Mauro
Perfetti‡§
^{a},
Maren
Gysler‡
^{a},
Yvonne
Rechkemmer-Patalen
^{a},
Peng
Zhang
^{a},
Hatice
Taştan
^{a},
Florian
Fischer
^{a},
Julia
Netz
^{a},
Wolfgang
Frey
^{b},
Lucas W.
Zimmermann
^{c},
Thomas
Schleid
^{c},
Michael
Hakl
^{d},
Milan
Orlita
^{de},
Liviu
Ungur
^{f},
Liviu
Chibotaru
^{f},
Theis
Brock-Nannestad
^{g},
Stergios
Piligkos
^{g} and
Joris
van Slageren
*^{a}
^{a}Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany. E-mail: slageren@ipc.uni-stuttgart.de
^{b}Institut für Organische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
^{c}Institut für Anorganische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
^{d}Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, UGA, 38042 Grenoble, France
^{e}Institute of Physics, Charles University, Ke Karlovu 5, 12116 Praja 2, Czech Republic
^{f}Theory of Nanomaterials Group, Katholieke Universiteit Leuven, Celestijnenlaan 220F, 3001 Leuven, Belgium
^{g}Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100, Denmark
First published on 12th December 2018
We present the in-depth determination of the magnetic properties and electronic structure of the luminescent and volatile dysprosium-based single molecule magnet [Dy_{2}(bpm)(fod)_{6}] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2′-bipyrimidine). Ab initio calculations were used to obtain a global picture of the electronic structure and to predict possible single molecule magnet behaviour, confirmed by experiments. The orientation of the susceptibility tensor was determined by means of cantilever torque magnetometry. An experimental determination of the electronic structure of the lanthanide ion was obtained combining Luminescence, Far Infrared and Magnetic Circular Dichroism spectroscopies. Fitting these energies to the full single ion plus crystal field Hamiltonian allowed determination of the eigenstates and crystal field parameters of a lanthanide complex without symmetry idealization. We then discuss the impact of a stepwise symmetry idealization on the modelling of the experimental data. This result is particularly important in view of the misleading outcomes that are often obtained when the symmetry of lanthanide complexes is idealized.
Even in most polynuclear complexes, the magnetic properties are largely determined by the individual rare earth ions and their immediate surroundings.^{25} Weak, essentially dipolar interactions between lanthanide ions can cause (undesirable) relaxation enhancement.^{26} However, in the presence of an inversion center, interactions can lead to exchange-bias-like effects suppressing under-barrier tunneling.^{27} A different situation arises, when strong magnetic interactions are present, which typically involves lanthanide-radical species. The prime example is the N_{2}^{3−} bridged terbium dimer with a hysteresis blocking temperature of 14 K.^{28} Less exotic species have featured polypyridyl-like bridging ligands that can be reduced to a radical form.^{29–34} The latter are especially attractive, because the magnetic properties may be switched (electro)chemically by reducing and oxidizing the bridging ligand.^{31,34}
Although the magnetic properties of lanthanide complexes are intimately linked to the electronic structure, spectroscopic investigations of the electronic structure are still rather few.^{35–41} Magnetic interactions between the ground Kramers doublets in dinuclear lanthanide complexes have been studied in detail by EPR.^{26,42}
Diketonate complexes with polypyridine-related ligands are a widely studied class of complexes due to their great relevance in many fields of science. Their magnetic properties have been the subject of many investigations since the discovery of slow relaxation of the magnetic moment in mononuclear [Ln(acac)_{3}(H_{2}O)_{2}] (Hacac = acetyl acetone).^{4,43,44} Trinuclear^{45} and binuclear complexes with pyrazine,^{46} bipyrimidine,^{29,47,48} tetrapyridyl pyrazine^{30} and bispyridyl tetrazine^{31} have also been widely investigated. The electronic structure of diketonate ligands is very efficient in sensitizing the luminescence of lanthanide ions.^{49,50} Moreover, many diketonate-metal complexes have been reported to be highly volatile^{51} and suitable for surface deposition.^{52} Fluorination of the diketonate ligand quenches non-radiative decay processes, leading to high luminescence quantum yields.^{53}
In this paper, we unravel the magnetic properties and the electronic structure of a dinuclear complex [Dy(fod)_{3}(μ-bpm)Dy(fod)_{3}] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2′-bipyrimidine), hereafter abbreviated as Dy_{2}. Ab initio calculations were performed to predict the magnetic and electronic structure of this complex. Single crystal torque magnetometry provided the orientation of the magnetic axes of the ground doublet, in excellent agreement with ab initio predictions. A combination of Luminescence, Far Infrared and Magnetic Circular Dichroism spectroscopies was used to carefully determine 38 energy levels belonging to 9 crystal field multiplets, thus allowing the first analysis of the crystal field of a lanthanide dimer without symmetry idealization.
