Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 7-Day Trial for You or Your Team.

Learn More →

An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes

An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes ARTICLE Received 15 Jul 2013 | Accepted 4 Sep 2013 | Published 7 Oct 2013 DOI: 10.1038/ncomms3551 An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes 1 1 1 1 2 Nicholas F. Chilton , David Collison , Eric J.L. McInnes , Richard E.P. Winpenny & Alessandro Soncini Understanding the anisotropic electronic structure of lanthanide complexes is important in areas as diverse as magnetic resonance imaging, luminescent cell labelling and quantum computing. Here we present an intuitive strategy based on a simple electrostatic method, capable of predicting the magnetic anisotropy of dysprosium(III) complexes, even in low symmetry. The strategy relies only on knowing the X-ray structure of the complex and the well-established observation that, in the absence of high symmetry, the ground state of dysprosium(III) is a doublet quantized along the anisotropy axis with an angular momentum quantum number m ¼ / . The magnetic anisotropy axis of 14 low-symmetry mono- J 2 metallic dysprosium(III) complexes computed via high-level ab initio calculations are very well reproduced by our electrostatic model. Furthermore, we show that the magnetic anisotropy is equally well predicted in a selection of low-symmetry polymetallic complexes. 1 2 School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M19 3PL, UK. School of Chemistry, University of Melbourne, Parkville, Victoria 3010, Australia. Correspondence and requests for materials should be addressed to N.F.C. (email: [email protected]) or to A.S. (email: [email protected]). NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 1 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 III he fascinating magnetic properties of the lanthanides have complexes, the ground Kramers doublet of Dy is strongly continued to be a highly topical and strongly multi- axial with the principal values of the g-tensor approaching those 15 6 Tdisciplinary research area for over 60 years. Such is the of the m ¼ / levels of the atomic multiplet H J 2 15/2 diversity of this field that their application reaches from magnetic (g ¼ g ¼ 0, g ¼ 20). This empirical observation suggests that a x y z 1,2 resonance imaging and cell labelling , to potential building simple, but appropriate, variational ansatz for the many-electron blocks of quantum computers . The pursuit of such applications ground state wavefunction of these low-symmetry complexes relies on detailed knowledge of the magnetic anisotropy, which, consists of the atomic functions w (a,b) corresponding to the 15 6 while being completely defined in cases of high symmetry, m ¼ / states of the multiplet H . The variational J 2 15/2 is difficult to elucidate in low-symmetry complexes. Much parameters to be optimized in w (a,b) consist of the two polar recent work, where 4f complexes have shown slow magnetic angles a and b, which specify the orientation of the quantization 4–7 relaxation and unprecedented non-collinear magnetic textures axis with respect to the low-symmetry crystal field V defined by CF 8–10 at the single-molecule level , also depends on understanding the ligands. To determine these angles, and hence the full g-tensor III the orientation of the magnetic anisotropy. Of all the lanthanide of the ground Kramers doublet of the Dy complex, we can use III ions, it is Dy that continues to prove the most interesting, the variational principle and minimize the energy E ða; bÞ¼ 15=2 providing unexpected examples of new magnetic phenomena, byhi w ða; bÞj V j w ða; bÞ with respect to all possible CF virtue of its unique magnetic anisotropy . However, because of orientations (a,b) of the quantization axis. the intricate electronic structure of lanthanide complexes, simple This proposed strategy is readily mapped onto a classical models that can predict magnetic anisotropy in molecular solids electrostatic energy minimization problem. Following the work of of low symmetry are still missing. Sievers , the many-electron wavefunctions w (a,b) can be ðÞ a;b The single-ion properties of 4f metal ions, whether in mono- or described by an electron density distribution r ðÞ y; f , where 15=2 polymetallic complexes, are difficult to elucidate owing to the y and f are polar angles defined in the reference frame of V , CF shielded nature of the 4f orbitals giving rise to weak interactions expressing the angular dependence of the axially symmetric with the surrounding environment. Recent advances in post aspherical electron density. This aspherical f-electron density can Hartree-Fock multi-configurational ab initio methodology have be written as a linear combination of three spherical harmonics made accurate quantum chemical calculations on paramagnetic 4f Y (y,f), Y (y,f) and Y (y,f), where the coefficients of each 2,0 4,0 6,0 compounds possible . The Complete Active Space Self Consistent are fully determined by angular momentum coupling and average Field (CASSCF) method can accurately predict the magnetic atomic radial multipole moments . In the particular case of ðÞ a;b 13,14 III properties of lanthanide complexes , and calculations of this Dy , r ðÞ y; f can be approximated by an oblate spheroid 15=2 type have become an indispensable tool for the explanation of distribution owing to the dominant contribution of the 6,15–17 22,21 increasingly interesting magnetic phenomena .These quadrupolar term Y (y,f) to the expansion . 2,0 calculations are especially useful in cases of low symmetry, where As the crystal field is a one-electron potential, the many- previous methods have provided intractable, over parameterized electron variational integral E (a,b) can be exactly recast into 15/2 18,19 problems . Although CASSCF ab initio calculations are a simple electrostatic energy integral, describing the interaction extremely versatile and implicitly include all effects required to between the electric potential generated by the crystal field ðÞ a;b elucidate the magnetic properties, the results offer little in the way V (y,j) and the Sievers charge density r ðÞ y; f associated CF 15=2 III of chemically intuitive explanations and to obtain reliable results with the f-electrons in the central Dy ion (equation (1)). requires considerable intervention by expert theorists equipped with p 2p Z Z access to powerful computational resources. ðÞ a;b E 15ðÞ a; b ¼ V ðÞ y; j r ðÞ y; f sinðÞ y dydj ð1Þ CF Recently, some of us have applied a simple electrostatic model 15=2 to rationalize the unexpected direction of the calculated magnetic y¼0 j¼0 anisotropy in two related sets of monometallic 4f complexes . III Thus, we arrive at the hypothesis that in low-symmetry Dy This was based on the aspherical electron density distributions of complexes, the many-electron ground state wavefunction and, the lanthanide ions, pioneered by Sievers , and the design hence, the orientation of the magnetic anisotropy axis, can be principles for the exploitation of f-element anisotropy outlined by determined simply by solving a classical electrostatic energy Rinehart and Long . Other groups have also been coming to minimization problem. similar conclusions . Although the use of crystal field methods to 23–25 model anisotropic magnetic data is widespread , models for the prediction of magnetic anisotropy in low symmetry are Constructing the crystal field potential of charged ligands.To 26,27 few . These methods are based on the diagonalization of a use this hypothesis, we must determine the explicit form of crystal field Hamiltonian, which, especially in cases of low V (y,j) appearing in equation (1), by using an appropriate CF symmetry, requires a large number of parameters that often can model for the charge distribution on the ligands. This may appear only be reliably determined by fitting experimental data. Such an a difficult problem; here, we use a simple model for charged III approach can obscure the rationalization of magnetic anisotropy ligands that are common in many low-symmetry Dy com- and its predictive power is uncertain. plexes. The charge on the ligands is expected to have a dominant Here we report a quantitative method based on a straightfor- role in the determination of the electrostatic potential experienced III ward electrostatic energy minimization for the prediction of the by Dy , and thus, we can calculate the electrostatic field pro- orientation of the ground state magnetic anisotropy axis of duced by charge on the ligands within a minimal valence bond dysprosium(III) ions, which does not rely on the fitting of (VB) model. Within this model, the charge is delocalized as a experimental data, requiring only the determination of an X-ray resonance hybrid that can be seen as a weighted sum of all crystal structure. ‘chemically stable’ Lewis structures (Fig. 1); this is a representa- tion of the leading contribution to the full VB wavefunction. By taking the sum of the partial charges accumulated by each atom Results in the VB resonance hybrid, q , we arrive at a very simple frac- Many electron wavefunction and electrostatic minimization. tional charge distribution for the ligand, where, typically, very few An increasing number of ab initio CASSCF calcula- atoms will accommodate a charge and most will remain neutral. 