Chiroptical activity of holmium pyrogermanate: tetragonal Ho2Ge2O7

Chiroptical luminescence and circular dichroism measurements are reported for single crystals of Ho₂Ge₂O₇. These crystals belong to the tetragonal space group P4,2,2 (or P4₃2₁2) with Z=4. Each Ho³⁺ ion in the crystal structure is coordinated to seven oxygens to form a distorted pentagonal bipyramid. The Ho³⁺ ions exhibit luminescence from several excited multiplet levels; chiroptical luminescence spectra are reported for ⁶I₈ → ⁶F₆, ⁶S₂, and ⁶F₃ at a sample temperature of 10 K. Room-temperature absorption and circular dichroism measurements are reported for the ⁶I₈ → ⁶F₆, ⁵S₂, ⁶F₄, and ⁶F₃ transition regions.     

Crystal fields in (La1−xGdx)OCl:Eu solid solutions

The formation of cation solid solution in the (La_1−xGd_x)OCl:Eu³⁺ (0≤x_Gd≤1; Δx_Gd=0.1) series was studied by photoluminescence spectroscopy. The luminescence from the ⁵D_0–2 to the ⁷F_0–4 levels of the Eu³⁺ ion in the (La_1−xGd_x)OCl series was recorded at 77 K by using argon ion laser excitation (457.9 nm). The interpretation of the spectra according to the C_4v site symmetry of the Eu³⁺ ion in the tetragonal PbFCl-type structure yielded nearly complete sets (18 to 19 levels) for the ⁷F_0–4 levels. Simulations of the Stark level schemes were carried out with the aid of a phenomenological c.f. theory utilizing the five non-zero c.f. B_q^k parameters (B₀², B₀⁴, B₄⁴, B₀⁶ and B₄⁶) allowed for the C_4v site symmetry. By using the calculated c.f. parameter sets a quantitative measure was obtained to monitor the formation of cation solid solutions. The strength of the c.f. effect was estimated with the c.f. strength parameters S and S^k (k=2, 4 and 6). The c.f. parameter sets reproduced the experimental ⁷F_J (J=0–4) energy level schemes with the rms deviations between 4 and 11 cm⁻¹. The individual parameters as well as the c.f. strength parameters were found to evolve in a smooth manner indicating complete solid solubility in the (La_1−xGd_x)OCl series. Some local distortions from the C_4v symmetry — probably of long range—leading to the splitting of the ⁷F₁ doubly degenerate E level were observed, however.     

Synthesis, characterization and microwave dielectric properties of nanocrystalline CaZrO3 ceramics

The energy-transfer mechanisms and frequency upconversion emissions in 0.5Er³⁺/xHo³⁺ co-doped tellurite glasses by exciting at 980 nm have been investigated. Three intense upconversion luminescence emissions are observed at around 525, 548, and 660 nm, which correspond to Er³⁺:²H_11/2 → ⁴I_15/2, Er³⁺:⁴S_3/2 → ⁴I_15/2 + Ho³⁺:⁵S₂(⁵F₄) → ⁵I₈, and Er³⁺:⁴F_9/2 → ⁴I_15/2 + Ho³⁺:⁵F₅ → ⁵I₈ transitions, respectively. The upconversion emissions reach the maximum values when Ho₂O₃ is 0.5 mol%, and the intensities of the green and red light emissions were about 4.5 and 6 times stronger than those un-doped Ho₂O₃, respectively. The possible upconversion mechanisms and energy transfer between Er³⁺ and Ho³⁺ were also estimated and evaluated. All the three emissions are based on two photon absorption processes.     

Properties of ytterbium and neodymium doped alkali metal yttrium double phosphates of the M3Y1−xLnx(PO4)2 type

The spectroscopic behaviour of the Nd³⁺ and Yb³⁺ doped alkaline metal yttrium double phosphates, M₃Y_1−xLn_x(PO₄)₂ (M=Na, Rb; x=0.01–0.3) were studied for both powder and single crystal samples. The high resolution absorption and emission spectra were measured in the visible and IR regions. Spectral changes with the Nd³⁺ and Yb³⁺ concentration were interpreted. The absorption strengths of the 4f–4f transitions were analysed and used to assess the structural modifications of the two double phosphates. Based on the 4 K absorption spectra the number of metal sites occupied by the dopants was investigated.