Ab initio calculations can provide a detailed picture of the electronic and magnetic structure of lanthanide complexes.^{56} Therefore, we carried out such calculations on Dy_{2} within the well-known CASSCF/RASSI/single_aniso framework. The g tensor of the ground Kramers doublet of Dy_{2} was calculated to be extremely axial (g_{x} = g_{y} = 0.01, g_{z} = 19.55, to be compared with a perfectly axial g tensor g_{x} = g_{y} = 0, g_{z} = 20), due to the essentially pure (96%) |±15/2〉 character (see Table S3† for the orientation and magnitude of the g tensors of all the doublets). Interestingly, the easy axis was predicted to be almost orthogonal to the Dy–Dy direction. The first excited doublet (80% |±13/2〉), separated by 150 cm^{−1} from the ground state, was also calculated to be axial (g_{x} = 0.26, g_{y} = 0.39, g_{z} = 16.09) and almost collinear with the ground state (8° tilting), thus disfavoring quantum tunnelling of the magnetization. The calculated CF levels of the ground multiplet are reported as red lines in the inset of Fig. 2. The calculated CF parameters are reported in Table S4.† Given the absence of symmetry, an indication of the influence of the parameters of a given order can be obtained calculating the CF strength factors^{32} (S_{k}, where k = 2, 4, 6 is the order of the parameters), as reported in Table S5.† The calculations predict a total CF strength S_{tot} = 292 cm^{−1}, dominated by the parameters of fourth order (S_{4} > S_{2} > S_{6}). In Table S6† the composition of the CF levels belonging to the ground multiplet is presented.
Fig. 2 Experimental (green) and fitted (black) energy level splitting. The inset is a zoom on the ground ^{6}H_{15/2} term, where also the ab initio (red) energies are reported. |
The picture that emerges from ab initio calculations is an extremely axial system, likely to exhibit single molecule magnet behaviour. We thus measured the static and dynamic magnetic properties of this complex and compare them with the outcome of the calculations. In Fig. 3 we report the experimental χT vs. T curve. The χT value at room temperature (27.8 emu K mol^{−1}) is slightly lower than two times the Curie constant of a free Dy^{3+} ion (28.3 emu K mol^{−1}). The decrease of the χT product on lowering the temperature is mainly attributed to the CF splitting and possibly to the presence of magnetic interactions. The simulated χT product, reported as a red curve in Fig. 3, was obtained using the ab initio-calculated CF parameters and adding an isotropic intramolecular antiferromagnetic (AFM) coupling constant j = 4.2(1) × 10^{−3} cm^{−1} (following the +j·Ĵ_{1}·Ĵ_{2} convention). The AFM interaction is readily explained by the almost perpendicular orientation of the easy axes and the Dy_{1}⋯Dy_{2} axis.^{57} In order to estimate the relative magnitudes of the exchange and the dipolar couplings, we calculated the dipolar contribution within the point dipole approximation using the orientation and magnitude of the calculated ground g tensor obtaining j_{dip} = 2.3 × 10^{−3} cm^{−1}. The calculated value is approximately half of the fitted coupling constant, indicating that the exchange and dipolar contributions in this system have comparable magnitudes. Previous studies in literature reported both similar^{57} and different^{58,59} ratios between the dipolar and the exchange contributions. The disagreement between experiments and ab initio simulation at intermediate temperatures (30 < T < 200 K) is attributed to the imperfectly calculated energies and compositions of the CF states. To clarify this discrepancy, we carried out a detailed spectroscopic characterization (see below). In the inset of Fig. 3 we also report the measured and simulated field dependence of the magnetization at low temperature. The excellent agreement with the simulation (red line), provides further evidence of the strong axiality of the ground state. The expected magnetic bistability is experimentally supported by the presence of magnetic hysteresis at temperatures below 2 K (blue line in Fig. 4). Interestingly, the curve shows a double butterfly shape, closing both at zero field and at ±500 Oe. The latter is exactly at the position where simulations according to parameters taken from the ab initio calculations predict a field-induced level crossing. Similar relaxation enhancement at level crossings have been observed in a Dy_{3} complex.^{60} In contrast, in a dilute sample of [(Y:Dy = 19:1)_{2}(fod)_{6}(μ-bpm)] (Dy@Y_{2}), the hysteresis loop only closes at zero field (red line in Fig. 4). This corroborates that indeed there is a significant interaction between the two dysprosium ions.
