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Lanthanoid ions are well-known for their characteristic optical and magnetic properties interesting for a wide range of applications. Most of these properties show a subtle dependence on the surrounding ligands. Unlike the transition metal ions with their often encountered octahedral or tetrahedral coordination in compounds, rare earth ions are typically found in coordination geometries with low symmetries and high coordination numbers. The quantitative treatment of the ligand field in the so-called Wybourne scheme then becomes overparametrized and not readily insightful but merely a technical tool. In this review, we want to present the alternative approach by the chemically intuitive angular overlap model (AOM) of ligand field theory that is independent from symmetry and allows to decompose any coordination geometry into its separate metal–ligand bonds with well-known bonding character. It is the goal of this review to demonstrate its strength in the semi-quantitative description of opto-magnetic properties of the rare earth ions on carefully selected examples from practice. Finally, we compare the AOM to conventional Wybourne-parametrized ligand field theory and show how the two schemes of ligand field theory are related to one another. Overall, this review offers a perspective on future approaches to ligand field calculations with f elements with the benefit of full transparency and intuitive understanding rather than technical fitting.

The theoretical rationalization of the open-shell 4f and 5d configuration of Eu 2+ is by far not trivial because it involves a non-standard version of ligand field theory, based on a two-shell Hamiltonian. Here we present our methodology based on ligand field theory, taking the system CsCaBr 3 :Eu 2+ as a case study with an octahedral coordination sphere of Eu 2+ . The ligand field, interelectronic and spin-orbit coupling parameters are deduced from experimental data. The assignment of the transitions to the corresponding irreducible representations of the double group was performed together with the intensity modelling resulting in an excellent match to the experimental spectra.

In this work, we predict and measure the optical behaviour of Pr 3+ in different binary and ternary fluorides. We use a validated model based on Ligand Field Theory and Density Functional Theory to calculate the multiplet energy levels arising from the ground [Xe]4f 2 and excited [Xe]4f 1 5d 1 electron configurations of Pr 3+ in its chemical environment. Moreover, the luminescence spectra of the considered materials were recorded. In overall the theoretical determination corroborates to the experimental findings. The phenomenon of the photon cascade emission is particularly stressed, being important for the design of modern phosphors with quantum efficiencies larger than 100%.

We present a recipe for the calculation of the optical properties of Ce 3+ -doped systems. The model implies the use of ligand field phenomenology in conjunction with Density Functional Theory (DFT). The particular procedures enable the reliable prediction of the 4f 1 → 4f 0 5d 1 transitions in Cs 2 NaYCl 6 :Ce 3+ . The analysis of the doping of Ce 3+ into the host is accomplished by band structure calculations. The calculated multiplet energy levels are in agreement with the experimental observation, the outlined treatment being, to the best of our knowledge, unprecedented clear and conclusive application of DFT for the rather complex problems of structure and spectroscopy of cerium-doped systems.

The three novel gadolinium(III) containing compounds (NH3CH3)[Gd(CF3CF2COO)4(H2O)] (1), (NH3C2H5)[Gd(CF3CF2COO)4(H2O)] (2) and ((CH3)4N)[Gd(CF3CF2COO)3(H2O)2]CF3CF2COO (3) were synthesized and structurally characterized by X-ray crystallography. In the crystal structures of 1 and 2, the gadolinium ions are bridged by carboxylate groups to dimers with a Gd3+–Gd3+ distance of 451.6(2) (1) and 451.8(3) pm (2), respectively. In the crystal structure of 3 the Gd3+ ions are bridged by carboxylate groups to chains with almost the same Gd3+–Gd3+ distances (494.0(8) and 503.4(7) pm). The magnetic behaviour of 1 and 2 was investigated in the temperature range of 1.76–300 K. The magnetic data indicate weak antiferromagnetic interactions within the dimeric unit.

Single crystals of [NH3C2H5][Gd(Cl2HCCOO)4] have been obtained by reaction of Gd2O3 with NH3C2H5Cl in an aqueous solution of Cl2HCCOOH. The compound crystallizes in the triclinic space group P 1 ¯ (no. 2, Z = 2, a = 813.7(3) pm, b = 1246.9(4) pm, c = 1263.9(4) pm, α = 61.67(4)°, β = 87.39(4)°, γ = 84.84(4)°). The Gd3+ ion is eight-fold coordinated by oxygen atoms. The magnetic behavior of the compound was investigated in the temperature range of 1.72–300 K. The magnetic data indicate an intramolecular ferromagnetic interaction within a dimeric unit (Jintra = + 0.029 cm−1) on which an intermolecular antiferromagnetic interaction is imposed (Jinter = −0.010 cm−1).