Strong emission from Na₃Y_1−xNd_x(PO₄)₂ involving the ⁴F_3/2→⁴I_9/2,⁴I_11/2,⁴I_13/2,⁴I_15/2 transitions were observed whereas the corresponding emission from the rubidium phosphate was presumably quenched by multiphonon processes due to the water molecules absorbed in the channel-like structure.

The IR spectra were used to assign the vibronic components of the electronic transitions. The Yb³⁺ emission bands were broadened depending on the Yb³⁺ concentration (1–10 mol%). The tentative energy level scheme of the ground and excited ²F_J (J=7/2, 5/2) levels was described.     

Upconversion-induced ultraviolet emission in Ho doped SrLaGa3O7 and SrLaGaO4 crystals

An analysis of the red to ultraviolet wavelength upconversion in Ho³⁺ in SrLaGa₃O₇ and SrLaGaO₄ crystals is given. Upconverted, ultraviolet emission from the ³D₃ level under cw 647 nm excitation at room temperature was observed. Excitation of the ⁵F₅ level, corresponding to the ⁵I₈→⁵F₅ transition, leads to intense emission from the ⁵I₇, ⁵I₆, ⁵F₅, ⁵S₂, ⁵F₃, ³G₅ and ³D₃ levels. Based on the energy level diagram of Ho³⁺, the pump intensity dependencies and experimental time dependencies of the observed emissions, an excitation scheme is proposed.     

Optical study of praseodymium dicarboxylate [Pr(H2O)]2[O2C(CH2)3CO2]3.4H2O

Praseodymium dicarboxylate, [Pr(H₂O)]₂[O₂C(CH₂)₃CO₂]₃.4H₂O]–glutarate, Pr[glut], is synthesized by hydrothermal techniques. The title compound crystallizes in the monoclinic space group C2/c (No. 15). The rare earth cation is coordinated by nine oxygen atoms, eight oxygen atoms from the carboxylate groups and one from the water molecule. The local symmetry of Pr site is low, C_s. The absorption spectra of Pr[glut] are recorded from the visible to the far IR domain at 300, 77 and 9 K. Under various Ar⁺ laser excitations no emission is detected from ³P₀ and ¹D₂ excited levels of Pr³⁺ ion. In the low temperature absorption spectra only one electronic line is recorded for ³H₄→³P₀ transition. It confirms a unique local environment for the rare earth ion in Pr[glut]. The utility of the ‘barycenter curves’ in the attribution of electronic lines is demonstrated. Energy level scheme of 36 Stark components is deduced from the absorption spectra. The parametric calculation was performed on the whole 4f² (Pr³⁺) configuration with the starting set of crystal field parameters obtained previously for the Eu³⁺ ion in the isostructural compound. Eight free ion and nine phenomenological crystal field parameters in C_2v symmetry reproduce quite well several electronic levels of Pr³⁺ ion experimentally observed in Pr[glut]. A good r.m.s. standard deviation of 14.8 cm⁻¹ is obtained.     

Spectral properties of Yb ions in LiNbO3 single crystals: influences of other rare-earth ions, OH ions, and γ-irradiation

Absorption spectra have been studied in 190–3100 nm region at various temperatures from 16 to 292 K for Yb³⁺-doped and Yb³⁺/Nd³⁺-, Yb³⁺/Er³⁺- and Yb³⁺/Pr³⁺-co-doped LiNbO₃ single crystals before and after γ-irradiation with a dose of 10⁵–10⁷ Gy. Intense 400 and 500 nm absorption bands were observed after γ-irradiation, which are due to the creation of oxygen vacancy (F-type color center) and Nb⁴⁺ polaron, respectively. Different change was observed in the 2870 nm OH⁻ absorption band intensity among the various rare-earth doped crystals. These are interpreted by discrepancy of ionic radii between substituting rare earth dopant ion and Li⁺ or Nb⁵⁺ host ion. The observed temperature dependence of the hot bands is understood by electronic transition from the thermally populated ²F_7/2 Stark levels to the excited ²F_5/2 level. The position of the Yb^{3+ 2}F_7/2→²F_5/2 first resonant line was observed to be slightly different among the co-doped crystals. This is due to the perturbation of Yb³⁺ by co-doped rare earth ion which is located at the neighborhood of theYb³⁺.     