6,14,15,20,28 tions have shown that in most low-symmetry Our strategy is to construct the crystal field potential solely from 2 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE H H H 2 1 1 1 1 1 – / – / + / + / + / – / 2 5 5 5 3 C N C CH HC C C C paaH* NO Na NH HC O O O O 1 1 C 2 N O 1 1 2 1 – / – / – / + / + / 3 3 – / – / 3 5 5 3 2 1 H – / 1 – / N O Na – Na DOTA Na O N – / 1 H 1 – 1 2 – / 1 – / 2 acac : R ,R = CH 2 1 3 R R 3 – / 2 – 1 2 O N tfpb : R = CF3, R = Ph C C – 1 2 tta : R = CF , R = 2-thienyl O O – 1 2 O hfac : R ,R = CF – / – / 3 – / Br Ph 1 1 – / – / C –1 5 5 Ph Si S Ph SiS HCC MeCp – / Ph HC CH NH O 1 1 – / – / 5 5 –1 –1 3– teabmpH O 3 –1 N HN 2– Br teaH –1 –1 i – PrO N Pr HO O –1 Br Figure 1 | Partial charges assigned to the formally charged ligands in complexes 1–17. The zwitterionic N-(2-pyridyl)-acetylacetamide (paaH*) has two formal charges owing to the deprotonation of the a-carbon and protonation of the pyridyl nitrogen. Each pendant carboxylate arm of the macrocyclic 0 00 000 trisodium 1,4,7,10-tetraazacyclododecane N,N ,N ,N -tetraacetate ligand (Na DOTA ) has a single negative charge that is delocalized evenly over the two oxygen atoms; three of the four acetate arms bind sodium cations, which each have a single positive charge. The aromatic anion of methylcyclopentadienyl (MeCp ) has a single negative charge that is delocalized evenly over the five cyclic carbon atoms. Not shown: Compounds 12 and 2 þ 2 13 contain Zn ions, which have formal charges of positive two in our model. Compound 17 contains a central oxide (O ) ligand, which has a formal charge of negative two in our model. the fractional charges determined by the VB resonance hybrid, determination of magnetic anisotropy in cases of low excluding neutral atoms entirely (see Fig. 1 illustrating the frac- symmetry. In high symmetry, the orientation of the ground tional charges of the resonance hybrids for the ligands of interest Kramers doublet is pre-determined; note that in this case if ðÞ a;b here). The partitioning of the charge without any need for V (y,j) does not stabilize the r ðÞ y; f electron density CF 15=2 computation illustrates the elegance of our model. along the symmetry axis, then m ¼ / will not be the J 2 Once the partitioning of the charge over the ligand is ground state. There is no such restriction in low-symmetry determined, the resulting partial charges are arranged around environments. III the central Dy ion using the known X-ray crystal structure of the complex, allowing the electrostatic potential to be easily Monometallic complexes. The energy spectra and g-tensors of calculated using crystal field theory (equation (2), where the ground H multiplets for compounds 1–14, as calculated th 15/2 (R ,y ,j ) are the spherical coordinates of the n charged atom, n n n ab initio, are given in Supplementary Tables S1–S18. Table 1 see Methods section). presents, for each complex, the principal value of the diagonal g- k m tensor of the ground Kramers doublet (g ) and the electrostatic X X 4pð 1Þ deviation angle, defined as the angle between the electrostatic V ðÞ y; j ¼ hr iY ðÞ y; j CF k;m 2k þ 1 anisotropy axis and the ab initio anisotropy axis along which g is k¼2;4;6 m¼ k z ð2Þ defined. q Y ðy ; j Þ n k;m n We note that the anisotropy axis is accurately predicted by k þ 1 employing this minimal VB model, without taking into account different electron withdrawing or donating groups in the charged Minimization of the electrostatic energy in equation (1) in ligands, for example, hfac will have less electron density at the conjunction with this minimal VB model yields an orientation oxygen donor atoms compared with acac because of the of the anisotropy axis, which compares remarkably well electron withdrawing nature of the CF groups in the former with that obtained via rigorous ab initio calculations ligand. (Table 1). To exemplify this correlation, we have calculated the magnetic properties of 14 low-symmetry monometallic dysprosium(III) complexes using the CASSCF ab initio Polymetallic complexes. Calculating the ab initio properties of methodology (see Methods) and compare them directly with the following polymetallic complexes is extremely computation- our electrostatic model. In this work, we focus on the ally expensive. Hence, to demonstrate the power of our simple NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 3 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 III Table 1 | Comparison of ab initio and electrostatic calculations for Dy complexes. Compound g Electrostatic deviation () Reference 1 [Dy(acac) (H O) ] 19.62 10.9 3 2 2 2 [Dy(acac) (phen)] 19.55 10.0 3 [Dy(acac) (dpq)] 19.42 2.9 4 [Dy(acac) (dppz)] 19.57 6.1 5 [Dy(tfpb) (dppz)] 19.48 9.0 6 [Dy(tta) (bipy)] 19.76 12.4 7 [Dy(tta) (phen)] 19.66 8.0 8 [Dy(tta) (pinene-bipy)] 19.81 6.9 9 [Dy(hfac) (dme)] 19.65 11.0 3 þ 20 10 [Dy(paaH*) (H O) ] 19.78 2.4 2 2 4 1 þ 20 11 [Dy(paaH*) (NO ) (MeOH)] 19.68 7.4 2 3 2 1 þ 7 12 [DyZn (teabmpH ) (MeOH)] 19.98 6.6 2 3 2 1 þ 7 13 [DyZn (teabmpH ) ] 19.90 8.0 2 3 2 2 þ z y 14,37 14 [Dy(DOTA)(H O)Na ] 19.46 14.8 2 3 bipy, 2,2 -bipyridine; dme, dimethoxyethane; dpq, dipyridoquinoxaline; dppz, dipyridophenazine; pinene-bipy, 4,5-pinene bipyridine; phen, 1,10-phenanthroline. Angle between anisotropy axis calculated by ab initio and electrostatic methods. Average g value over four calculations, see Supplementary Tables S14–S18. Angles between the experimentally determined and the ab initio and electrostatic anisotropy axes are 3.9 and 12.1, respectively. approach, we have performed a semi-quantitative comparison interact strongly with the two basal oxygen atoms. If, however, between the electrostatic calculations and published ab initio the quantization axis was parallel with the base and top of the results for three compounds: [Dy(MeCp) (Ph SiS)] 15 (ref. 28) trapezium, there would be less interaction with the negative 2 3 2 [Dy (teaH) (NO ) ] 16 (refs 30,31) and [Dy O( PrO) ] 17 charges thus stabilizing the orientation. This is the orientation of 6 6 3 6 5 13 (refs 32,33). The methodology for the calculation of the the anisotropy axis (Fig. 2c and Supplementary Fig. S9) calculated electrostatic anisotropy axes in polymetallic complexes is by our electrostatic model and it provides a simple explanation identical to that of monometallic complexes and is performed for the ab initio results. Analogous arguments can be made for III III for each Dy ion independently. The Dy ions that are not the compound 11 where the b-diketonate oxygen donors are in a focus of the calculation are treated as part of the ligand and are similar trapezium-shaped arrangement, however, the coordina- given a þ 3 charge. The charged ligands in complexes 15–17 are tion environment now contains two chelating nitrate anions. The given in Fig. 1, which describes the charge partitioning based on oxygen atoms in NO have a larger negative partial charge than the minimal VB model. those in the b-diketonates, but this is offset by the positive charge on the nitrogen atom, which has an attractive effect on the electron density. Therefore, more-or-less the same anisotropy axis Discussion as in compound 10 is observed for compound 11, along the The form of the potential (equation (2)) contains terms of for diketonate-diketonate vector (Supplementary Fig. S10). k þ 1 each charged atom in the ligand, which implies that the closer to Compounds 1–10 have distorted square anti-prismatic geo- III the Dy ion and larger the magnitude of the charge, the greater metries and the calculated anisotropy axis of the ground state is its effect on the orientation of the anisotropy axis. Complexes 1–9 not found to be coincident with the pseudo-fourfold axis. This contain three b-diketonate ligands in a ‘paddle-wheel’-like observation, shown here to be due to simple electrostatic arrangement, with two b-diketonate ligands trans- to each other arguments, is contrary to many reports in the literature that and the third trans- to a neutral ligand (Fig. 2a). If the employ a fourfold axial interpretation to model the magnetic data ðÞ a;b quantization axis of the r ðÞ y; f electron density was along (refs 25,34–36). Clearly, in these cases, the electrostatics are more 15=2 the ‘paddle-wheel’ axis, then the radial plane of the approximately important than pseudo-symmetry. ‘oblate’ density would be coincident with all three charged Compounds 12 and 13, chosen as a departure from b- ligands, representing a high-energy orientation. Therefore, the diketonate-based complexes in addition to their very interesting anisotropy axis is perpendicular to the ‘paddle-wheel’ axis, and we magnetic properties, are intimately related and can be inter- find that it passes through the two trans-b-diketonate ligands. converted reversibly by drying or soaking in methanol, via a single The radial plane of the oblate electron density is thus coincident crystal to single crystal transformation . The difference between with only one charged ligand as opposed to two (Fig. 2b and the dysprosium(III) coordination environments is the removal of Supplementary Figs S1–S8). a terminal methanol molecule, changing the local symmetry from For compound 10, the negatively charged oxygen atoms of the a distorted pentagonal bipyramid to a distorted octahedron. III III two b-diketonate ligands are the closest to Dy and therefore Considering the local Dy coordination environment, a pair of have the greatest effect on the orientation of the anisotropy axis. trans- phenoxo oxygen atoms in both 12 and 13 have much These four atoms are roughly coplanar with the dysprosium(III) shorter Dy–O bond lengths than all others, at 2.21(2) Å compared ion and are arranged in a trapezium (Fig. 2c). The oblate electron with 2.39(2) Å for 12 and 2.186(4) Å compared with 2.3(1) Å for ðÞ a;b density r ðÞ y; f will be in a high-energy configuration when 13, thus defining both geometries as axially compressed. In both 15=2 the quantization axis is normal to this plane of four negative cases, the three metal atoms are roughly coplanar with the charges, and therefore the minimum electrostatic energy and equatorial planes of the coordination polyhedra. The close oxygen anisotropy axis will lie in the plane of the b-diketonate oxygen atoms define an axially repulsive potential for dysprosium(III), III 2 þ atoms. The Dy ion is much closer to the base of the trapezium which, coupled with the attractive nature of the Zn cations in and therefore if the quantization axis was to bisect the two the equatorial plane, explains the observed magnetic anisotropy parallel edges, then the radial plane of the electron density would axes (Supplementary Figs S11 and S12). 