Single crystals of Gd(HF 2 CCOO) 3 (H 2 O) 2 .H 2 O have been obtained by reaction of Gd 2 O 3 with HF 2 CCOOH in water. Data collection was carried out using a STOE imaging plate diffractometer at 173 K. The compound crystallizes in the triclinic space group P1 (Z = 2) with a = 833.1(2) pm, b = 943.5(2) pm, c = 944.9(2) pm; a = 66.78(3), β = 79.54(3) and y = 77.61(3). The corresponding residual (all data) for the refined structure is 2.98%. The magnetic behaviour of the compound was investigated in the temperature range of 1.7-300 K. The magnetic data were interpreted considering exchange interaction effects in the dinuclear Gd 3+ -Gd 3+ unit. The exchange coupling constant J = -0.024 cm -1 indicates antiferromagnetic interaction, whereas J = +0.05 cm -1 for Gd(H 3 CCOO) 3 (H 2 O) 2 .2H 2 O a ferromagnetic one.

The magnetism of the three compounds Pr 3 X[SiS 4 ] 2 (X=Cl, Br, I) has been measured in the temperature range between 1.7 and 300 K. For the theoretical calculations to interpret the magnetic behavior the angular overlap model was employed to reproduce the ligand field influence and the molecular field approach to take magnetic interaction into account.

Single crystals of the title compound were prepared from the elements by a solid state reaction in an iodine atmosphere. Data collection were carried out using a STOE image plate detector at 293 K. The compound crystallizes in the space group P 2 1 /n of the monoclinic system isotypically to Tb 4 [SiS 4 ] 3 with four formular units in cells of dimensions: a =986.7(2) pm, b =1099.69(19) pm, c =1646.2(4) pm, β =102.67(3)°. The corresponding residual (all data) for the refined structure is 3.09%. The magnetic behavior of the compound was investigated on powdered samples in a temperature range between 1.7 and 300 K. The deviations from the Curie-behavior could be interpreted by the molecular field approach.

Single crystals of Nd3ClS2[SiS4] were prepared from the elements. Data collection was carried out using a STOE image plate detector at 293 K. The compound crystallizes in the orthorhombic space group Pnma with eight familiar units in a cell of dimension: a=1240.3(2),b=1035.8(2),c=1616.4(3) pm The corresponding residual (all data) for the refined structures is 3.45%. In the crystal structure, the chloride ions form chains along [0 1 0] with trigonal coordination by the lanthanide ions. The magnetic behavior of powdered crystals was interpreted by ligand field calculations where the influence of the ligand field was taken into account by applying the angular overlap model and magnetic exchange by the molecular field approximation.

The complex chloride (2-methylpyridinium)2[TbCl4(H2O)3]Cl has been prepared for the first time. (2-Methylpyridinium)2[TbCl4(H2O)3]Cl crystallizes monoclinically in the space group P21/n (Z=4) with a=1327.0 pm, b=886.3 pm, c=1911.3 pm and β=105.52°. The coordination polyhedron containing terbium is a pentagonal bipyramid [TbCl4(H2O)3]−. The magnetic behaviour of (2-methylpyridinium)2[TbCl4(H2O)3]Cl and (2-methylpyridinium)3[TbCl6] has been studied. The magnetic data are interpreted by ligand field calculations applying the angular overlap model.

Single crystals of Ln 3 Cl[SiS 4 ] 2 (Ln=La, Ce, Pr) were prepared by the reaction of lanthanide metal, sulfur, silicon and chlorine. Data collection was carried out using a STOE imaging plate detector at 293 K. The homologue compounds crystallize in the space group C2/c of the monoclinic system isotypically to Ln 3 X[SiS 4 ] 2 (X=Br, I) and the A-type of the halide oxosilicates Ln 3 X[SiO 4 ] 2 (X=Cl, Br; Ln=La, Ce, Pr) with four formula units in cells of dimensions: • La 3 Cl[SiS 4 ] 2 : a =1567.2(3) pm, b =777.8(2) pm, c =1101.5(2) pm, β =96.88(2)° • Ce 3 Cl[SiS 4 ] 2 : a =1559.4(3) pm, b =770.2(2) pm, c =1096.9(2) pm, β =97.07(2)° • Pr 3 Cl[SiS 4 ] 2 : a =1555.9(3) pm, b =764.2(1) pm, c =1093.2(2) pm, β =97.40(2)° The corresponding residuals (all data) for the refined structures are 2.28% (La), 2.15% (Ce), and 3.17% (Pr), respectively. In the crystal structures, the chloride ions form chains along [0 0 1] with trigonal coordination by the lanthanide ions.