Raman active phonons of RFe3(BO3)4, R=La or Nd, single crystals

Oriented single crystals of RFe₃(BO₃)₄, with R=La or Nd, have been studied by Raman spectroscopy. Spectra with the relevant polarization configurations have been recorded in order to obtain the symmetry of the observed phonons. The factor group analysis and the correlation with the free (BO₃)³⁻ ion are done in order to identify most of the phonons associated with the two different types of (BO₃)³⁻ ion present in the crystal. The number and symmetries of the optical Raman active modes are 7A₁+19E, among which 4A₁+8E can be assigned as mostly due to (BO₃)³⁻ vibrations. 7A₁+18E modes were observed.

The highest energy peaks have been assigned to the regular planar (BO₃)³⁻ and to the three irregular (BO₃)³⁻ groups. The two lowest energy peaks of A₁ symmetry (around 180 and 300 cm⁻¹) are very probably related to the BO₃ rotatory mode and to Fe displacements. R ions do not participate in A₁ symmetry modes. The E mode around 90 cm⁻¹ (the lowest frequency mode) is probably due to the R ions which have the longest bonds and are the heaviest ions.     

Spectroscopic and 1.06 μm laser properties of Nd-doped K–Sr–Al phosphate and fluorophosphate glasses

Optical absorption, fluorescence and decay curves for the ⁴F_3/2 level of Nd³⁺ ions in phosphate (P₂O₅–K₂O–SrO–Al₂O₃) and fluorophosphate (P₂O₅–K₂O–SrO–Al₂O₃–AlF₃ and P₂O₅–K₂O–SrO–Al₂O₃–BaF₂) glasses doped with three concentrations (0.1, 1.0 and 2.0 mol%) of Nd³⁺ ions have been investigated. The Judd–Ofelt (JO) theory has been applied to the absorption spectra of 1.0 mol% Nd³⁺-doped glasses to derive JO intensity parameters which are in turn used to calculate the radiative properties of the Nd³⁺ ion fluorescent levels. The assigned energy level data of Nd³⁺ (4f³) ions are analysed in terms of a parametrized free-ion Hamiltonian model that consists of 20 interaction parameters of atomic nature. The stimulated emission cross section and branching ratios have been calculated using the emission spectra. The relatively higher branching ratio for ⁴F_3/2 → ⁴I_11/2 transition shows the suitability of these glasses for laser application. It is interesting to note that the measured decay curves of the ⁴F_3/2 level remain nearly single exponential even for higher Nd³⁺ ion concentration but with shortening of lifetime.     

Optical spectroscopy of yttrium double phosphates doped by cerium and praseodymium ions

This paper reports the spectroscopic properties of cerium- and praseodymium-doped alkali metal yttrium double phosphates, M₃Y(PO₄)₂:Pr³⁺, Ce³⁺; M = Na, Rb. These phosphates were obtained by a solid state reaction between lanthanide phosphate hydrates and M₃PO₄. The absorption, reflection, emission and excitation spectra were measured at room temperature, 77 and 4 K in the IR-vis-ultraviolet (UV) range. For both the Ce³⁺- and Pr³⁺-doped double phosphates, the 4f^N↔4f^N−15d transitions were detected. For the Pr³⁺-doped double phosphates, the 4f–4f transitions from the ³H₄ ground manifold were analyzed. The low temperature ³H₄→³P₀ absorption spectra were used to characterize the structural modifications between the sodium and rubidium salts. For the Ce³⁺-doped double phosphate, the strong blue 5d¹→4f¹ emission band splits into two components due to the ²F_5/2−²F_7/2 splitting of the 4f¹ configuration. Intense emission occurs mainly from the ³P₀ level at high dopant concentrations, since the ¹D₂ emission is strongly quenched but was detected at the 2 mol% doping level. In spite of the forbidden 4f–4f character, the ³P₀ transitions have very short decay times, of the order of one μs. Dynamics of the excited states will be discussed based on the decay times and selective excited emission.     