4 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. H H H C N C CH HC C C C HC NH OO NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE a c 1 2 R C R C C O O 1 1 R R C O O C Dy HC CH C O O C 2 2 R R E E 2.765 2.752 2.766 Dy 4.308 Figure 2 | Magnetic anisotropy and electrostatic potential of b-diketonate species. (a) Idealized ‘paddle-wheel’ geometry of complexes 1–9 viewed down the ‘paddle-wheel axis’. (b) Comparison of the ab initio (blue rod) and electrostatic (green rod) anisotropy axes for the ground Kramers doublet in 1, ðÞ a;b with the form of the oblate r ðÞ y; f f-electron density using the representation of Sievers , magnified approximately  5 for clarity; Dy ¼ green, 15=2 O ¼ red, C ¼ grey and H ¼ white. (c) Idealized electrostatic potential generated by a pair of paaH* ligands in the trapezium-shaped coordination environment present in the bis-b-diketonate-dysprosium(III) plane of compounds 10 and 11 and the resultant anisotropy axis (green line); red ¼ positive potential, blue ¼ negative potential. (°) b 90 90  (°) –200 –400 ðÞ a;b Figure 3 | Orthogonal configurations for the magnetic anisotropy axis in compound 14. The form of the oblate r ðÞ y; f f-electron density, visualized 15=2 in the central structural diagrams, follows the representation of Sievers , and has been magnified approximately  5 for clarity; Dy ¼ green, Na ¼ yellow, O ¼ red, N ¼ blue, C ¼ grey and H ¼ white. The rods in the central structural diagrams represent the magnetic anisotropy axes, identified by various methods: green ¼ electrostatic calculation, dark blue ¼ ab initio calculation (this work), light blue ¼ ab initio calculation and pink ¼ experimentally determined. The energies of each configuration have been calculated using our electrostatic approach. The electrostatic energy surface is calculated by considering all possible orientations (a,b) of the anisotropy axis in the potential generated by the charged ligands of compound 14. The electrostatic energy ðÞ a;b surface shows double degeneracy of the minimum, maximum and saddle points due to the axial symmetry of the r ðÞ y; f electron density. 15=2 2 þ In [Dy(DOTA)(H O)Na ] 14, for which the magnetic configuration (Fig. 3a). Therefore, the anisotropy axis is 2 3 anisotropy axis has been determined experimentally, the perpendicular to the pseudo-tetragonal axis of the molecule. 4  þ dysprosium(III) ion is encapsulated by the macrocyclic DOTA The radial plane of the ‘oblate’ density is attracted by two Na ligand (ref. 37). The H atoms of the apical water molecule were ions more strongly than just a single Na ion (Fig. 3b), thus not found experimentally, so were placed in calculated positions determining the observed orientation of the anisotropy axis based on crystallographically characterized water molecules (Fig. 3c), which agrees well with the experimentally determined III bound to Ln ions (ref. 20). If the anisotropy axis was and ab initio axes (Table 1). We have rotated the apical water coincident with the pseudo-tetragonal axis, the radial plane of molecule in the ab initio calculations and found no dependence the oblate electron density would have a large interaction with the on the orientation of the ground state anisotropy axis to this four negatively charged acetate groups, yielding a high-energy perturbation, contrary to ref. 14. NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 5 & 2013 Macmillan Publishers Limited. All rights reserved. H H N CH C C HC C C C HC NH OO –1 Energy (cm ) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 Compound 15 contains two dysprosium(III) ions bridged by presented, we propose that this model can be used to aid in the two anionic Ph SiS ligands and each capped by two classical rational design of molecular architectures displaying novel organometallic ligands, MeCp (ref. 28). The two ions are magnetic properties, exploiting and stabilizing the strong axiality related by inversion symmetry and therefore possess the same of the ground state of low-symmetry dysprosium(III), through single-ion electronic structure. The electrostatic potential at each the use of formally charged ligands. The simplicity of the proposal paramagnetic ion is dominated by the two MeCp ligands, is so profound that the model resonates strongly with the III which are closer to the Dy ion than the sulfur atoms at conclusions drawn in the 1950s and 1960s that the bonding of the 2.65(3) Å (average Dy–C distance) compared with 2.76(2) Å. This lanthanides is almost purely ionic (refs 38,39). leads to the anisotropy axis of the ground state lying By entirely neglecting the influence of neutral ligands in our perpendicular to the Dy-S-S-Dy plane (Supplementary model, we have shown the dominant nature of charged ligands in Fig. S13), in good agreement with ab initio calculations (ref. 28). the determination of the magnetic anisotropy of dysprosium(III) The hexametallic dysprosium(III) wheel (16) contains highly complexes. Compounds lacking any charged ligands are rare, but anisotropic paramagnetic centres, yet due to crystallographic S would likely show magnetic anisotropies that are much more symmetry, possesses a diamagnetic ground state with a toroidal sensitive to the type of ligands present, with contributions due to III 2 moment. Each Dy ion is encapsulated by the teaH ligand dipoles and higher order multipoles as well as the spatial extent of and also has one chelating nitrate anion . Applying our ligand electron density becoming important. The minimal VB electrostatic model to this compound yields the anisotropy axis model for the partitioning of charges on ligands works well for of each dysprosium(III) site in excellent agreement with the ab the formally charged ligands presented here. Other more general initio results (Supplementary Fig. S14) . The anisotropy axis for schemes for the partitioning of atomic charges over the ligands III each Dy ion is canted around the ring in an alternating up/ are also being investigated, which may offer an improvement over down manner, which, due to the S symmetry of the molecule, the minimal VB model. causes the net cancellation of the out-of-plane magnetization in We are also extending the method to other lanthanide ions, 31 8 the ground state , leading to a toroidal moment , similar to that examining whether this approach can work for other oblate ions 9,10 III observed in a Dy triangle . It is remarkable that such a simple (for example, Tb ) and whether the reverse electrostatic principles III electrostatic approach can rationalize such complex physics. will apply to prolate ions (for example, Er ). Although the Compound 17, with one of the highest energy barriers to the treatment presented here cannot be rigorously applied to non- III reversal of the ground state magnetization, contains five Kramers ions in low-symmetry environments, Tb complexes that III dysprosium(III) ions arranged in a pyramid, with each Dy possess a pseudo-doublet ground state with m ¼ 6(g ¼ g ¼ 0, J x y ion at the centre of an axially compressed octahedron. The g ¼ 18) should follow similar electrostatic arguments to those equatorial plane of each ion is formed by four bridging discussed here for the determination of the magnetic anisotropy. isopropoxide ( PrO ) ligands and the axial positions are Conversely, preliminary results suggest that the ground state III occupied by the single m -oxide bridge at the centre of the wavefunctions of Er ions in low-symmetry environments are not molecule and a terminal isopropoxide ligand . The oxygen atom well defined and consist of strongly mixed m states, precluding the i  III of the terminal PrO ligand is substantially closer to the Dy application of the treatment presented here. ion than all other donor atoms, at 2.04(1) Å compared with The work presented here is an advance not only for the chemistry 2.35(8) Å, and the central m oxide has a double negative charge. and physics communities involved with molecular magnetism, but 5- These two features define a strongly repulsive axial potential for also for all areas concerned with the magnetic and spectroscopic ðÞ a;b the r ðÞ y; f electron density, where the energy is minimized properties of the lanthanides. Specifically, this work provides some 15=2 when the quantization axis is coincident with this direction much-needed insight into the complex and continually intriguing (Fig. 4). The presence of the other charged ligands and the magnetic properties of dysprosium(III). High-level quantum trivalent dysprosium ions is a small perturbation in this case, chemical calculations such as CASSCF are computationally because of the strongly directional nature of the almost linear expensive and require intervention by experts to produce reliable i  2 PrO -Dy-O axis. The results obtained using our electrostatic results. The complementary approach we outline here is available to model compare extremely well with those obtained using ab initio any chemist with minimal computational requirements. calculations (see Supplementary Table S19). Calculation of the ground state magnetic anisotropy axis of Methods III Dy in low-symmetry environments, employing an electrostatic Electrostatic calculations. The electrostatic calculations were performed on the minimization strategy, shows how simple chemical intuition can complete monometallic structures (excluding lattice solvent or non-coordinated counter ions) using the reported X-ray geometry with no optimization. The charges aid in the understanding of a complex problem of electronic were assigned to the ligands as described in the text and all other atoms did not structure. Given the success of the electrostatic model in the cases contribute to the potential. The angles describing the orientation of the ðÞ a;b r ðÞ y; f electron density with respect to the experimental geometry, (a,b), 15=2 were then optimized to minimize the electrostatic energy. In applying this strategy, we have evaluated the uncertainty associated with using X-ray coordinates by moving the atomic positions by a random factor within the estimated standard deviations and found that the change in the orientation of the anisotropy axis over all monometallic compounds studied is on the order of 1. We have elected to use the Freeman and Watson values for the average radial integrals (ref. 40), /r S,and have investigated the effect of these values on the calculated anisotropy direction and also found deviations on the order of 1 when their values are altered non- systematically by up to 20%. The electrostatic calculations were implemented in a FORTRAN program, MAGELLAN, which is available from the authors upon request. Ab initio calculations. CASSCF calculations were performed with MOLCAS 7.6 Figure 4 | Ground state magnetic anisotropy of compound 17. The blue (refs 12,41,42) on the same geometry as used for the electrostatic calculations. The rods represent the orientations of the anisotropy axes for each of the five ANO-RCC-VTZP, VTZ and VDZ basis sets were used for the dysprosium ion, first III Dy ions in complex 17 as calculated by our electrostatic model; coordination sphere atoms and all other atoms, respectively. The calculations Dy ¼ green, O ¼ red, C ¼ grey and H ¼ white. employed the second order Douglas–Kroll–Hess Hamiltonian, where scalar 6 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE relativistic contractions are taken into account in the basis set and the spin-orbit 26. Baldovı´,J.J. et al. Rational design of single-ion magnets and spin qubits based coupling is handled separately in the RASSI module. The active space for dys- on mononuclear lanthanoid complexes. Inorg. Chem. 51, 12565–12574 (2012). prosium was, in all cases, nine electrons in seven orbitals. It was found that the 27. Baldovı´, J. J., Borra´s-Almenar, J. J., Clemente Juan, J. M., Coronado Miralles, E. effect of the spin quartets and doublets was negligible on the orientation of the & Gaita-Arin˜o, A. Modeling the properties of lanthanoid single-ion magnets magnetic anisotropy and therefore only the 21 spin sextets were included in the using an effective point-charge approach. Dalton Trans. 