Black crystals of Nd 3 Ti 3 O 8 Se 2 have been synthesized by the reaction of neodymium sesquioxide and titanium sesquiselenide (Nd 2 O 3 :Ti 2 Se 3 =1:1) with a small amount of iodine at 1000°C. The compound crystallizes in the monoclinic space group P2 i /m (Z=2) with the cell parameters a=982.69(17) pm, b=391.78(4) pm, c=1349.9(2) pm, β=111.370(19)°.

Crystal structures of the new complex lanthanide chlorides with organic cations [(CH3)2NH2]4[LnCl6]Cl (Ln=Ho–Tm) have been determined. The air sensitive compounds have been prepared by the reaction of LnCl3·xH2O with [(CH3)2NH2]Cl in ethanol/butanol. The complex chlorides are isotypic with each other and crystallize in the orthorhombic space group P21212 (Z=2). The magnetic behaviour of these complex lanthanide chlorides has been studied. The magnetic data were interpreted by ligand field calculations applying the angular overlap model.

The conduction behaviour of Pr 3+ ion-exchanged Na + –β″-Al 2 O 3 crystals varying in degree of exchange (ξ) has been investigated by impedance spectroscopy in the temperature range 300–1000 K. The Arrhenius plots show a curvature at about 560 K to higher activation energies explainable by the beginning of lanthanide ion motion. With growing Pr 3+ exchange, the ionic conductivity (σ) is lowered combined with an increasing activation energy ( E a ). For a given degree of exchange, σ scatters about one to two orders of magnitude and E a within 0.15–0.2 eV. These deviations can be understood by the different crystal compositions influencing the thickness of the conduction slabs and the ionic distributions. A lower in-plane cation concentration (for a given ξ) induces widened conduction channels, resulting in an increased conductivity and reduced activation energies.

The structures of completely exchanged Na + /Pr 3+ –β″-Al 2 O 3 crystals have been investigated by single crystal X-ray diffraction methods at room temperature. The ionic distributions within the conduction layers are correlated with the crystal compositions. A decreasing cation content in the layers increases the lattice parameter c connected with an expansion of the conduction slabs resulting in an increased Beevers–Ross (BR) site occupancy by Pr 3+ ions. Up to 52% of the lanthanide ions are found to occupy the lower coordinated BR positions.

The Na + ions in the solid electrolyte β″alumina (Na + -β″-Al 2 O 3 ) have been exchanged with Pr 3+ ions. The Pr 3+ ion has been used as an optical and magnetic probe to investigate the local structure within the conduction planes of this oxide. With this aim, optical spectra and susceptibility measurements have been carried out. Both fluorescence and excitation spectra, related to the 3 P o → 3 F 2 , 3 H 4 transitions, have been recorded on single crystals. The magnetic susceptibility shows temperature-independent paramagnetism at low temperatures. The physical properties have been interpreted with the help of ligand-field calculations by applying the angular overlap model. It has been deduced that the Pr 3+ ions occupy mostly the eightfold-coordinated mid-oxygen (mO) sites.

Crystals of Na+−β″-Al2O3 and Na + Ho 3+ −β″-Al 2 O 3 , with varying degrees of exchange, have been investigated by impedance spectroscopy using sputtered chromium films as electrodes. For this work a sample holder was developed to enable studies of the in-plane conductivity of even very thin β″-alumina crystals. The ionic conductivities of the investigated Na+−β″-Al2O3 crystals were found to be one order of magnitude lower than those reported in the literature, a discrepancy caused by a lower charge carrier concentration. On the other hand, the activation energy and the diffusion coefficients of the sodium ions, as deduced from the Nernst-Einstein equation, agree well with previous studies. In the case of the Na + Ho 3+ −β″-Al 2 O 3 crystals, a strong decrease of the ionic conductivity has been observed with increasing degree of exchange. To determine the bulk conductivities an equivalent circuit had to be applied which differed from the one used in case of Na+−β″-Al2O3. With an additional RC-element in parallel these spectra could be fitted with satisfying results. This RC-element may be regarded as a second relaxation process of the Na+ ions.

Zusammenfassung Bei der Umsetzung von Pr2Se3 mit Natrium wurden die Verbindungen NaPr8Se12 und NaPr2Se3 in Pulverform erhalten. Die dargestellten Verbindungen wurden analytisch und rontgenographisch charakterisiert. NaPr8Se12 ist von schwarzer Farbe und kristallisiert im Th3P4-Typ (Raumgruppe, I43d; Z = 4 3 , a = 8,9095(4) A ). NaPr2Se3 besitzt eine dunkelblaue Farbe und kristallisiert im NaCl-Typ (Raumgruppe, Fm3m; Z = 4 3 , a = 5,974(1) A ). In den Verbindungen tritt Praseodym in den ungewohnlichen Oxidationsstufen + 2,875 bzw. + 2,5 auf.

