Nanostructures as the Substrate for Single-Molecule Magnet Deposition

Anchoringsingle-molecule magnets (SMMs) on the surface of nanostructures is gaining particular interest in the field of molecular magnetism. The accurate organization of SMMs on low-dimensional substrates enables controlled interactions and the possibility of individual molecules' manipulation, paving the route for a broad range of nanotechnological applications. In this comprehensive review article, the most studied types of SMMs are presented, and the quantum-mechanical origin of their magnetic behavior is described. The nanostructured matrices were grouped and characterized to outline to the reader their relevance for subsequent compounding with SMMs. Particular attention was paid to the fact that this process must be carried out in such a way as to preserve the initial functionality and properties of the molecules. Therefore, the work also includes a discussion of issues concerning both the methods of synthesis of the systems in question as well as advanced measurement techniques of the resulting complexes. A great deal of attention was also focused on the issue of surface-molecule interaction, which can affect the magnetic properties of SMMs, causing molecular crystal field distortion or magnetic anisotropy modification, which affects quantum tunneling or magnetic hysteresis, respectively. In our opinion, the analysis of the literature carried out in this way will greatly help the reader to design SMM-nanostructure systems.

DNA methylation-dependent epigenetic regulation of Verticillium dahliae virulence in plants

As a conserved epigenetic mark, DNA cytosine methylation, at the 5' position (5-mC), plays important roles in multiple biological processes, including plant immunity. However, the involvement of DNA methylation in the determinants of virulence of phytopathogenic fungi remains elusive. In this study, we profiled the DNA methylation patterns of the phytopathogenic fungus Verticillium dahliae, one of the major causal pathogens of Verticillium wilt disease that causes great losses in many crops, and explored its contribution in fungal pathogenicity. We reveal that DNA methylation modification is present in V. dahliae and is required for its full virulence in host plants. The major enzymes responsible for the establishment of DNA methylation in V. dahliae were identified. We provided evidence that DNA methyltransferase-mediated establishment of DNA methylation pattern positively regulates fungal virulence, mainly through repressing a conserved protein kinase VdRim15-mediated Ca2+ signaling and ROS production, which is essential for the penetration activity of V. dahliae. In addition, we further demonstrated that histone H3 lysine 9 trimethylation (H3K9me3), another heterochromatin marker that is closely associated with 5-mC in eukaryotes, also participates in the regulation of V. dahliae pathogenicity, through a similar mechanism. More importantly, DNA methyltransferase genes VdRid, VdDnmt5, as well as H3K9me3 methyltransferase genes, were greatly induced during the early infection phase, implying that a dynamic regulation of 5-mC and H3K9me3 homeostasis is required for an efficient infection. Collectively, our findings uncover an epigenetic mechanism in the regulation of phytopathogenic fungal virulence.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42994-023-00117-5.

The crystal structure of 5,10,15,20-tetrakis(4-(tert-butyl)phenyl)porphyrin-21,23-diido-κ4 N 4-naphthalocyanido-κ4 N 4-neodymium(IV) - chloroform (1/6) C114H90N12Cl18Nd

C114H90N12Cl18Nd, triclinic, P 1 ‾ $P\overline{1}$ (no. 2), a = 17.3389(7) Å, b = 18.7671(5) Å, c = 19.1454(8) Å, α = 79.600(3)°, β = 68.752(4)°, γ = 68.572(3)°, V = 5396.7(4) Å3, Z = 2, R gt (F) = 0.0722, wR ref (F 2) = 0.1979, T = 298 K.

Rare-earth based tetrapyrrolic sandwiches: chemistry, materials and applications

This review summarises advances in chemistry of tetrapyrrole sandwiches with rare earth elements and highlights the current state of their use in single-molecule magnetism, organic field-effect transistors, conducting materials and nonlinear optics.

Modern physical methods for the molecular design of single-molecule magnets

Many paramagnetic metal complexes have emerged as unique magnetic materials (single-molecule magnets), which behave as conventional magnets at the single-molecule level, thereby making it possible to use them in modern devices for data storage and processing. The rational design of these complexes, however, requires a deep understanding of the physical laws behind a single-molecule magnet behaviour, the mechanisms of magnetic relaxation that determines the magnetic properties and the relationship of these properties with the structure of single-molecule magnets. This review focuses on the physical methods providing such understanding, including different versions and various combinations of magnetometry, electron paramagnetic and nuclear magnetic resonance spectroscopy, optical spectroscopy and X-ray diffraction. Many of these methods are traditionally used to determine the composition and structure of new chemical compounds. However, they are rarely applied to study molecular magnetism.

