N−1 5d configuration (i.e., the extended f-shell programs, developed by Prof. M. F. Reid) and exchange charge model (developed by Prof. B. Z. Malkin) have been used together to estimate the crystal field parameters and implement the spectral simulations. On the basis of the results of the performed theoretical analysis, we suggest the most probable positions occupied by optically active ions. Although the spectra of only eight lanthanide ions have been studied, the Hamiltonian parameters of the 4f N−1 5d configuration have been evaluated for the whole lanthanide series and reported here for the first time, to give a complete and unified description of the spectroscopic properties of the trivalent rare earth ions in the chosen host. In addition to the studies of the 4f−5d transitions, various possible competitive excitation channels overlapping with 4f−5d ones have also been discussed, where a theoretical scheme giving rudiments to understand 4f−6s spectra are proposed for the first time. An excellent agreement between the calculated and measured excitation spectra shapes confirms validity of the performed analysis. The obtained parameters of the crystal field Hamiltonians for different ions and various electron configurations can be used in a straightforward way to generate the energy level positions and calculate the particular transition intensities for any rare earth ion in any particular spectral region. With the aid of the obtained parameters, the positions of the lowest energy levels of the 4f N , 4f N−1 5d ,and 4f N−1 6s configurations of rare earth ions and 4f N+1 (np) 5 configuration of rare earth ions and ligands (corresponding to the ligand−impurity ion charge transfer transitions) in the band gap of K 3 YF 6 have all been estimated. The obtained Hamiltonian parameters and energy levels diagrams, which include the electronic structure of a host material, can be used as a starting point for analysis of spectroscopic properties of trivalent lanthanides in similar fluorides.
A complete 4 f n energy level diagram for all trivalent lanthanide ions
Journal of Solid State Chemistry, 2005
We describe the calculations of the 4f n energy levels, reduced matrix elements for 4f n-4f n transitions and the simulation of absorption and emission spectra. A complete 4f n energy level diagram is calculated for all trivalent lanthanide ions in LaF3: 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.
4FN↔4FN−15D Transitions of the Trivalent Lanthanides: Experiment and Theory
Journal of Luminescence, 2001
Emission and excitation spectra of 4f n 24f nÀ1 5d transitions of lanthanide ions in LiYF 4 are reported and are succesfully reproduced by energy level calculations using a theoretical model that extends established models for the 4f n configuration to include fd states. Some interesting trends are observed. Lifetime measurements for the spin-allowed fd emission show that the electric dipole matrix element for the fd transition decreases through the lanthanide series. Also the splitting between the high spin and low spin fd states decreases through the lanthanide series. Both effects are reproduced by our model.
Some aspects of configuration interaction of the 4f(N) configurations of tripositive lanthanide ions
The journal of physical chemistry. A, 2014
Some features of the interaction of the 4f(N) configuration of tripositive lanthanide ions (Ln(3+)) with excited configurations have been investigated. The calculated barycenter energies of the same parity 4f(N-1)6p, 4f(N+1)5p(5), and 4f(N-1)5f configurations for Ln(3+), relative to those of 4f(N), are fitted well by exponential functions. The 4f(N) barycenter energies of Ln(3+) in Y3Al5O12/Ln(3+) lie in the band gap, with the exceptions of Tb(3+) and Yb(3+), where they are situated in the conduction and valence bands, respectively. The configuration interaction parameters α, β, and γ, which are fitted in the usual phenomenological Hamiltonian to calculate the crystal field energies of Ln(3+), exhibit quite variable magnitudes in the literature due to incomplete energy level data sets, energy level misassignments and fitting errors. For LaCl3/Ln(3+), 83% of the variation of α and 50% of that for β can be explained by the change in the difference in barycenter energy with the predomi...
Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes
We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron s...