Fig. 4 Hysteresis curves recorded on powder samples of Dy_{2} and Dy@Y_{2} at 1.8 K with field sweep rates of 100 Oe s^{−1}. The lines are the ab initio calculated energy levels. |
The axiality suggests the possible occurrence of slow relaxation of the magnetization. We thus carried out a study of the magnetization dynamics, where we detected slow relaxation of the magnetic moment both with and without an external applied magnetic field (Fig. S2†). The field scan at the lowest temperature (T = 1.8 K) reveals a double peak in the imaginary component at low fields (H < 500 Oe). This indicates the presence of two active relaxation pathways, as already observed in other mono^{61} and polynuclear^{59,62–67} Dy-based complexes. However, in the present case this cannot be attributed to two distinct coordination environments for the Dy(III) ions because the two dysprosium ions are crystallographically related by an inversion centre. A possible explanation is instead the presence of (relatively small) intermolecular interactions that may open an alternative relaxation channel compared to the single ion relaxation, as already observed for other lanthanide complexes.^{68} When the magnetic field is raised, the relaxation time rapidly increases towards frequencies outside of the experimental window. We thus focused our attention on the temperature scan in zero field and in an optimum field of 0.1 T. The zero-field temperature scan is shown in Fig. 5a (real component reported in Fig. S3†). The out of phase susceptibility (χ′′) vs. frequency (ν) curves were fitted as reported in ESI (Fig. S4† and explanation thereafter) to extract the relaxation times (τ), the width of the distribution (α) and the difference between isothermal and adiabatic susceptibility (χ_{T} − χ_{S}). The extracted χ_{T} − χ_{S} values are in good agreement with the χ_{dc} values (Fig. S5†), testifying that the observed relaxation processes involve the entire magnetic ensemble. The extracted relaxation times for the slow process are reported in Fig. 5b (red triangles). The almost constant value of τ at low temperatures (T < 3 K) reflects the proximity to the quantum tunneling regime, while at higher temperatures the linear trend of log(τ) vs. log(T) suggests a Raman process as the preferential relaxation channel. Importantly, the experimental data could not be fitted using an Orbach process fixing the energy barrier for the reversal of the magnetization to the calculated energy of the first excited state (151 cm^{−1}) as illustrated in Fig. S6.† The relaxation time was instead well reproduced using the following equation:
τ^{−1} = τ_{TI}^{−1} + CT^{n} | (1) |
Sample | Field (T) | τ _{TI} | C | n |
---|---|---|---|---|
Dy_{2} | 0 | 0.761(7) | 1.32(3) × 10^{−2} | 4.79(2) |
0.1 | — | 1.85(2) × 10^{−3} | 5.52(5) | |
4% Dy in Y_{2} | 0 | 0.32(1) | 3.8(4) × 10^{−2} | 4.38(6) |
0.1 | — | 1.57(2) × 10^{−3} | 5.54(5) |
To shed further light on the relaxation mechanisms, we performed a dilution experiment using an approximate ratio 1:19 between Dy(fod)_{3} and Y(fod)_{3} as starting material. The χT product of the resulting compound (hereafter called Dy@Y_{2}) is reported in Fig. S7† and reveals a magnetic dilution of 4% (close to the expected 5%). The field scan of the ac magnetic susceptibility reveals a similar trend compared to the Dy_{2} derivative (Fig. S8†), however the considerably narrower character of the imaginary component reveals a single relaxation process. Indeed, the ac magnetic susceptibility recorded in zero field (Fig. S9†) could be fitted using only one relaxation process in the whole temperature regime. This reinforces the hypothesis that the second relaxation process observed in Dy_{2} is produced by intermolecular interactions. The obtained relaxation times, reported in Fig. 5b (black diamonds), were fitted using eqn (1) and the results are reported in Table 1.
Although at T > 5 K the two curves are almost superimposable (testified by the similar Raman exponent and pre-factor), the temperature independent relaxation time decreases by a factor 2.4 in the diluted sample, pointing out that the quantum tunneling is enhanced by intermolecular interactions.