41, 13705–13710 state averaged CASSCF and spin-orbit coupling calculations. The effect of CASPT2 (2012). corrections for dynamic electron correlation were investigated, but found to have a 28. Tuna, F. et al. A high anisotropy barrier in a sulfur-bridged organodysprosium minor role in the orientation of the magnetic anisotropy, where the extent of the single-molecule magnet. Angew. Chem. Int. Ed. 51, 6976–6980 (2012). basis set had much more of an impact, and therefore CASPT2 corrections were not 29. Hutchings, M. Point-charge calculations of energy levels of magnetic ions in performed. Cholesky decomposition of the two-electron integrals was performed to crystalline electric fields. Solid State Phys. 16, 227–273 (1964). save disk space and computational time. These three approximations combined led 30. Langley, S. K., Moubaraki, B., Forsyth, C. M., Gass, I. A. & Murray, K. S. to differences in the calculated ground state orientation for 1 of less than 1, which Structure and magnetism of new lanthanide 6-wheel compounds utilizing is comparable with the uncertainty in the calculation of the electrostatic orienta- triethanolamine as a stabilizing ligand. Dalton Trans. 39, 1705–1708 (2010). tions, vide supra. 31. Ungur, L. et al. Net toroidal magnetic moment in the ground state of a {Dy }- triethanolamine ring. J. Am. Chem. Soc. 134, 18554–18557 (2012). References 32. Blagg, R. J., Muryn, C. A., McInnes, E. J. L., Tuna, F. & Winpenny, R. E. P. Single pyramid magnets: Dy pyramids with slow magnetic relaxation to 40 K. 1. Bottrill, M., Kwok, L. & Long, N. J. Lanthanides in magnetic resonance imaging. Chem. Soc. Rev. 35, 557–571 (2006). Angew. Chem. Int. Ed. 50, 6530–6533 (2011). 2. Thompson, K. H. & Orvig, C. Editorial: Lanthanide compounds for therapeutic 33. Blagg, R. J. et al. Magnetic relaxation pathways in lanthanide single-molecule and diagnostic applications. Chem. Soc. Rev. 35, 499–499 (2006). magnets. Nat. Chem. 5, 673–678 (2013). 3. Aromı´, G., Aguila`, D., Gamez, P., Luis, F. & Roubeau, O. Design of magnetic 34. Jiang, S.-D., Wang, B.-W., Su, G., Wang, Z.-M. & Gao, S. A mononuclear coordination complexes for quantum computing. Chem.Soc.Rev. 41, 537–546 (2012). dysprosium complex featuring single-molecule-magnet behavior. Angew. 4. Ishikawa, N., Sugita, M., Ishikawa, T., Koshihara, S. & Kaizu, Y. Lanthanide Chem. Int. Ed. 49, 7448–7451 (2010). 35. Bi, Y. et al. Capping ligand perturbed slow magnetic relaxation in dysprosium double-decker complexes functioning as magnets at the single-molecular level. J. Am. Chem. Soc. 125, 8694–8695 (2003). single-ion magnets. Chem. Eur. J. 17, 12476–12481 (2011). 14– 5. Habib, F. et al. The use of magnetic dilution to elucidate the slow magnetic 36. Ritchie, C. et al. Utilizing the adaptive polyoxometalate [As W O (H O)] 2 19 67 2 relaxation effects of a Dy single-molecule magnet. J. Am. Chem. Soc. 133, to support a polynuclear lanthanoid-based single-molecule magnet. Inorg. Chem. 50, 7004–7014 (2011). 8830–8833 (2011). III III 6. Langley, S. K. et al. Heterometallic tetranuclear [Ln Co ] complexes 37. Car, P.-E. et al. Giant field dependence of the low temperature relaxation of the 2 2 including suppression of quantum tunneling of magnetization in the magnetization in a dysprosium(III)–DOTA complex. Chem. Commun. 47, III III 3751–3753 (2011). [Dy Co ] single molecule magnet. Inorg. Chem. 51, 11873–11881 (2012). 2 2 7. Liu, J.-L. et al. Switching the anisotropy barrier of a single-ion magnet by 38. Bleaney, B. & Stevens, K. W. H. Paramagnetic resonance. Rep. Prog. Phys. 16, symmetry change from quasi-D to quasi-O . Chem. Sci. 4, 3310–3316 (2013). 108–159 (1953). 5h h 8. Soncini, A. & Chibotaru, L. Toroidal magnetic states in molecular wheels: 39. Wybourne, B. G. Spectroscopic Properties of Rare Earths (Interscience Publishers, 1965). interplay between isotropic exchange interactions and local magnetic anisotropy. Phys. Rev. B 77, 220406 (2008). 40. Freeman, A. J. & Watson, R. E. Theoretical investigation of some magnetic and 9. Chibotaru, L. F., Ungur, L. & Soncini, A. The origin of nonmagnetic Kramers spectroscopic properties of rare-earth ions. Phys. Rev. 127, 2058–2075 (1962). 41. Karlstro¨m, G. et al. MOLCAS: a program package for computational chemistry. doublets in the ground state of dysprosium triangles: evidence for a toroidal magnetic moment. Angew. Chem. Int. Ed. 47, 4126–4129 (2008). Comput. Mater. Sci. 28, 222–239 (2003). 10. Luzon, J. et al. Spin chirality in a molecular dysprosium triangle: the archetype 42. Veryazov, V., Widmark, P., Serrano-Andre´s, L., Lindh, R. & Roos, B. O. of the noncollinear Ising model. Phys. Rev. Lett. 100, 247205 (2008). MOLCAS as a development platform for quantum chemistry software. Int. J. Quant. Chem. 100, 626–635 (2004). 11. Gatteschi, D. Anisotropic dysprosium. Nat. Chem. 3, 830–830 (2011). 12. Aquilante, F. et al. MOLCAS 7: the next generation. J. Comput. Chem. 31, 43. Chen, G.-J. et al. Coordination-perturbed single-molecule magnet behaviour of 224–247 (2010). mononuclear dysprosium complexes. Dalton Trans. 40, 5579–5583 (2011). 44. Chen, G. et al. Enhancing anisotropy barriers of dysprosium(III) single-ion 13. Bernot, K. et al. Magnetic anisotropy of dysprosium(III) in a low-symmetry environment: a theoretical and experimental investigation. J. Am. Chem. Soc. magnets. Chem. Eur. J. 18, 2484–2487 (2012). 131, 5573–5579 (2009). 45. Wang, Z.-G. et al. Single-ion magnet behavior of a new mononuclear 14. Cucinotta, G. et al. Magnetic anisotropy in a dysprosium/DOTA dysprosium complex. Inorg. Chem. Commun. 27, 127–130 (2013). 46. Wang, Y., Li, X.-L., Wang, T.-W., Song, Y. & You, X.-Z. Slow relaxation single-molecule magnet: beyond simple magneto-structural correlations. Angew. Chem. Int. Ed. 51, 1606–1610 (2012). processes and single-ion magnetic behaviors in dysprosium-containing 15. Guo, Y.-N. et al. Strong axiality and Ising exchange interaction suppress zero- complexes. Inorg. Chem. 49, 969–976 (2010). field tunneling of magnetization of an asymmetric Dy single-molecule magnet. 47. Fatila, E. M., Hetherington, E. E., Jennings, M., Lough, A. J. & Preuss, K. E. J. Am. Chem. Soc. 133, 11948–11951 (2011). Syntheses and crystal structures of anhydrous Ln(hfac) (monoglyme). Ln ¼ 16. Habib, F. et al. Supramolecular architectures for controlling slow magnetic La, Ce, Pr, Sm, Eu, Gd, Tb, Dy, Er, Tm. Dalton Trans. 41, 1352–1362 (2012). relaxation in field-induced single-molecule magnets. Chem. Sci. 3, 2158–2164 (2012). Acknowledgements 17. Boulon, M. E. et al. Magnetic anisotropy and spin-parity effect along the series of This work was supported by the EPSRC (UK). N.F.C. thanks the University of Man- lanthanide complexes with DOTA. Angew. Chem. Int. Ed. 125, 368–372 (2013). chester for a President’s Doctoral Scholarship and Mr. J.P.S. Walsh for assistance with 18. Sorace, L., Benelli, C. & Gatteschi, D. Lanthanides in molecular magnetism: old figures. R.E.P.W. thanks The Royal Society for a Wolfson research merit award. tools in a new field. Chem. Soc. Rev. 40, 3092–3104 (2011). 19. Sessoli, R. & Luzo´n, J. Lanthanides in molecular magnetism: so fascinating so challenging. Dalton Trans. 41, 13556–13567 (2012). Author contributions 20. Chilton, N. F. et al. Single molecule magnetism in a family of mononuclear N.F.C. and A.S. designed the research and performed the calculations. E.J.L.M., D.C. and b-diketonate lanthanide(III) complexes: rationalization of magnetic anisotropy R.E.P.W. provided detailed critique of the approach. N.F.C. and A.S. wrote the manu- in complexes of low symmetry. Chem. Sci. 4, 1719–1730 (2013). script with input from the other authors. 21. Sievers, J. Asphericity of 4f-shells in their Hund’s rule ground states. Z. Phys. B Con. Mat. 45, 289–296 (1982). 22. Rinehart, J. D. & Long, J. R. Exploiting single-ion anisotropy in the design of Additional information Supplementary Information accompanies this paper at http://www.nature.com/ f-element single-molecule magnets. Chem. Sci. 2, 2078–2085 (2011). naturecommunications 23. Jiang, S.-D. et al. Series of lanthanide organometallic single-ion magnets. Inorg. Chem. 51, 3079–3087 (2012). Competing financial interests: The authors declare no competing financial interests. 24. Yamashita, K. et al. A luminescent single-molecule magnet: observation of magnetic anisotropy using emission as a probe. Dalton Trans. 42, 1987–1990 Reprints and permission information is available online at http://npg.nature.com/ (2013). reprintsandpermissions/ 25. Pointillart, F. et al. A series of tetrathiafulvalene-based lanthanide complexes displaying either single molecule magnet or luminescence—direct magnetic and How to cite this article: Chilton, N.F. et al. An electrostatic model for the determination photo-physical correlations in the ytterbium analogue. Inorg. Chem. 52, of magnetic anisotropy in dysprosium complexes. Nat. Commun. 4:2551 doi: 10.1038/ 5978–5990 (2013). ncomms3551 (2013). NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 7 & 2013 Macmillan Publishers Limited. All rights reserved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Communications Springer Journals

An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes

Download PDF
7 pages

Loading next page...