The bibliography includes 224 references.

Lanthanoid Complexes as Molecular Materials: The Redox Approach

The development of molecular materials with novel functionality offers promise for technological innovation. Switchable molecules that incorporate redox-active components are enticing candidate compounds due to their potential for electronic manipulation. Lanthanoid metals are most prevalent in their trivalent state and usually redox-activity in lanthanoid complexes is restricted to the ligand. The unique electronic and physical properties of lanthanoid ions have been exploited for various applications, including in magnetic and luminescent materials as well as in catalysis. Lanthanoid complexes are also promising for applications reliant on switchability, where the physical properties can be modulated by varying the oxidation state of a coordinated ligand. Lanthanoid-based redox activity is also possible, encompassing both divalent and tetravalent metal oxidation states. Thus, utilization of redox-active lanthanoid metals offers an attractive opportunity to further expand the capabilities of molecular materials. This review surveys both ligand and lanthanoid centered redox-activity in pre-existing molecular systems, including tuning of lanthanoid magnetic and photophysical properties by modulating the redox states of coordinated ligands. Ultimately the combination of redox-activity at both ligands and metal centers in the same molecule can afford novel electronic structures and physical properties, including multiconfigurational electronic states and valence tautomerism. Further targeted exploration of these features is clearly warranted, both to enhance understanding of the underlying fundamental chemistry, and for the generation of a potentially important new class of molecular material.

Quintuple-Decker Heteroleptic Phthalocyanine Heterometallic Samarium-Cadmium Complexes. Synthesis, Crystal Structure, Electrochemical Behavior, and Spectroscopic Investigation

A one-pot synthesis methodology was employed for obtaining diverse quintuple-decker phthalocyanine heterometallic lanthanide-cadmium complexes. By using the reaction of a double-decker homoleptic/heteroleptic phthalocyanine samarium compound with metal-free phthalocyanine and cadmium acetate in 1,2,4-trichlorobenzene at 200 °C, two novel quintuple-decker heteroleptic phthalocyanine heterometallic samarium-cadmium compounds, {(Pc)Sm(Pc)Cd(Pc*)Cd(Pc)Sm(Pc)} (1) and {(Pc)Sm(Pc*)Cd(Pc*)Cd(Pc*)Sm(Pc)} (2), together with one homoleptic phthalocyanine species, {(Pc*)Sm(Pc*)Cd(Pc*)Cd(Pc*)Sm(Pc*)} (3), were successfully fabricated, where H₂Pc and H₂Pc* represent unsubstituted phthalocyanine and 2,3,9,10,16,17,23,24-octakis(n-pentyloxy)phthalocyanine, respectively. Their quintuple-decker structures have been disclosed by various spectroscopic techniques and single-crystal X-ray diffraction. In addition, valence tautomerization of these three quintuple-decker complexes has been achieved by the addition of phenoxathiin hexachloroantimonate, giving three oxidized forms including one-, two-, and three-electron oxidation products. From 1 to 3 with the same oxidation state, the increased number of n-pentyloxy substituents of phthalocyanine ligands induces the blue shift of electronic absorption in the IR region due to the increased gap associated with the introduction of electron-donating substituents. In particular, the electronic absorption spectra of one- and two-electron oxidation products for 1 exhibit a rare band in the middle-IR region around 3000 nm, being one of the farthest electronic transitions captured by UV-vis spectroscopy. The three-electron oxidation product of 1 displays two bands at 2231 and 2740 nm, respectively. These data are well confirmed by IR spectroscopic data and theoretical calculation results.

Bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato]terbium Double-Decker Single-Ion Magnets

For the purpose of further exploring the effect of nonperipherally attached substituents on single-ion magnet (SIMs) performance, tetrasubstituted bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato]terbium double-deckers, in both the reduced form TbH[Pc(α-OC₅H₁₁)₄]₂ (1) and the neutral form Tb[Pc(α-OC₅H₁₁)₄]₂ (2), were prepared. Single-crystal X-ray diffraction analysis for 2 unambiguously demonstrates the pinwheellike molecular structure with C₄ symmetry. Magnetic investigations of the two bis(phthalocyaninato)terbium double-deckers reveal their characteristic SIM nature. 2 exhibits SIM performance superior to that of 1, as revealed by the larger energy barrier of 466 K for the former species and 431 K for the latter species due to the presence of organic radical-f (radical-Tb) interactions. The enhanced SIM performance of 2 in comparison to 1 actually stems from the presence of radical-f interactions and an enhanced ligand field strength. The latter positive factor is indicated by the electrostatic potential around the terbium ion on the basis of density functional theory (DFT) calculations.

Fabricating Bis(phthalocyaninato) Terbium SIM into Tetrakis(phthalocyaninato) Terbium SMM with Enhanced Performance through Sodium Coordination

The non-peripherally substituted 1,4,8,11,15,18,22,25-octa(butoxy)-phthalocyanine-involved unsymmetrical heteroleptic bis(phthalocyaninato) terbium double-decker, Tb(Pc){H[Pc(α-OC₄ H₉ )₈ ]} (Pc=unsubstituted phthalocyanine) (1), was revealed to exhibit typical single ion magnet (SIM) behavior with effective energy barrier, 180 K (125 cm^-1 ), and blocking temperature, 2 K, due to the severe deviation of the terbium coordination polyhedron from square-antiprismatic geometry. Fabrication of this double-decker compound into the novel tetrakis(phthalocyaninato) terbium pseudo-quadruple-decker Na₂ {Tb(Pc)[Pc(α-OC₄ H₉ )₈ ]}₂ (2) single molecule magnet (SMM) not only optimizes the coordination polyhedron of terbium ion towards the square-antiprismatic geometry and intensifies the coordination field strength, but more importantly significantly enhances the molecular magnetic anisotropy in the unsymmetrical bis(phthalocyaninato) double-decker unit, along with the change of the counter cation from H⁺ of 1 to Na⁺ of 2, leading to an significantly enhanced magnetic behavior with spin-reversal energy barrier, 528 K (367 cm^-1 ), and blocking temperature, 25 K. The present result is surely helpful towards developing novel tetrapyrrole lanthanide SMMs through rational design and self-assembly from bis(tetrapyrrole) lanthanide single ion magnet (SIM) building block.

Chiral bis(phthalocyaninato) terbium double-decker compounds with enhanced single-ion magnetic behavior

Introducing chirality into bis(phthalocyaninato) terbium single-ion magnets was revealed to be an alternative method towards enhancing magnetic behavior.

Elucidation of Dual Magnetic Relaxation Processes in Dinuclear Dysprosium(III) Phthalocyaninato Triple-Decker Single-Molecule Magnets Depending on the Octacoordination Geometry

When applying single-molecule magnets (SMMs) to spintronic devices, control of the quantum tunneling of the magnetization (QTM) as well as a spin-lattice interactions are important. Attempts have been made to use not only coordination geometry but also magnetic interactions between SMMs as an exchange bias. In this manuscript, dinuclear dysprosium(III) (Dy^III ) SMMs with the same octacoordination geometry undergo dual magnetic relaxation processes at low temperature. In the dinuclear Dy^III phthalocyaninato (Pc^2- ) triple-decker type complex [(Pc)Dy(ooPc)Dy(Pc)] (1) (ooPc^2- =2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyaninato) with a square-antiprismatic (SAP) geometry, the ground state is divided by the Zeeman effect, and level intersection occurs when a magnetic field is applied. Due to the ground state properties of 1, since the Zeeman diagram where the levels intersect in an H_dc of 2500 Oe, two kinds of QTM and direct processes occur. However, dinuclear Dy^III -Pc systems with C₄ geometry, which have a twist angle (ϕ) of less than 45° do not undergo dual magnetic relaxation processes. From magnetic field and temperature dependences, the dual magnetic relaxation processes were clarified.