Another efficient way to remove the tunneling of the magnetization is the application of an external magnetic field. Indeed, the imaginary component of the magnetic susceptibility, reported in Fig. S10† for Dy_{2} and in Fig. S11† for 4% Dy in Y_{2}, can be reproduced considering a single Raman relaxation process in the whole investigated temperature range. The extracted relaxation times for the pure and diluted compounds are virtually superimposable (blue circles in Fig. 4b for Dy_{2}, and Fig. S11† for 4 Dy in Y_{2}). In Table 1 we report the fit parameters.
Given the discrepancy between experimental and calculated susceptibility at intermediate temperatures, we performed a completely experimental determination of the electronic structure of Dy_{2}. Although appealing, the experimental determination of the CF of a molecular lanthanide complex without idealized symmetry has never been performed due to the practical challenge in measuring a sufficient number of energy levels to meaningfully fit all the required CF parameters. We tried to overcome this obstacle combining two spectroscopic techniques, namely Luminescence and Magnetic Circular Dichroism, that provide access to CF excitations in a broad energy range.
Luminescence has been demonstrated to be a powerful tool to study magnetic properties of molecules, and several works have established a strong correlation between luminescence and magnetic properties.^{69–73} We performed luminescence measurements at T = 5 K irradiating at λ = 341 nm (ca. 29300 cm^{−1}), exciting electronic transitions of the ligands. The triplet excited states of the ligands (E(T_{1}(fod)) = 22500 cm^{−1} and E(T_{1}(bpm)) = 27200 cm^{−1}) are close to the excited ^{4}F_{9/2} state (ca. 21000 cm^{−1}) of Dy^{3+}, allowing for efficient energy transfer. These measurements allowed to resolve the CF splitting of the ground ^{6}H_{15/2} state (Fig. 6) and of the ^{6}H_{13/2} excited multiplet (Fig. S13†). The spectrum reported in Fig. 6 could be satisfactorily reproduced using eleven Gaussian functions, while in principle only 8 components must be detected for a ^{6}H_{15/2} ground state. We attribute the additional, broader features to vibronic excitations.^{73} Note that only the crystal field fitting of all experimental energies allowed for unambiguous assignment of the luminescence bands.
A comparison with the energies calculated ab initio (the green and the red lines in the inset of Fig. 2) reveals that the experimentally derived splitting is larger than that obtained from ab initio calculations. The ratio of experimental and ab initio energies appears to be almost constant for all the KDs. Indeed, a scaling of the calculated energies by a factor 1.2, as reported in Fig. S14,† greatly improves the agreement with the experiments. The applicability of a scaling factor for CASSCF/RASSI-derived energies to match experiments was already reported^{24,26,42} and recently attributed to the necessity to include the presence of an extended crystal lattice using, e.g., point charges.^{42}
Molecular vibrations are crucial to determine the dynamics of the magnetization,^{8,74–76} and their presence can be detected using field-dependent FIR spectroscopy. Indeed, the FIR spectra reported in Fig. S15† exhibit several field-dependent weak features (2–3% of the intensity at zero field) between 150 cm^{−1} and 250 cm^{−1}. The two downward pointing peaks at ca. 184 and 205 cm^{−1} are attributed to the zero-field crystal field transitions.^{42,77} Because of the weakness of the signal and the ensuing uncertainty in the exact peak position we did not include the FIR peak energies in the fitting procedure (see below). However, the final fit does yield energy levels in this region.
The number of experimental energies extracted from luminescence data (15 in total) was not sufficient to fully parametrize the CF potential acting on the Dy^{3+} ion. We thus performed Magnetic Circular Dichroism (MCD) spectroscopy in the Vis-NIR range (5000–15000 cm^{−1}, Fig. S16†) to observe transitions between the ground state and 7 excited multiplets (^{6}H_{11/2}, ^{6}H_{9/2}, ^{6}F_{11/2}, ^{6}H_{7/2}, ^{6}F_{9/2}, ^{6}F_{5/2}, ^{6}F_{3/2}, see Fig. S17†). All the experimentally extracted energies are reported in Fig. 2 as green lines and numerically in Table S7.†
The luminescence and the MCD results together provided a set of 38 experimental energy levels that was used to perform the fit of the CF parameters. We used the full |S,L,J,m_{J} 〉 basis of the states that for an 4f^{9} ion gives rise to 2002 states. The single ion Hamiltonian used to describe the system is the sum of a free ion term and a CF term.^{78} The free ion term can be written as:
(2) |
The CF term of the Hamiltonian in Wybourne notation is:
(3) |
In eqn (3) the number of the B_{q}^{k} parameters related to the C_{q}k spherical tensor operators is dependent on the single site symmetry. For the studied compounds, no symmetry restrictions could be applied, and the total number of parameters was therefore 27. The coupling term of the Hamiltonian was neglected at this stage in view of the small coupling strength predicted by the ab initio calculations. The results of the fit are reported in Tables S8 and S9† (last two columns). Due to the large number of experimental parameters, a good initial guess is needed: we thus used the CF parameters obtained from ab initio calculations.