Near-infrared to visible photon upconversion in Mn and Yb containing materials

Near-infrared (NIR) laser excitation into the Yb^{3+ 2}F_7/2→²F_5/2 absorption transition around 10,200 cm⁻¹ at 12 K leads to red and green upconversion emission in MnCl₂:Yb³⁺ and Zn₂SiO₄:Yb³⁺; Mn²⁺, respectively. The photon upconversion (UC) emission is centered around 15,240 cm⁻¹ for MnCl₂:Yb³⁺ and around 19,050 cm⁻¹ for Zn₂SiO₄:Yb³⁺; Mn²⁺ and is ascribed to the Mn^{2+ 4}T₁→⁶A₁ transition in both compounds. The shift of the Mn²⁺ emission energy is due to the different coordination and ligand strength. Pulsed measurements indicate a sequence of ground-state absorption (GSA) and excited-state absorption (ESA) steps for the upconversion process. We conclude that the UC process in both compounds occurs by an exchange mechanism involving Yb³⁺ and Mn²⁺ ions. Zn₂SiO₄:Yb³⁺; Mn²⁺ is the first example of a Yb³⁺–Mn²⁺ upconversion system to show visible (VIS) by eye Mn²⁺ UC emission at room temperature.     

Spectroscopy, magnetism and non-radiative processes in heteronuclear Cu:Pr squarate; [Pr2Cu(C4O4)4(H2O)16]·2H2O

In the present work, the spectroscopic and magnetic properties of heteronuclear Cu:Pr squarate are reported. Single crystals of [Pr₂Cu(C₄O₄)₄(H₂O)₁₆]·2H₂O were obtained by reaction of squaric acid, praseodymium chloride and copper chloride in water solution according to the procedure described earlier. The crystals of title compound are isomorphic with [La₂Cu(C₄O₄)₄(H₂O)₁₆]·2H₂O crystal, where squarate anions participate as bridging ligands between metal ions.

The UV region of absorption spectra of the title compound is dominated by C–T band of Cu(II), f–d transition of Pr(III) and internal π–π*(A_1g→E_u) and π–π*(A_1g→E_g) ligand transitions. In visible and IR regions, t_2g–e_g of copper Cu(II) as well as ³H₄→³P_J, ¹D₂, ¹G₄, ³F_J, ³H₆ Pr(III) transitions at 293 and 4 K were recorded. At low temperature splitting given by Jahn–Teller effect can be observed. Significant anisotropy of d–d transitions intensities confirms well the Jahn–Teller effect, too. Unexpectedly high intensity of ³H₄→¹G₄ transition is probably due to the intensity borrowing from the Cu (II) d–d transition.

The ³P₀ and ¹D₂ emission of Pr(III) in the [Pr₂Cu(C₄O₄)₄(H₂O)₁₆]·2H₂O crystals is quenched even at 77 K. Whereas emission of appropriate polynuclear europium squarate was detected. The pathways of excited state quenching by e_g levels of Cu(II), multhiphonon relaxation and concentration quenching can be considered in the system under studies. Magnetic susceptibility measurements were carried out in 300–1.7 K temperature range and are discussed in relation to the structure.

Effect of the polymeric structure on spectroscopic behaviour is presented. Selectivity of polymeric europium squarate in vitro test for different tumor cells is shown.     

Luminescence properties of La1−χTmχTa7O19

The luminescence properties of Tm³⁺ in La_1−χTm_χTa₇O₁₉ solid solutions were examined systematically. The substitution of Tm³⁺ for La³⁺ was carried out by a decomposition reaction of nitrates involving the corresponding constituents at 1200 °C in air. X-Ray diffraction patterns of the solid solutions indicated that the crystal structure consisted of a network of (La_1−χ³⁺Tm_χ^staggered|3+, Ta⁵⁺)—O²⁻ polyhedra interstratified with a double layer of Ta⁵⁺—O²⁻ polyhedra. According to the excitation and emission spectra, the most intense emission was found near 460 nm and quenched above χ=0.14 in La_1−χTm_χTa₇O₁₉. Also, lifetime results verified that the emission could be assigned not to the transition ¹G₄ å ³H₆, but to the transition ¹D₂ å³H₄. Upon cathode ray excitation some emissions of Tm³⁺ were superimposed by a broad emission due to the clusters of Ta⁵⁺—O²⁻ polyhedra. As a result, a low dimensional arrangement of Tm³⁺ was much more preferable for getting intense emission because it reduced the energy migration between Tm³⁺ ions.     