 
/lp/springer-journals/an-electrostatic-model-for-the-determination-of-magnetic-anisotropy-in-t0Rr3g3m6p

References (50)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.
Subject
Science, Humanities and Social Sciences, multidisciplinary; Science, Humanities and Social Sciences, multidisciplinary; Science, multidisciplinary
eISSN
2041-1723
DOI
10.1038/ncomms3551
Publisher site
See Article on Publisher Site

Abstract

ARTICLE Received 15 Jul 2013 | Accepted 4 Sep 2013 | Published 7 Oct 2013 DOI: 10.1038/ncomms3551 An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes 1 1 1 1 2 Nicholas F. Chilton , David Collison , Eric J.L. McInnes , Richard E.P. Winpenny & Alessandro Soncini Understanding the anisotropic electronic structure of lanthanide complexes is important in areas as diverse as magnetic resonance imaging, luminescent cell labelling and quantum computing. Here we present an intuitive strategy based on a simple electrostatic method, capable of predicting the magnetic anisotropy of dysprosium(III) complexes, even in low symmetry. The strategy relies only on knowing the X-ray structure of the complex and the well-established observation that, in the absence of high symmetry, the ground state of dysprosium(III) is a doublet quantized along the anisotropy axis with an angular momentum quantum number m ¼ / . The magnetic anisotropy axis of 14 low-symmetry mono- J 2 metallic dysprosium(III) complexes computed via high-level ab initio calculations are very well reproduced by our electrostatic model. Furthermore, we show that the magnetic anisotropy is equally well predicted in a selection of low-symmetry polymetallic complexes. 1 2 School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M19 3PL, UK. School of Chemistry, University of Melbourne, Parkville, Victoria 3010, Australia. Correspondence and requests for materials should be addressed to N.F.C. (email: [email protected]) or to A.S. (email: [email protected]). NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 1 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 III he fascinating magnetic properties of the lanthanides have complexes, the ground Kramers doublet of Dy is strongly continued to be a highly topical and strongly multi- axial with the principal values of the g-tensor approaching those 15 6 Tdisciplinary research area for over 60 years. Such is the of the m ¼ / levels of the atomic multiplet H J 2 15/2 diversity of this field that their application reaches from magnetic (g ¼ g ¼ 0, g ¼ 20). This empirical observation suggests that a x y z 1,2 resonance imaging and cell labelling , to potential building simple, but appropriate, variational ansatz for the many-electron blocks of quantum computers . The pursuit of such applications ground state wavefunction of these low-symmetry complexes relies on detailed knowledge of the magnetic anisotropy, which, consists of the atomic functions w (a,b) corresponding to the 15 6 while being completely defined in cases of high symmetry, m ¼ / states of the multiplet H . The variational J 2 15/2 is difficult to elucidate in low-symmetry complexes. Much parameters to be optimized in w (a,b) consist of the two polar recent work, where 4f complexes have shown slow magnetic angles a and b, which specify the orientation of the quantization 4–7 relaxation and unprecedented non-collinear magnetic textures axis with respect to the low-symmetry crystal field V defined by CF 8–10 at the single-molecule level , also depends on understanding the ligands. To determine these angles, and hence the full g-tensor III the orientation of the magnetic anisotropy. Of all the lanthanide of the ground Kramers doublet of the Dy complex, we can use III ions, it is Dy that continues to prove the most interesting, the variational principle and minimize the energy E ða; bÞ¼ 15=2 providing unexpected examples of new magnetic phenomena, byhi w ða; bÞj V j w ða; bÞ with respect to all possible CF virtue of its unique magnetic anisotropy . However, because of orientations (a,b) of the quantization axis. the intricate electronic structure of lanthanide complexes, simple This proposed strategy is readily mapped onto a classical models that can predict magnetic anisotropy in molecular solids electrostatic energy minimization problem. Following the work of of low symmetry are still missing. Sievers , the many-electron wavefunctions w (a,b) can be ðÞ a;b The single-ion properties of 4f metal ions, whether in mono- or described by an electron density distribution r ðÞ y; f , where 15=2 polymetallic complexes, are difficult to elucidate owing to the y and f are polar angles defined in the reference frame of V , CF shielded nature of the 4f orbitals giving rise to weak interactions expressing the angular dependence of the axially symmetric with the surrounding environment. Recent advances in post aspherical electron density. This aspherical f-electron density can Hartree-Fock multi-configurational ab initio methodology have be written as a linear combination of three spherical harmonics made accurate quantum chemical calculations on paramagnetic 4f Y (y,f), Y (y,f) and Y (y,f), where the coefficients of each 2,0 4,0 6,0 compounds possible . The Complete Active Space Self Consistent are fully determined by angular momentum coupling and average Field (CASSCF) method can accurately predict the magnetic atomic radial multipole moments . In the particular case of ðÞ a;b 13,14 III properties of lanthanide complexes , and calculations of this Dy , r ðÞ y; f can be approximated by an oblate spheroid 15=2 type have become an indispensable tool for the explanation of distribution owing to the dominant contribution of the 6,15–17 22,21 increasingly interesting magnetic phenomena .These quadrupolar term Y (y,f) to the expansion . 2,0 calculations are especially useful in cases of low symmetry, where As the crystal field is a one-electron potential, the many- previous methods have provided intractable, over parameterized electron variational integral E (a,b) can be exactly recast into 15/2 18,19 problems . Although CASSCF ab initio calculations are a simple electrostatic energy integral, describing the interaction extremely versatile and implicitly include all effects required to between the electric potential generated by the crystal field ðÞ a;b elucidate the magnetic properties, the results offer little in the way V (y,j) and the Sievers charge density r ðÞ y; f associated CF 15=2 III of chemically intuitive explanations and to obtain reliable results with the f-electrons in the central Dy ion (equation (1)). requires considerable intervention by expert theorists equipped with p 2p Z Z access to powerful computational resources. ðÞ a;b E 15ðÞ a; b ¼ V ðÞ y; j r ðÞ y; f sinðÞ y dydj ð1Þ CF Recently, some of us have applied a simple electrostatic model 15=2 to rationalize the unexpected direction of the calculated magnetic y¼0 j¼0 anisotropy in two related sets of monometallic 4f complexes . III Thus, we arrive at the hypothesis that in low-symmetry Dy This was based on the aspherical electron density distributions of complexes, the many-electron ground state wavefunction and, the lanthanide ions, pioneered by Sievers , and the design hence, the orientation of the magnetic anisotropy axis, can be principles for the exploitation of f-element anisotropy outlined by determined simply by solving a classical electrostatic energy Rinehart and Long . Other groups have also been coming to minimization problem. similar conclusions . Although the use of crystal field methods to 23–25 model anisotropic magnetic data is widespread , models for the prediction of magnetic anisotropy in low symmetry are Constructing the crystal field potential of charged ligands.To 26,27 few . These methods are based on the diagonalization of a use this hypothesis, we must determine the explicit form of crystal field Hamiltonian, which, especially in cases of low V (y,j) appearing in equation (1), by using an appropriate CF symmetry, requires a large number of parameters that often can model for the charge distribution on the ligands. This may appear only be reliably determined by fitting experimental data. Such an a difficult problem; here, we use a simple model for charged III approach can obscure the rationalization of magnetic anisotropy ligands that are common in many low-symmetry Dy com- and its predictive power is uncertain. plexes. The charge on the ligands is expected to have a dominant Here we report a quantitative method based on a straightfor- role in the determination of the electrostatic potential experienced III ward electrostatic energy minimization for the prediction of the by Dy , and thus, we can calculate the electrostatic field pro- orientation of the ground state magnetic anisotropy axis of duced by charge on the ligands within a minimal valence bond dysprosium(III) ions, which does not rely on the fitting of (VB) model. Within this model, the charge is delocalized as a experimental data, requiring only the determination of an X-ray resonance hybrid that can be seen as a weighted sum of all crystal structure. ‘chemically stable’ Lewis structures (Fig. 1); this is a representa- tion of the leading contribution to the full VB wavefunction. By taking the sum of the partial charges accumulated by each atom Results in the VB resonance hybrid, q , we arrive at a very simple frac- Many electron wavefunction and electrostatic minimization. tional charge distribution for the ligand, where, typically, very few An increasing number of ab initio CASSCF calcula- atoms will accommodate a charge and most will remain neutral. 