Molecular Orientation of a Terbium(III)-Phthalocyaninato Double-Decker Complex for Effective Suppression of Quantum Tunneling of the Magnetization

Single-molecule magnet (SMM) properties of crystals of a terbium(III)-phthalocyaninato double-decker complex with different molecular packings (1: TbPc₂, 2: TbPc₂·CH₂Cl₂) were studied to elucidate the relationship between the molecular packing and SMM properties. From single crystal X-ray analyses, the high symmetry of the coordination environment of 2 suggested that the SMM properties were improved. Furthermore, the shorter intermolecular Tb–Tb distance and relative collinear alignment of the magnetic dipole in 2 indicated that the magnetic dipole–dipole interactions were stronger than those in 1. This was confirmed by using direct current magnetic measurements. From alternating current magnetic measurements, the activation energy for spin reversal for 1 and 2 were similar. However, the relaxation time for 2 is three orders of magnitude slower than that for 1 in the low-T region due to effective suppression of the quantum tunneling of the magnetization. These results suggest that the SMM properties of TbPc₂ highly depend on the molecular packing.

Sandwich rare earth complexes simultaneously involving aromatic phthalocyanine and antiaromatic hemiporphyrazine ligands showing a predominantly aromatic nature

Two mixed (phthalocyaninato)(hemiporphyrazinato) and two homoleptic bis(hemiporphyrazinato) rare earth double-decker complexes have been synthesized and structurally characterized. The EPR and NMR results clarified the protonated nature of these sandwich double-deckers. Spectroscopic and theoretical calculation results clearly reveal the predominantly aromatic nature of the mixed ring sandwich double-deckers.

Novel bis(phthalocyaninato) rare earth complexes with the bulky and strong electron-donating dibutylamino groups: synthesis, spectroscopy, and SMM properties

Dibutylamino groups were incorporated onto the bis(phthalocyaninato) terbium, leading to excellent SIM performance.

Weak DyIII-DyIII Interactions in DyIII-Phthalocyaninato Multiple-Decker Single-Molecule Magnets Effectively Suppress Magnetic Relaxation

The Dy^III quintuple-decker complex DyCdCdDy and hetero quadruple-decker complex DyCdY were synthesized, and their magnetic properties were compared with those of the quadruple-decker complex DyCdDy. Single-crystal X-ray analysis revealed that the coordination geometries around the Dy^III ions of DyCdCdDy, DyCdY, and DyCdDy were similar. dc (direct current) magnetic measurements indicated that DyCdCdDy had very weak ferromagnetic Dy^III-Dy^III interactions but DyCdY did not. From a comparison of the magnetic relaxation times (τ) of the three complexes, the τ values of DyCdCdDy and DyCdDy, which have weak Dy^III-Dy^III interactions, are longer than that of DyCdY. In other words, weak Dy^III-Dy^III interactions effectively suppress magnetic relaxation.

Symmetry of octa-coordination environment has a substantial influence on dinuclear TbIII triple-decker single-molecule magnets

This work shows that the SMM properties can be fine-tuned by introducing different octa-coordination geometries while maintaining the same Tb^III–Tb^III distances.

Single-molecule magnet (SMM) properties of terbium(iii)-phthalocyaninato and porphyrinato mixed ligand triple-decker complexes, [(TTP)Tb(Pc)Tb(TTP)] (1) and [(Pc)Tb(Pc)Tb(TTP)] type (2), were studied and were compared with those of the Tb^III homoleptic triple-decker complex [(obPc)Tb(obPc)Tb(obPc)] (3) in order to elucidate the relationship between octa-coordination environments and SMM properties (Tb^III = terbium(iii), TTP^2– = tetraphenylporphyrinato, Pc^2– = phthalocyaninato, obPc^2– = 2,3,9,10,16,17,23,24-octabutoxyphthalocyaninato). By combining TTP^2– and Pc^2– with Tb^III ions, it is possible to make three octa-coordination environments: SP–SP, SAP–SP and SAP–SAP sites, where SAP is square-antiprismatic and SP is square-prismatic. The direction and magnitude of the ligand field (LF) strongly affect the magnetic properties. Complexes 2 and 3, which have SAP–SAP sites, undergo dual magnetic relaxation processes in the low temperature region in a direct current magnetic field. On the other hand, 1, which has an SP–SP environment, undergoes a single magnetic relaxation process, indicating that the octa-coordination environments strongly influence the SMM properties. The SMM behaviour of dinuclear Tb^III SMMs 1–3 were explained by using X-ray crystallography and static and dynamic susceptibility measurements. This work shows that the SMM properties can be fine-tuned by introducing different octa-coordination geometries with the same Tb^III–Tb^III distances.