Excitons and rare-earth ions in CsCdBr3

CsCdBr₃ has a quasi-linear crystal structure. It consists of covalently bound [CdBr]₆⁴⁻ chains separated by chains of Cs⁺ ions. The trivalent rare-earth (RE) ions substitute for divalent Cd ions forming predominantly pair centers of the type RE³⁺-(Cd vacancy)-RE³⁺. A minority of RE ions forms “single-ion” centers with more distant charge compensation. The electronic structure around the band gap is determined by the [CdBr]₆⁴⁻ octahedra. The lowest excitonic states of the lattice are charge-transfer states of these octahedra. At low temperatures they form self-trapped excitons which become mobile around 80 K.

In addition we find defect-localized excitons at the RE pairs and single ions with slightly modified spectra. There is a strong energy transfer between the RE ions and the defect-localized excitons in both directions with transition times below 10⁻⁸ s. For the cooperative fluorescence transition ¹D₂×¹G₄→³H₄׳H₄ in Pr³⁺: CsCdBr₃ a frequency-modulated vibronic sideband spectrum was found with up to four repetitions of the frequency of the localized optical phonon mode at the ion pair.     

High pressure spectroscopy of Pr in LiNbO3

Absorption, emission, and luminescence excitation spectra of the LiNbO₃ crystal doped with 0.5% Pr³⁺ and 0.8% Yb³⁺ are presented. Additionally the photoluminescence spectra at high pressure have been measured. Hydrostatic pressures up to 135 kbar were applied with a diamond anvil cell. Absorption of the Pr³⁺:LiNbO₃ crystal is characterized by the strong threshold at about 400 nm, related to the band-to band-transitions and the sharp structure in the visible region attributed to the transitions to ³P_J and ¹D₂ levels of Pr³⁺ ion. After the 488 nm excitation the yellow emission related to the ¹D₂→³H_J transition of Pr³⁺ have been observed when the ³P₀ emission has not been detected. The excitation spectra of the ¹D₂ luminescence consist of the sharp lines related to the ³H₄→³P_J (J=0, 1, 2) transitions and two broad bands peaked at 340 and 400 nm related probably to the bound exciton. The ¹D₂→³H_J emission shifts with pressure toward the lower energies with the rate of −2.4 cm⁻¹ kbar⁻¹. Additionally, for higher pressures the ¹D₂ emission is considerably quenched. This is explained as being due to the decrease of the energy of the bound exciton with pressure which results in the higher nonradiative depopulation rate of the ¹D₂ state.     

Structural studies in lead fluorogermanate and fluorosilicate glasses

We report the results of structural studies by means of Eu³⁺ fluorescence line narrowing techniques in the binary systems PbF₂-GeO₂ and PbF₂-SiO₂. Several features characteristic of the europium fluorescence in lead glasses are put forward. The absence of selectively excited emission at room temperature demonstrates an unusually large homogeneous broadening of the electronic levels. A relative increase in the ⁵D₀ → ⁷F₁ (magnetic dipole) with respect to the ⁶D₀ → ⁷F₂ (electric dipole) transition is observed with time-resolved. detection. This effect shows that accidental coincidences of ⁵D₀ → ⁷F₀ energies and ⁷F₁ splitting do occur between europium sites differing only by their ⁶D₀ lifetimes and magnetic dipole: electric dipolar relative intensities. The general characteristics are interpreted with oxygen neighbours for Eu³⁺ rather than fluorine ions. The crystal field strength expressed as N_v = [∑_k,a (B_g^k)² × 4π/(2k + 1)]^1/2 (limited to k=2 parameters) is slightly higher in the germanate than in the silicate matrix.     

Red photoluminescence and morphology of Eu doped Ca3La3(BO3)5 phosphors

Europium doped phosphors Ca₃La₃(BO₃)₅ were first synthesized by a sol–gel process technique. The reaction temperature of the sol–gel process was 300 °C lower than that of the solid-state reaction and the reaction time of the sol–gel process was shorter. The photoluminescence properties of Eu³⁺ doped Ca₃La₃(BO₃)₅ indicated that the phosphors exhibited a strong luminescence of ⁵D₀–⁷F₂ transition at 612 nm under the excitation at 237 nm. The emission intensity of the phosphors prepared by the sol–gel process was higher than those prepared by the solid-state reaction. The relationship between optical properties and morphologies were studied. In particular, Li⁺ ion doping effectively enhanced the luminescent properties of the Eu³⁺ doped Ca₃La₃(BO₃)₅ phosphors. The highest brightness was observed in the phosphor Ca₃La_2.82Eu_0.1Li_0.08B₅O_15−δ prepared by the sol–gel process.     