6,14,15,20,28 tions have shown that in most low-symmetry Our strategy is to construct the crystal field potential solely from 2 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE H H H 2 1 1 1 1 1 – / – / + / + / + / – / 2 5 5 5 3 C N C CH HC C C C paaH* NO Na NH HC O O O O 1 1 C 2 N O 1 1 2 1 – / – / – / + / + / 3 3 – / – / 3 5 5 3 2 1 H – / 1 – / N O Na – Na DOTA Na O N – / 1 H 1 – 1 2 – / 1 – / 2 acac : R ,R = CH 2 1 3 R R 3 – / 2 – 1 2 O N tfpb : R = CF3, R = Ph C C – 1 2 tta : R = CF , R = 2-thienyl O O – 1 2 O hfac : R ,R = CF – / – / 3 – / Br Ph 1 1 – / – / C –1 5 5 Ph Si S Ph SiS HCC MeCp – / Ph HC CH NH O 1 1 – / – / 5 5 –1 –1 3– teabmpH O 3 –1 N HN 2– Br teaH –1 –1 i – PrO N Pr HO O –1 Br Figure 1 | Partial charges assigned to the formally charged ligands in complexes 1–17. The zwitterionic N-(2-pyridyl)-acetylacetamide (paaH*) has two formal charges owing to the deprotonation of the a-carbon and protonation of the pyridyl nitrogen. Each pendant carboxylate arm of the macrocyclic 0 00 000 trisodium 1,4,7,10-tetraazacyclododecane N,N ,N ,N -tetraacetate ligand (Na DOTA ) has a single negative charge that is delocalized evenly over the two oxygen atoms; three of the four acetate arms bind sodium cations, which each have a single positive charge. The aromatic anion of methylcyclopentadienyl (MeCp ) has a single negative charge that is delocalized evenly over the five cyclic carbon atoms. Not shown: Compounds 12 and 2 þ 2 13 contain Zn ions, which have formal charges of positive two in our model. Compound 17 contains a central oxide (O ) ligand, which has a formal charge of negative two in our model. the fractional charges determined by the VB resonance hybrid, determination of magnetic anisotropy in cases of low excluding neutral atoms entirely (see Fig. 1 illustrating the frac- symmetry. In high symmetry, the orientation of the ground tional charges of the resonance hybrids for the ligands of interest Kramers doublet is pre-determined; note that in this case if ðÞ a;b here). The partitioning of the charge without any need for V (y,j) does not stabilize the r ðÞ y; f electron density CF 15=2 computation illustrates the elegance of our model. along the symmetry axis, then m ¼ / will not be the J 2 Once the partitioning of the charge over the ligand is ground state. There is no such restriction in low-symmetry determined, the resulting partial charges are arranged around environments. III the central Dy ion using the known X-ray crystal structure of the complex, allowing the electrostatic potential to be easily Monometallic complexes. The energy spectra and g-tensors of calculated using crystal field theory (equation (2), where the ground H multiplets for compounds 1–14, as calculated th 15/2 (R ,y ,j ) are the spherical coordinates of the n charged atom, n n n ab initio, are given in Supplementary Tables S1–S18. Table 1 see Methods section). presents, for each complex, the principal value of the diagonal g- k m tensor of the ground Kramers doublet (g ) and the electrostatic X X 4pð 1Þ deviation angle, defined as the angle between the electrostatic V ðÞ y; j ¼ hr iY ðÞ y; j CF k;m 2k þ 1 anisotropy axis and the ab initio anisotropy axis along which g is k¼2;4;6 m¼ k z ð2Þ defined. q Y ðy ; j Þ n k;m n We note that the anisotropy axis is accurately predicted by k þ 1 employing this minimal VB model, without taking into account different electron withdrawing or donating groups in the charged Minimization of the electrostatic energy in equation (1) in ligands, for example, hfac will have less electron density at the conjunction with this minimal VB model yields an orientation oxygen donor atoms compared with acac because of the of the anisotropy axis, which compares remarkably well electron withdrawing nature of the CF groups in the former with that obtained via rigorous ab initio calculations ligand. (Table 1). To exemplify this correlation, we have calculated the magnetic properties of 14 low-symmetry monometallic dysprosium(III) complexes using the CASSCF ab initio Polymetallic complexes. Calculating the ab initio properties of methodology (see Methods) and compare them directly with the following polymetallic complexes is extremely computation- our electrostatic model. In this work, we focus on the ally expensive. Hence, to demonstrate the power of our simple NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 3 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 III Table 1 | Comparison of ab initio and electrostatic calculations for Dy complexes. Compound g Electrostatic deviation () Reference 1 [Dy(acac) (H O) ] 19.62 10.9 3 2 2 2 [Dy(acac) (phen)] 19.55 10.0 3 [Dy(acac) (dpq)] 19.42 2.9 4 [Dy(acac) (dppz)] 19.57 6.1 5 [Dy(tfpb) (dppz)] 19.48 9.0 6 [Dy(tta) (bipy)] 19.76 12.4 7 [Dy(tta) (phen)] 19.66 8.0 8 [Dy(tta) (pinene-bipy)] 19.81 6.9 9 [Dy(hfac) (dme)] 19.65 11.0 3 þ 20 10 [Dy(paaH*) (H O) ] 19.78 2.4 2 2 4 1 þ 20 11 [Dy(paaH*) (NO ) (MeOH)] 19.68 7.4 2 3 2 1 þ 7 12 [DyZn (teabmpH ) (MeOH)] 19.98 6.6 2 3 2 1 þ 7 13 [DyZn (teabmpH ) ] 19.90 8.0 2 3 2 2 þ z y 14,37 14 [Dy(DOTA)(H O)Na ] 19.46 14.8 2 3 bipy, 2,2 -bipyridine; dme, dimethoxyethane; dpq, dipyridoquinoxaline; dppz, dipyridophenazine; pinene-bipy, 4,5-pinene bipyridine; phen, 1,10-phenanthroline. Angle between anisotropy axis calculated by ab initio and electrostatic methods. Average g value over four calculations, see Supplementary Tables S14–S18. Angles between the experimentally determined and the ab initio and electrostatic anisotropy axes are 3.9 and 12.1, respectively. approach, we have performed a semi-quantitative comparison interact strongly with the two basal oxygen atoms. If, however, between the electrostatic calculations and published ab initio the quantization axis was parallel with the base and top of the results for three compounds: [Dy(MeCp) (Ph SiS)] 15 (ref. 28) trapezium, there would be less interaction with the negative 2 3 2 [Dy (teaH) (NO ) ] 16 (refs 30,31) and [Dy O( PrO) ] 17 charges thus stabilizing the orientation. This is the orientation of 6 6 3 6 5 13 (refs 32,33). The methodology for the calculation of the the anisotropy axis (Fig. 2c and Supplementary Fig. S9) calculated electrostatic anisotropy axes in polymetallic complexes is by our electrostatic model and it provides a simple explanation identical to that of monometallic complexes and is performed for the ab initio results. Analogous arguments can be made for III III for each Dy ion independently. The Dy ions that are not the compound 11 where the b-diketonate oxygen donors are in a focus of the calculation are treated as part of the ligand and are similar trapezium-shaped arrangement, however, the coordina- given a þ 3 charge. The charged ligands in complexes 15–17 are tion environment now contains two chelating nitrate anions. The given in Fig. 1, which describes the charge partitioning based on oxygen atoms in NO have a larger negative partial charge than the minimal VB model. those in the b-diketonates, but this is offset by the positive charge on the nitrogen atom, which has an attractive effect on the electron density. Therefore, more-or-less the same anisotropy axis Discussion as in compound 10 is observed for compound 11, along the The form of the potential (equation (2)) contains terms of for diketonate-diketonate vector (Supplementary Fig. S10). k þ 1 each charged atom in the ligand, which implies that the closer to Compounds 1–10 have distorted square anti-prismatic geo- III the Dy ion and larger the magnitude of the charge, the greater metries and the calculated anisotropy axis of the ground state is its effect on the orientation of the anisotropy axis. Complexes 1–9 not found to be coincident with the pseudo-fourfold axis. This contain three b-diketonate ligands in a ‘paddle-wheel’-like observation, shown here to be due to simple electrostatic arrangement, with two b-diketonate ligands trans- to each other arguments, is contrary to many reports in the literature that and the third trans- to a neutral ligand (Fig. 2a). If the employ a fourfold axial interpretation to model the magnetic data ðÞ a;b quantization axis of the r ðÞ y; f electron density was along (refs 25,34–36). Clearly, in these cases, the electrostatics are more 15=2 the ‘paddle-wheel’ axis, then the radial plane of the approximately important than pseudo-symmetry. ‘oblate’ density would be coincident with all three charged Compounds 12 and 13, chosen as a departure from b- ligands, representing a high-energy orientation. Therefore, the diketonate-based complexes in addition to their very interesting anisotropy axis is perpendicular to the ‘paddle-wheel’ axis, and we magnetic properties, are intimately related and can be inter- find that it passes through the two trans-b-diketonate ligands. converted reversibly by drying or soaking in methanol, via a single The radial plane of the oblate electron density is thus coincident crystal to single crystal transformation . The difference between with only one charged ligand as opposed to two (Fig. 2b and the dysprosium(III) coordination environments is the removal of Supplementary Figs S1–S8). a terminal methanol molecule, changing the local symmetry from For compound 10, the negatively charged oxygen atoms of the a distorted pentagonal bipyramid to a distorted octahedron. III III two b-diketonate ligands are the closest to Dy and therefore Considering the local Dy coordination environment, a pair of have the greatest effect on the orientation of the anisotropy axis. trans- phenoxo oxygen atoms in both 12 and 13 have much These four atoms are roughly coplanar with the dysprosium(III) shorter Dy–O bond lengths than all others, at 2.21(2) Å compared ion and are arranged in a trapezium (Fig. 2c). The oblate electron with 2.39(2) Å for 12 and 2.186(4) Å compared with 2.3(1) Å for ðÞ a;b density r ðÞ y; f will be in a high-energy configuration when 13, thus defining both geometries as axially compressed. In both 15=2 the quantization axis is normal to this plane of four negative cases, the three metal atoms are roughly coplanar with the charges, and therefore the minimum electrostatic energy and equatorial planes of the coordination polyhedra. The close oxygen anisotropy axis will lie in the plane of the b-diketonate oxygen atoms define an axially repulsive potential for dysprosium(III), III 2 þ atoms. The Dy ion is much closer to the base of the trapezium which, coupled with the attractive nature of the Zn cations in and therefore if the quantization axis was to bisect the two the equatorial plane, explains the observed magnetic anisotropy parallel edges, then the radial plane of the electron density would axes (Supplementary Figs S11 and S12). 