Modulating single-molecule magnet behaviour of phenoxo-O bridged lanthanide(iii) dinuclear complexes by using different β-diketonate coligands

Three Dy₂ complexes with similar crystal structure have been synthesized. Magnetic studies reveal that they exhibit different magnetic relaxation behaviors, originating from the different chemical environments of the center Dy³⁺ ions with different β-diketonate coligands.

Towards Clarifying the Role of O2 during the Phthalocyanine Synthesis

The role of O2 within the synthesis of phthalocyanines (Pcs) has remained unclear in the past century. Here, we demonstrate that O2 , in cooperation with the solvent n-pentanol, participates in the cyclic tetramerization of phthalonitriles over the half-sandwich complex template [Lu(Pc)(acac)] (acac=acetylacetonate) and terminates the reaction at the stage of uncyclized isoindole oligomeric derivatives rather than the phthalocyanine chromophores, resulting in the isolation of the heteroleptic (phthalocyaninato)(triisoindole-1-one) lutetium double-decker complexes [(Pc)Lu(TIO-I)] (TIO-I=3,4,7,8,11,12-sexi(2,6-diisopropylphenoxy)-15-[4,5-di(2,6-diisopropylphenoxy)-2-cyanobenzimidamido]triisoindole-1-one) and [(Pc)Lu(TIO-II)] (TIO-II=3,4,7,8,11,12-sexi(2,6-dimethylphenoxy)-15-[4,5-di(2,6-dimethylphenoxy)-2-cyanobenzimidamido]triisoindole-1-one) with the help of bulky substituents at the phthalonitrile periphery and an unsubstituted phthalocyanine ligand in the double-decker skeleton. Nevertheless, the cyclic tetramerization of the phthalonitriles was revealed to be sensitive to O2 with the reaction progression also depending on the oxygen concentration/content, leading to the O2 -senstive and -dependent nature for the isolation of phthalocyanine derivatives.

Effects of f-f interactions on the single-molecule magnet properties of terbium(III)-phthalocyaninato quintuple-decker complexes

Single-molecule magnet (SMM) properties of terbium(III)-phthalocyaninato quintuple-decker complex TbCdCdTb were studied and were compared with those of other multiple-decker complexes (triple-decker: TbTb, quadruple-decker: TbCdTb) to elucidate the relationship between magnetic dipole interactions and SMM properties. From X-ray crystallography performed with synchrotron radiation, the Tb(III)-Tb(III) distance in TbCdCdTb was determined to be 9.883 Å. From alternating current magnetic studies on TbCdCdTb, the activation energy for spin reversal (Δ) increased with an increase in the direct current magnetic field (Hdc). This behavior is similar to that of TbCdTb, although the increase in Δ for TbCdTb is smaller. On the other hand, for TbTb, which has shortest Tb(III)-Tb(III) distance, Δ did not depend on Hdc, indicating that there is a correlation between SMM properties and the strength of the Tb(III)-Tb(III) interactions. By comparing the Zeeman diagrams for multiple-decker complexes, we found that the Tb(III)-Tb(III) interactions affected the magnetic field regions where quantum tunnelling of the magnetization was active. The results obtained from Zeeman diagrams are consistent with the results obtained from the magnetic studies.

Peripheral substitution: an easy way to tuning the magnetic behavior of tetrakis(phthalocyaninato) dysprosium(III) SMMs

Two tetrakis(phthalocyaninato) dysprosium(III)-cadmium(II) single-molecule magnets (SMMs) with different extent of phthalocyanine peripheral substitution and therefore different coordination geometry for the Dy ions were revealed to exhibit different SMM behavior, providing an easy way to tuning and controlling the molecular structure and in turn the magnetic properties of tetrakis(tetrapyrrole) lanthanide SMMs through simple tetrapyrrole peripheral substitution.

Syntheses, structures, and magnetic properties of homodinuclear lanthanide complexes based on dinucleating Schiff base ligands

Two series of homodinuclear lanthanide(iii) complexes were synthesized and characterized. Magnetic studies reveal the weakly antiferromagnetic coupling between paramagnetic Ln ions and enhanced relaxation of magnetization for Dy₂ complexes.