IR- und ramanspektren der rheniumclusterverbindungen Rb4Re6S13 und Cs4Re6S13,5

IR and Raman spectra of Rb₄Re₆S₁₃Rb₄[Re₆S₈]S_2/2(S₂)_4/2 and Cs₄Re₆S_13,5Cs₄[Re₆S₈]S_2/2(S₂)_3/2(S₃)_1/2 are presented and discussed with respect to the S₂ and S₃ bridging units and the ([Re₆S₈]S₆) clusters. The S---S stretching modes observed (425–480 cm⁻¹), which correlate fairly well with the respective S---S bond lengths, reveal mainly covalent nature of the disulfide groups present. The S₃ group could be identified by the spectra of Cs₄Re₆S_13,5. The bands of the rhenium sulfide units are significantly shifted to higher wavenumbers compared to those of ([Mo₆Cl₈]Cl₆)²⁻ and [Mo₆S₈] units (Chevrel compounds) despite the larger mass of rhenium. This indicates strong Re---Re and Re---S bonding.

Zusammenfassung

Die IR- und Raman-Spektren von Rb₄Re₆S₁₃Rb₄[Re₆S₈]S_2/2(S₂)_4/2 und Cs₄Re₆S_13,5Cs₄[Re₆S₈]S_2/2(S₂)_3/2(S₃)_1/2 werden mitgeteilt und im Hindblick auf die S₂- und S₃-Brücken sowie die ([Re₆S₈]S₆)-Baugruppen diskutiert. Die beobachteten S---S-Streckschwingungen (425–480 cm⁻¹) korrelieren mit den zugehörigen S---S-Bindungsabständen und weisen auf weitgehend kovalente Disulfid-Brücken hin. Die Trisulfid-Brücken konnten in den Spektren des Cs₄Re₆S_3,5 nachgewiesen werden. Die Schwingungsbanden der Rhenium-Schwefel-Baueinheiten sind im Vergleich zu denen der ([Mo₆Cl₈]Cl₆)²⁻- und [Mo₆S₈]-Einheiten (Chevrel-Phasen) trotz der gröβeren Masse des Rheniums deutlich zu gröβeren Wellenzahlen verschoben. Dies läβt auf sehr starke Re---Re- und Re---S-Bindungen schlieβen.     

Synthesis, crystal structure and properties of the new semiconductor (EVT)4·[Pt(CN)4]

A novel radical cation salt based on of the donor (4,5-ethylenedithio-4′,5′-vinylenedithio)tetrathiafulvalene (EVT) with the square planar anion Pt(CN)₄²⁻ has been synthesized: (EVT)₄·[Pt(CN)₄] (1). According to the X-ray analysis its crystal structure includes EVT cation layers alternating with anion layers along the a-axis of the unit cell. The radical cation layer is formed by EVT stacks with β-packing type, the donors in stacks are tetramerized. The EPR spectra of a plate-like crystal of (EVT)₄·[Pt(CN)₄] salt shows a very weak signal with typical parameters of TTF derivative. The room temperature conductivity of salt 1 is 8×10⁻² Ω⁻¹ cm⁻¹ and the temperature dependence of the conductivity exhibits semiconducting character.     

Measurements and simulation of the Zeeman splitting in NdOCl and Nd:LiYF4

Measurements and simulation of the Zeeman effect in NdOCl and 1%Nd³⁺:LiYF₄ single crystals were carried out. The rare earth local symmetries are C_4v and D_2d respectively. The isomorphism between these two point groups allows discussion on symmetry assignments. The attention is focused on the ⁴G_7/2 and ⁴G_9/2 levels for NdOCl and on the ⁴F_9/2 and ⁴G_7/2 levels for Nd³⁺:LiYF₄, because they are representative of the general splitting behaviour. We have first revisited the simulation of the energy level scheme in order to deal with confident wave functions. In the experimental magnetic field (B) range we have obtained linear, non-linear, undefined crossing and anti-crossing levels. These features depend on the orientation of B, on the irreducible representation and on the transition closeness. The line widths have been the main obstacle in confirming crossing regions, because their average values are 8 cm⁻¹ at liquid helium temperature. The simulations were performed by introducing the magnetic Hamiltonian μ_BB(L+g_eS) in the secular determinant before diagonalisation. A magnetic accidental degeneracy is considered when discussing the crossing and anti-crossing cases.