4 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. H H H C N C CH HC C C C HC NH OO NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE a c 1 2 R C R C C O O 1 1 R R C O O C Dy HC CH C O O C 2 2 R R E E 2.765 2.752 2.766 Dy 4.308 Figure 2 | Magnetic anisotropy and electrostatic potential of b-diketonate species. (a) Idealized ‘paddle-wheel’ geometry of complexes 1–9 viewed down the ‘paddle-wheel axis’. (b) Comparison of the ab initio (blue rod) and electrostatic (green rod) anisotropy axes for the ground Kramers doublet in 1, ðÞ a;b with the form of the oblate r ðÞ y; f f-electron density using the representation of Sievers , magnified approximately  5 for clarity; Dy ¼ green, 15=2 O ¼ red, C ¼ grey and H ¼ white. (c) Idealized electrostatic potential generated by a pair of paaH* ligands in the trapezium-shaped coordination environment present in the bis-b-diketonate-dysprosium(III) plane of compounds 10 and 11 and the resultant anisotropy axis (green line); red ¼ positive potential, blue ¼ negative potential. (°) b 90 90  (°) –200 –400 ðÞ a;b Figure 3 | Orthogonal configurations for the magnetic anisotropy axis in compound 14. The form of the oblate r ðÞ y; f f-electron density, visualized 15=2 in the central structural diagrams, follows the representation of Sievers , and has been magnified approximately  5 for clarity; Dy ¼ green, Na ¼ yellow, O ¼ red, N ¼ blue, C ¼ grey and H ¼ white. The rods in the central structural diagrams represent the magnetic anisotropy axes, identified by various methods: green ¼ electrostatic calculation, dark blue ¼ ab initio calculation (this work), light blue ¼ ab initio calculation and pink ¼ experimentally determined. The energies of each configuration have been calculated using our electrostatic approach. The electrostatic energy surface is calculated by considering all possible orientations (a,b) of the anisotropy axis in the potential generated by the charged ligands of compound 14. The electrostatic energy ðÞ a;b surface shows double degeneracy of the minimum, maximum and saddle points due to the axial symmetry of the r ðÞ y; f electron density. 15=2 2 þ In [Dy(DOTA)(H O)Na ] 14, for which the magnetic configuration (Fig. 3a). Therefore, the anisotropy axis is 2 3 anisotropy axis has been determined experimentally, the perpendicular to the pseudo-tetragonal axis of the molecule. 4  þ dysprosium(III) ion is encapsulated by the macrocyclic DOTA The radial plane of the ‘oblate’ density is attracted by two Na ligand (ref. 37). The H atoms of the apical water molecule were ions more strongly than just a single Na ion (Fig. 3b), thus not found experimentally, so were placed in calculated positions determining the observed orientation of the anisotropy axis based on crystallographically characterized water molecules (Fig. 3c), which agrees well with the experimentally determined III bound to Ln ions (ref. 20). If the anisotropy axis was and ab initio axes (Table 1). We have rotated the apical water coincident with the pseudo-tetragonal axis, the radial plane of molecule in the ab initio calculations and found no dependence the oblate electron density would have a large interaction with the on the orientation of the ground state anisotropy axis to this four negatively charged acetate groups, yielding a high-energy perturbation, contrary to ref. 14. NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 5 & 2013 Macmillan Publishers Limited. All rights reserved. H H N CH C C HC C C C HC NH OO –1 Energy (cm ) ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 Compound 15 contains two dysprosium(III) ions bridged by presented, we propose that this model can be used to aid in the two anionic Ph SiS ligands and each capped by two classical rational design of molecular architectures displaying novel organometallic ligands, MeCp (ref. 28). The two ions are magnetic properties, exploiting and stabilizing the strong axiality related by inversion symmetry and therefore possess the same of the ground state of low-symmetry dysprosium(III), through single-ion electronic structure. The electrostatic potential at each the use of formally charged ligands. The simplicity of the proposal paramagnetic ion is dominated by the two MeCp ligands, is so profound that the model resonates strongly with the III which are closer to the Dy ion than the sulfur atoms at conclusions drawn in the 1950s and 1960s that the bonding of the 2.65(3) Å (average Dy–C distance) compared with 2.76(2) Å. This lanthanides is almost purely ionic (refs 38,39). leads to the anisotropy axis of the ground state lying By entirely neglecting the influence of neutral ligands in our perpendicular to the Dy-S-S-Dy plane (Supplementary model, we have shown the dominant nature of charged ligands in Fig. S13), in good agreement with ab initio calculations (ref. 28). the determination of the magnetic anisotropy of dysprosium(III) The hexametallic dysprosium(III) wheel (16) contains highly complexes. Compounds lacking any charged ligands are rare, but anisotropic paramagnetic centres, yet due to crystallographic S would likely show magnetic anisotropies that are much more symmetry, possesses a diamagnetic ground state with a toroidal sensitive to the type of ligands present, with contributions due to III 2 moment. Each Dy ion is encapsulated by the teaH ligand dipoles and higher order multipoles as well as the spatial extent of and also has one chelating nitrate anion . Applying our ligand electron density becoming important. The minimal VB electrostatic model to this compound yields the anisotropy axis model for the partitioning of charges on ligands works well for of each dysprosium(III) site in excellent agreement with the ab the formally charged ligands presented here. Other more general initio results (Supplementary Fig. S14) . The anisotropy axis for schemes for the partitioning of atomic charges over the ligands III each Dy ion is canted around the ring in an alternating up/ are also being investigated, which may offer an improvement over down manner, which, due to the S symmetry of the molecule, the minimal VB model. causes the net cancellation of the out-of-plane magnetization in We are also extending the method to other lanthanide ions, 31 8 the ground state , leading to a toroidal moment , similar to that examining whether this approach can work for other oblate ions 9,10 III observed in a Dy triangle . It is remarkable that such a simple (for example, Tb ) and whether the reverse electrostatic principles III electrostatic approach can rationalize such complex physics. will apply to prolate ions (for example, Er ). Although the Compound 17, with one of the highest energy barriers to the treatment presented here cannot be rigorously applied to non- III reversal of the ground state magnetization, contains five Kramers ions in low-symmetry environments, Tb complexes that III dysprosium(III) ions arranged in a pyramid, with each Dy possess a pseudo-doublet ground state with m ¼ 6(g ¼ g ¼ 0, J x y ion at the centre of an axially compressed octahedron. The g ¼ 18) should follow similar electrostatic arguments to those equatorial plane of each ion is formed by four bridging discussed here for the determination of the magnetic anisotropy. isopropoxide ( PrO ) ligands and the axial positions are Conversely, preliminary results suggest that the ground state III occupied by the single m -oxide bridge at the centre of the wavefunctions of Er ions in low-symmetry environments are not molecule and a terminal isopropoxide ligand . The oxygen atom well defined and consist of strongly mixed m states, precluding the i  III of the terminal PrO ligand is substantially closer to the Dy application of the treatment presented here. ion than all other donor atoms, at 2.04(1) Å compared with The work presented here is an advance not only for the chemistry 2.35(8) Å, and the central m oxide has a double negative charge. and physics communities involved with molecular magnetism, but 5- These two features define a strongly repulsive axial potential for also for all areas concerned with the magnetic and spectroscopic ðÞ a;b the r ðÞ y; f electron density, where the energy is minimized properties of the lanthanides. Specifically, this work provides some 15=2 when the quantization axis is coincident with this direction much-needed insight into the complex and continually intriguing (Fig. 4). The presence of the other charged ligands and the magnetic properties of dysprosium(III). High-level quantum trivalent dysprosium ions is a small perturbation in this case, chemical calculations such as CASSCF are computationally because of the strongly directional nature of the almost linear expensive and require intervention by experts to produce reliable i  2 PrO -Dy-O axis. The results obtained using our electrostatic results. The complementary approach we outline here is available to model compare extremely