The first synthesis of sandwich-type complex based on tetradiazepinoporphyrazine ligand

Sandwich-type complex based on tetradiazepinoporphyrazine ligand — bis{tetrakis(5,7-di(4-tert-butylphenyl)-6H-1,4-diazepino)[2,3-b,g,l,q]porphyrazinato}lutetium — was synthesized for the first time. The structure of the compound has been confirmed by UV-vis/NIR, 1 H NMR spectroscopy, and MALDI-TOF mass spectrometry data. The introduction of annulated diazepine heterocycles to porphyrazine molecule significantly changes macrocycle reactivity and results in sandwich-type complex under conditions used for the selective synthesis of lanthanide(III) monophthalocyanines.

Mixed (phthalocyaninato)(Schiff-base) di-dysprosium sandwich complexes. Effect of magnetic coupling on the SMM behavior

Reaction between Schiff-base ligand and half-sandwich complex M(Pc)(acac) led to the isolation of new sandwich-type mixed (phthalocyaninato)(Schiff-base) di-lanthanide compounds M2(Pc)2(L)H2O (M = Dy, Gd) (1, 2) [H2Pc = metal free phthalocyanine, Hacac = acetylacetone, H2L = N,N'-bis(3-methyloxysalicylidene)benzene-1,2-diamine] with the triple-decker molecular structure clearly revealed by single crystal X-ray diffraction analysis. For the comparative studies, sandwich triple-decker analogues with pure Schiff-base ligand M2(L)3H2O (M = Dy, Gd) (3, 4) were also prepared. Dynamic magnetic measurement result reveals the single-molecule magnet (SMM) nature of the di-dysprosium derivative 1, while the static magnetic investigation over both pure and the diamagnetic diluted samples of this compound discloses the interionic ferromagnetic coupling between the two dysprosium ions, which in turn effectively suppresses the QTM and enhances the energy barrier of this SMM. Nevertheless, comparative studies over the static magnetic properties of the di-dysprosium triple-decker complexes 1 and 3 indicate the stronger magnetic coupling between the two lanthanide ions in mixed (phthalocyaninato)(Schiff-base) species than in the pure Schiff-base triple-decker analogue, suggesting the special coordination sphere around the dysprosium ions in the former compound over the latter one on the more intense inter-ionic ferromagnetic coupling. As a very small step towards understanding the structure-property relationship, the present result will be surely helpful for the design and synthesis of the multinuclear lanthanide-based SMMs with good properties.

Binuclear phthalocyanine-based sandwich-type rare earth complexes: unprecedented two π-bridged biradical-metal integrated SMMs

Mini-magnets: Sandwich-type rare earth complexes involving two fused bis(phthalocyaninato) dysprosium(III) units, represent the first example of biradical-metal single molecule magnets (SMMs). These materials were synthesized and structurally characterized. Comparative investigation reveals the effective suppression of quantum tunneling of magnetization (QTM) by the π-bridged biradical-based antiferromagnetic interaction in the di-dysprosium-ion-based SMM.

Syntheses, structures, and magnetic properties of seven-coordinate lanthanide porphyrinate or phthalocyaninate complexes with Kläui's tripodal ligand

A series of seven-coordinate mononuclear lanthanide(III) complexes of the general formula [(TPP)Ln(L(OEt))]·0.25H2O and [(Pc)Ln(L(OEt))] (Ln(3+) = Dy(3+), Tb(3+), Ho(3+), and Gd(3+); TPP = 5,10,15,20-tetraphenylporphyrinate; Pc = phthalocyaninate; L(OEt)(-) = [(η(5)-C5H5)Co(P(=O)(OEt)2)3](-)) are synthesized on the basis of the tripodal ligand L(OEt)(-) and either porphyrin or phthalocyanine ligands. All of the complexes are characterized by X-ray crystallography and by static and dynamic magnetic measurements. The Dy and Tb complexes show the field-induced slow relaxation of magnetization, and they are interesting seven-coordinate single-lanthanide-based SMMs. The magnetic relaxation properties of these double-decker sandwich complexes are influenced by the local molecular symmetry and are sensitive to subtle distortions of the coordination geometry of the paramagnetic lanthanide ions, such as metal-to-plane distances, plane center distances, and bending angles.