Fig. 2 depicts the experimental (green) and fitted (black) energy levels up to 14000 cm^{−1}. An excellent overall agreement is observed. The inset of Fig. 2 is a zoom of the ground ^{6}H_{15/2} term of Dy^{3+}, in which the average deviation from the experimental values is well-below the experimental error (≪1 cm^{−1}). The outcome of the fitting confirms that the ground KD is highly axial (84% |±15/2〉), as correctly predicted by ab initio calculations (compare Tables S6 and S10†), even though it has a minor (10%) |±13/2〉 component. The first excited state is instead highly mixed. HFEPR measurements performed at three different temperatures (T = 5, 10 and 20 K) revealed that the ground KD is EPR-silent, confirming its highly axial nature. The FIR spectra simulated starting from the set of CF parameters obtained ab initio and by fit are reported in Fig. S18,† together with the experimental results. In the spectra obtained from the ab initio output only the transition between the ground and the first excited doublet is strongly allowed, due to the substantial purity of the states. The simulated transition occurs at lower energy than expected, due to the underestimation of the first excited state. The simulation obtained from the fit of the experiments correctly reproduces both the relative intensity of the peaks and the position of the first peak (at ca. 190 cm^{−1}), while a 15% discrepancy can be seen in the position of the second excitation.
The CF strength, reported in Table S11,† is dominated by the fourth order terms (S_{4} = 537 cm^{−1}), in agreement with the ab initio prediction. Whilst the second order strength (S_{2} = 286 cm^{−1}) also compares well with ab initio calculations, the sixth order (S_{6} = 382 cm^{−1}) is almost doubled in the fit. This leads to the overall CF strength obtained from the fit (S_{t} = 402 cm^{−1}) being higher than the one predicted by calculations (S_{t} = 292 cm^{−1}).
Having obtained a satisfactory fit of all CF parameters, made possible by the large number of experimental energies, the question remains, if adequate fits could have been obtained with using fewer CF parameters. We therefore repeated the fit of the CF parameters using (physically unrealistic) higher symmetries (Fig. 7) compatible with the presence of eight donor atoms in the first coordination sphere (see Table S2†). Clearly, going to higher symmetries leads to more CF parameters being zero by symmetry (Table S9†), thus fewer fit parameters. Fig. 7 demonstrates that for all symmetries higher than C_{2v} satisfactory fits cannot be obtained, and thus that at least 15 CF parameters are required to accurately reproduce the energies. The assumption of C_{2v} symmetry suffices to reproduce the energy spectrum and quantities primarily determined by it, such as the magnetic susceptibility (Fig. S19†). However, the composition of the eigenstates derived from the fits in C_{1} and C_{2v} symmetries is substantially different (Tables S11 and S12†). Thus, whilst in C_{2v} symmetry, the ground KD is calculated to be essentially fully axial, it is much less so in C_{1} symmetry. The precise composition of the KDs is of great importance, because it determines the pathway of the relaxation of the magnetization, since all relaxation processes (direct, quantum tunnelling, Raman, Orbach) feature matrix elements of the CF eigenstates. Indeed, both the composition and the main relaxation channels in both symmetries are clearly different (Fig. 8). We thus conclude that models using fewer parameters than those allowed by symmetry lead to erroneous results in this case.