The new compounds NaSm2Se3 and MSm8Se12 (M  Na, Ca) were prepared by reduction of Sm2Se3 with sodium and calcium respectively. Synthesizing the educt, single crystals of Sm2Se3 in the U2S3-type structure were obtained for the first time. All compounds were characterized by chemical analysis and X-ray powder diffraction. The electronic structure of the selenides was investigated by magnetic measurements and band structure calculations.

The compounds MLn 2 Se 3 (M  Na, Ln  La to Sm) and MLn 8 Se 12 (M  Na, Ca; Ln  La to Sm) were prepared by reduction of the corresponding lanthanide sesquiselenides with sodium and calcium respectively, for the first time. Furthermore, MLa 8 Se 12 (M  Sr, Eu) could be obtained in an analogous way. All compounds were characterized by chemical analysis and X-ray powder diffraction. The electronic structures of these selenides were investigated by magnetic measurements and band structure calculations.

In order to study the influence of organic cations on the anionic structure of complex water containing lanthanide chlorides, we prepared the following new compounds: (pyridinium)[LnCl4(H2O)2] (Ln = La—Nd) [1,2], (4-picolinium) [LnCl4(H2O)3] (Ln = La—Nd) [3], and (2-picolinium)[LnCl4(H2O)3] (Ln = La—Nd). The crystal structures of the compounds have been determined on single crystals by X-ray methods.

Magnetic susceptibility measurements and neutron powder diffraction were performed on orthorhombic Na 2 TiCl 4 . The Ti 2+ ions occupy compressed Cl 6 octahedra sharing common edges to form Ti-Cl chains along the c -axis. The powder susceptibility can be fitted using a one-dimensional S = 1 Heisenberg model with | J |/ k B = (58 ± 5)K plus a Curie-Weiss contribution. Below T N = (13.0 ± 0.5)K, magnetic superstructure reflections show the onset of 3d antiferromagnetic order with μ = (0.89 ± 0.05) μ B at 1.8 K.

A superconducting transition with an onset temperature near 6 {Kappa} was observed for Bi/sub 2.04/Sr/sub 1.76/Mg/sub 0.30/Cu/sub 0.90/O/sub 6.20/ which crystallizes in the Bi/sub 2/Sr/sub 2/CuO/sub 6+{delta}/ type structure with partial replacement of strontium by magnesium.

The angular overlap model is applied to f electrons. General relationships are evaluated to express the ligand-field potential in angular overlap parameters for arbitrary ligand-fields. Comparison with the electrostatic model is presented for a specific example.

Host-and temperature-dependent ground-state crystal field splitting of Pr 3+ in LaCl 3 and GdCl 3 has been studied by fluorescence techniques

Crystal field theory fails if one tries to explain the difference in spectra of two tris(aminoacidato)cobalt(III) complexes with practically identical coordination geometry. The application of the angular overlap model with the assumption of anisotropic Co-O interaction gives an explanation for the difference.

The dependence of the ground state crystal field splitting of Pr 3+ in LaCl 3 on hydrostatic pressure up to 14.0 GPa has been studied by fluorescence techniques and interpreted by the angular overlap model. For the first time a crossing of crystal field levels has been observed directly.

Till now the crossing of crystal field levels has been observed indirectly as “high spin-low spin” transitions for transition metal compounds. This observation has become a wide field of research. Now for the first time the crossing of crystal field levels could be observed directly by investigating the ground state crystal field splitting of Pr3+ in LaCl3 at hydrostatic pressures up to 14.0 GPa.

The rare earth pentanitrates [(C6H5)4As]2M(NQ3)5 (M  Pr, Nd, Er, Yb) were prepared and were investigated using X-ray techniques. The magnetic behaviour of [(C6H5)4As]2M(NO3)5 (M  Pr, Nd, Yb) was studied in the temperature range 3–250 K. The magnetic data are interpreted using a model developed previously in which the influence of the crystal field is theoretically described by the angular overlap model.

Till now the crossing of crystal field levels has been observed indirectly as “high spin-low spin” transitions for transition metal compounds. This observation has become a wide field of research. Now for the first time the crossing of crystal field levels could be observed directly by investigating the ground state crystal field splitting of Pr3+ in LaCl3 at hydrostatic pressures up to 14.0 GPa.