Journal of Alloys and Compounds, 2014
Systematic consideration of the spectroscopic properties of the f NÀ1 d excited electronic configurations of the di-, tri-and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree-Fock calculated Slater parameters for the f NÀ1 d electron configurations, spin-orbit (SO) interaction constant f for the f and d electrons, and averaged values of the second, fourth and sixth powers of the 4f, 5f, 5d, 6d electrons' radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the Coulomb interaction parameters F 2 (ff), F 4 (ff), and F 6 (ff) for the f NÀ1 core increase linearly with the atomic number Z, whereas the direct and exchange Coulomb parameters F 2 (fd), F 4 (fd), G 1 (fd), G 3 (fd), G 5 (fd) for the f NÀ1 d configuration decrease linearly with Z. Since the SO interaction constant f 1/4 is also proportional to Z, it was possible to find linear relationships between the Coulomb interaction parameters and SO constants for the f and d electrons, which effectively reduce the number of independent parameters in the free ion Hamiltonian. The constraining relations between the free ion Hamiltonian's parameters obtained in the present paper can be used for simulations of the f-d transition spectra of these ions in various crystals.
4fn→4fn-15d transitions of the light lanthanides: Experiment and theory
Physical Review B, 2002
The 4 f n →4 f nϪ1 5d(f d) excitation spectra of the light lanthanides ͑Ce 3ϩ , Pr 3ϩ , Nd 3ϩ , Sm 3ϩ , and Eu 3ϩ ͒ incorporated in LiYF 4 , CaF 2 , and YPO 4 are investigated in the ultraviolet and vacuum-ultraviolet spectral region ͑100-250 nm͒. In these host lattices fine structure ͑zero-phonon lines and vibronic lines͒ is observed for fd transitions involving the lowest 5d crystal-field state. The observation of zero-phonon lines makes it possible to analyze the complicated structure in the fd spectra and to compare the experimentally observed spectra with energy-level calculations for the 4 f nϪ1 5d states. Energy-level and intensity calculations were performed by an extension of the commonly used theory for energy-level calculations of 4 f n states. A good agreement between experiment and theory is obtained for the overall structure using the crystal-field splitting ͑from the spectra of Ce 3ϩ ͒, the parameters for the splitting of the 4 f nϪ1 core ͑from the literature on energy level calculations for 4 f n states͒ and the spin-orbit coupling of the 5d electron and Coulomb interaction between 4 f and 5d electrons ͑from atomic parameters using the computer code of Cowan͒.
Inorganic Chemistry, 2011
The Pr 3+ ion in Cs 2 NaPr(NO 2 ) 6 is situated at a site of T h symmetry with 12-coordination to O atoms of bidentate nitrito groups. First-principles calculations of the vibrational modes of the complex were carried out using the density functional theory with the generalized gradient approximation PerdewÀBurkeÀErnzerhof exchange-correlation functional. The calculations that treated the Pr 3+ 4f electrons as valence electrons showed better agreement with the experimental vibrational assignments compared with those treating the 4f electrons a part of the inner core. The 1 D 2 f 3 H 4 emission spectra of Cs 2 NaPr(NO 2 ) 6 at 7 K enabled assignments to be made for the crystal-field (CF) levels of the ground-state multiplet. The emission of the dilute system Cs 2 NaY(NO 2 ) 6 :Pr 3+ was dominated by NO 2 À triplet emission, which was quenched at elevated temperatures by energy transfer to trace Eu 3+ impurity. From magnetic dipole calculations and the vibronic fingerprint, detailed assignments are given for the complex 10 K electronic absorption spectrum of Cs 2 NaPr(NO 2 ) 6 between 3940 and 18800 cm À1 , and the derived Pr 3+ 4f 2 energy-level data set has been fitted by calculation. By comparison with Cs 2 NaPrCl 6 , the fourth-order CF parameter in Cs 2 NaPr(NO 2 ) 6 is relatively small so that interaction with a 4fnp configuration is not important. From the NO 2 À absorption bands above 20 000 cm À1 , the NÀO bond length change upon excitation is small, whereas the angle OÀNÀO opens by more than 10°in the triplet state. By contrast to the NO 2 À internal vibration frequencies, which except for the wagging mode show only minor changes with the environment, the triplet-state energy shows a linear decrease with an increase of the lanthanide (Ln 3+ ) ionic radius in Cs 2 NaLn(NO 2 ) 6 . Using the eigenvectors from the energy-level fit, the variation of the inverse magnetic susceptibility with temperature has been calculated between 1 and 100 K and the values are somewhat lower than those from experiment.