Fig. 7 Best fit energy level diagrams on the basis of CF Hamiltonians containing only those terms belonging to the indicated symmetries. |
We employed cantilever torque magnetometry (CTM) to have an independent validation of the theoretically determined orientation of the easy axis of the Dy^{3+} ion. Since the studied complex crystallizes in the P triclinic space group, the experimental determination of the magnitude and orientation of magnetic anisotropy can be performed unambiguously by means of CTM.^{79} A sketch of the single crystal orientation is reported in Fig. S20.† The torque curves recorded at two different temperatures (T = 2 and 5 K) are reported in Fig. 9, while all the other measurements are reported in Fig. S21.† They appear very similar in shape and magnitude: they both exhibit two 90° spaced zero-torque points in the 0–180° angular range, in agreement with the crystallographically imposed collinearity of the susceptibility tensors. The zero-torque angles correspond to the projection of the easy axis in the plane of rotation being parallel (easy zero) or perpendicular (hard zero) to the applied field. To avoid overparametrization, the fit was performed fixing the CF parameters to the ones extracted from the fit of the experimental energy levels. In this way, the only parameters free to vary were the three Euler angles that define the orientation of the molecular anisotropy tensor reference frame with respect to the crystallographic one^{79} (see Table S13† for numerical results). The agreement between experiment and fit is remarkably good, confirming again the goodness of the CF parameters. The orientation of the magnetic susceptibility tensor that we obtained is pictorially reported as a cyan ellipsoid superimposed on the Dy atoms in Fig. 1. The longest axis of the ellipsoid corresponds to the most favoured direction, taken as the molecular z axis in Table S13.† The experimental and calculated z (easy) molecular axes are coincident (angle between the two axes ca. 2°, below the experimental error for the visual alignment of the crystal), while the x and y axes (hard and intermediate, respectively) are shifted by ca. 30° between experiment and theory (compare Table S13†). This discrepancy is expected in highly axial systems, where the identification of small deviations in the anisotropy of the hard plane are often problematic from both the experimental and the theoretical point of view.
Fig. 9 Rotation 1 (top) and rotation 2 (bottom) performed on a single crystal of Dy_{2} using CTM (see ESI† for details). Symbols refer to the experimental points while lines are the best fits. |
Fixing the Dy^{3+} CF parameters to the values extracted from the fit, we simulated the static magnetic properties. The χT curve was obtained an isotropic intramolecular AFM coupling constant j = 4.2(1) × 10^{−3} cm^{−1} (black line in Fig. 3), the same value obtained starting from the ab initio CF parameters. The dipolar part of the coupling obtained using the experimentally determined orientation of the easy axis and the g tensor extracted from the fit is substantially coincident with the one calculated using the ab initio results, confirming the approximate 1:1 ratio between dipolar and exchange contribution to the coupling. The inclusion of the coupling constant allows simulating the energetic structure of the Dy_{2} dimer that shows a level crossing at 503 Oe, in close proximity to the first closing point of the double butterfly hysteresis (500 Oe, compare Fig. 4). This crossing is obviously absent if the coupling is not included, in agreement to the single butterfly shape observed for the diluted sample.
Ab initio calculations were carried out on the full molecule by means of the CASSCF/RASSI-SO/SINGLE_ANISO routine using the MOLCAS 7.8 software package.^{84} One of the two Dy^{3+} ions was replaced with a diamagnetic Lu^{3+} ion. Basis sets were taken from the MOLCAS ANO-RCC library (Dy.ANO-RCC…8s7p5d4f2g1h). Complete active space self-consistent field (CASSCF) calculations include 9 electrons in the 7 4f orbitals. Spin–orbit mixing within the restricted active space state interaction (RASSI-SO) procedure included all sextet (^{6}H, ^{6}F, and ^{6}P), 128 quartet (^{4}I, ^{4}F, ^{4}M, ^{4}G, ^{4}K, ^{4}L, ^{4}D, ^{4}H, ^{4}P, ^{4}G, ^{4}F and ^{4}I) and 130 doublet terms (^{2}L, ^{2}K, ^{2}P, ^{2}N, ^{2}F, ^{2}M, ^{2}H, ^{2}D, ^{2}G and ^{2}O). The magnetic exchange interaction strength was calculated using the POLY_ANISO routine in combination with experimental magnetic data.
Footnotes |
† Electronic supplementary information (ESI) available: Synthesis and characterization, shape calculations. Ab initio composition and g-tensors. Magnetic, spectroscopic and thermodynamic characterization. Crystal field splitting and composition. CCDC 1829110. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c8sc03170c |
‡ Current address: Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100, Denmark. |
§ These authors contributed equally. |
This journal is © The Royal Society of Chemistry 2019 |