well with those obtained using ab initio any chemist with minimal computational requirements. calculations (see Supplementary Table S19). Calculation of the ground state magnetic anisotropy axis of Methods III Dy in low-symmetry environments, employing an electrostatic Electrostatic calculations. The electrostatic calculations were performed on the minimization strategy, shows how simple chemical intuition can complete monometallic structures (excluding lattice solvent or non-coordinated counter ions) using the reported X-ray geometry with no optimization. The charges aid in the understanding of a complex problem of electronic were assigned to the ligands as described in the text and all other atoms did not structure. Given the success of the electrostatic model in the cases contribute to the potential. The angles describing the orientation of the ðÞ a;b r ðÞ y; f electron density with respect to the experimental geometry, (a,b), 15=2 were then optimized to minimize the electrostatic energy. In applying this strategy, we have evaluated the uncertainty associated with using X-ray coordinates by moving the atomic positions by a random factor within the estimated standard deviations and found that the change in the orientation of the anisotropy axis over all monometallic compounds studied is on the order of 1. We have elected to use the Freeman and Watson values for the average radial integrals (ref. 40), /r S,and have investigated the effect of these values on the calculated anisotropy direction and also found deviations on the order of 1 when their values are altered non- systematically by up to 20%. The electrostatic calculations were implemented in a FORTRAN program, MAGELLAN, which is available from the authors upon request. Ab initio calculations. CASSCF calculations were performed with MOLCAS 7.6 Figure 4 | Ground state magnetic anisotropy of compound 17. The blue (refs 12,41,42) on the same geometry as used for the electrostatic calculations. The rods represent the orientations of the anisotropy axes for each of the five ANO-RCC-VTZP, VTZ and VDZ basis sets were used for the dysprosium ion, first III Dy ions in complex 17 as calculated by our electrostatic model; coordination sphere atoms and all other atoms, respectively. The calculations Dy ¼ green, O ¼ red, C ¼ grey and H ¼ white. employed the second order Douglas–Kroll–Hess Hamiltonian, where scalar 6 NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications & 2013 Macmillan Publishers Limited. All rights reserved. NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3551 ARTICLE relativistic contractions are taken into account in the basis set and the spin-orbit 26. Baldovı´,J.J. et al. Rational design of single-ion magnets and spin qubits based coupling is handled separately in the RASSI module. The active space for dys- on mononuclear lanthanoid complexes. Inorg. Chem. 51, 12565–12574 (2012). prosium was, in all cases, nine electrons in seven orbitals. It was found that the 27. Baldovı´, J. J., Borra´s-Almenar, J. J., Clemente Juan, J. M., Coronado Miralles, E. effect of the spin quartets and doublets was negligible on the orientation of the & Gaita-Arin˜o, A. Modeling the properties of lanthanoid single-ion magnets magnetic anisotropy and therefore only the 21 spin sextets were included in the using an effective point-charge approach. Dalton Trans. 41, 13705–13710 state averaged CASSCF and spin-orbit coupling calculations. The effect of CASPT2 (2012). corrections for dynamic electron correlation were investigated, but found to have a 28. Tuna, F. et al. A high anisotropy barrier in a sulfur-bridged organodysprosium minor role in the orientation of the magnetic anisotropy, where the extent of the single-molecule magnet. Angew. Chem. Int. Ed. 51, 6976–6980 (2012). basis set had much more of an impact, and therefore CASPT2 corrections were not 29. Hutchings, M. Point-charge calculations of energy levels of magnetic ions in performed. Cholesky decomposition of the two-electron integrals was performed to crystalline electric fields. Solid State Phys. 16, 227–273 (1964). save disk space and computational time. These three approximations combined led 30. Langley, S. K., Moubaraki, B., Forsyth, C. M., Gass, I. A. & Murray, K. S. to differences in the calculated ground state orientation for 1 of less than 1, which Structure and magnetism of new lanthanide 6-wheel compounds utilizing is comparable with the uncertainty in the calculation of the electrostatic orienta- triethanolamine as a stabilizing ligand. Dalton Trans. 39, 1705–1708 (2010). tions, vide supra. 31. Ungur, L. et al. Net toroidal magnetic moment in the ground state of a {Dy }- triethanolamine ring. J. Am. Chem. Soc. 134, 18554–18557 (2012). References 32. Blagg, R. J., Muryn, C. A., McInnes, E. J. L., Tuna, F. & Winpenny, R. E. P. Single pyramid magnets: Dy pyramids with slow magnetic relaxation to 40 K. 1. Bottrill, M., Kwok, L. & Long, N. J. Lanthanides in magnetic resonance imaging. Chem. Soc. Rev. 35, 557–571 (2006). Angew. Chem. Int. Ed. 50, 6530–6533 (2011). 2. Thompson, K. H. & Orvig, C. Editorial: Lanthanide compounds for therapeutic 33. Blagg, R. J. et al. Magnetic relaxation pathways in lanthanide single-molecule and diagnostic applications. Chem. Soc. Rev. 35, 499–499 (2006). magnets. Nat. Chem. 5, 673–678 (2013). 3. Aromı´, G., Aguila`, D., Gamez, P., Luis, F. & Roubeau, O. Design of magnetic 34. Jiang, S.-D., Wang, B.-W., Su, G., Wang, Z.-M. & Gao, S. A mononuclear coordination complexes for quantum computing. Chem.Soc.Rev. 41, 537–546 (2012). dysprosium complex featuring single-molecule-magnet behavior. Angew. 4. Ishikawa, N., Sugita, M., Ishikawa, T., Koshihara, S. & Kaizu, Y. Lanthanide Chem. Int. Ed. 49, 7448–7451 (2010). 35. Bi, Y. et al. Capping ligand perturbed slow magnetic relaxation in dysprosium double-decker complexes functioning as magnets at the single-molecular level. J. Am. Chem. Soc. 125, 8694–8695 (2003). single-ion magnets. Chem. Eur. J. 17, 12476–12481 (2011). 14– 5. Habib, F. et al. The use of magnetic dilution to elucidate the slow magnetic 36. Ritchie, C. et al. Utilizing the adaptive polyoxometalate [As W O (H O)] 2 19 67 2 relaxation effects of a Dy single-molecule magnet. J. Am. Chem. Soc. 133, to support a polynuclear lanthanoid-based single-molecule magnet. Inorg. Chem. 50, 7004–7014 (2011). 8830–8833 (2011). III III 6. Langley, S. K. et al. Heterometallic tetranuclear [Ln Co ] complexes 37. Car, P.-E. et al. Giant field dependence of the low temperature relaxation of the 2 2 including suppression of quantum tunneling of magnetization in the magnetization in a dysprosium(III)–DOTA complex. Chem. Commun. 47, III III 3751–3753 (2011). [Dy Co ] single molecule magnet. Inorg. Chem. 51, 11873–11881 (2012). 2 2 7. Liu, J.-L. et al. Switching the anisotropy barrier of a single-ion magnet by 38. Bleaney, B. & Stevens, K. W. H. Paramagnetic resonance. Rep. Prog. Phys. 16, symmetry change from quasi-D to quasi-O . Chem. Sci. 4, 3310–3316 (2013). 108–159 (1953). 5h h 8. Soncini, A. & Chibotaru, L. Toroidal magnetic states in molecular wheels: 39. Wybourne, B. G. Spectroscopic Properties of Rare Earths (Interscience Publishers, 1965). interplay between isotropic exchange interactions and local magnetic anisotropy. Phys. Rev. B 77, 220406 (2008). 40. Freeman, A. J. & Watson, R. E. Theoretical investigation of some magnetic and 9. Chibotaru, L. F., Ungur, L. & Soncini, A. The origin of nonmagnetic Kramers spectroscopic properties of rare-earth ions. Phys. Rev. 127, 2058–2075 (1962). 41. Karlstro¨m, G. et al. MOLCAS: a program package for computational chemistry. doublets in the ground state of dysprosium triangles: evidence for a toroidal magnetic moment. Angew. Chem. Int. Ed. 47, 4126–4129 (2008). Comput. Mater. Sci. 28, 222–239 (2003). 10. Luzon, J. et al. Spin chirality in a molecular dysprosium triangle: the archetype 42. Veryazov, V., Widmark, P., Serrano-Andre´s, L., Lindh, R. & Roos, B. O. of the noncollinear Ising model. Phys. Rev. Lett. 100, 247205 (2008). MOLCAS as a development platform for quantum chemistry software. Int. J. Quant. Chem. 100, 626–635 (2004). 11. Gatteschi, D. Anisotropic dysprosium. Nat. Chem. 3, 830–830 (2011). 12. Aquilante, F. et al. MOLCAS 7: the next generation. J. Comput. Chem. 31, 43. Chen, G.-J. et al. Coordination-perturbed single-molecule magnet behaviour of 224–247 (2010). mononuclear dysprosium complexes. Dalton Trans. 40, 5579–5583 (2011). 44. Chen, G. et al. Enhancing anisotropy barriers of dysprosium(III) single-ion 13. Bernot, K. et al. Magnetic anisotropy of dysprosium(III) in a low-symmetry environment: a theoretical and experimental investigation. J. Am. Chem. Soc. magnets. Chem. Eur. J. 18, 2484–2487 (2012). 131, 5573–5579 (2009). 45. Wang, Z.-G. et al. Single-ion magnet behavior of a new mononuclear 14. Cucinotta, G. et al. Magnetic anisotropy in a dysprosium/DOTA dysprosium complex. Inorg. Chem. Commun. 27, 127–130 (2013). 46. Wang, Y., Li, X.-L., Wang, T.-W., Song, Y. & You, X.-Z. Slow relaxation single-molecule magnet: beyond simple magneto-structural correlations. Angew. Chem. Int. Ed. 51, 1606–1610 (2012). processes and single-ion magnetic behaviors in dysprosium-containing 15. Guo, Y.-N. et al. Strong axiality and Ising exchange interaction suppress zero- complexes. Inorg. Chem. 49, 969–976 (2010). field tunneling of magnetization of an asymmetric Dy single-molecule magnet. 47. Fatila, E. M., Hetherington, E. E., Jennings, M., Lough, A. J. & Preuss, K. E. J. Am. Chem. Soc. 133, 11948–11951 (2011). Syntheses and crystal structures of anhydrous Ln(hfac) (monoglyme). Ln ¼ 16. Habib, F. et al. Supramolecular architectures for controlling slow magnetic La, Ce, Pr, Sm, Eu, Gd, Tb, Dy, Er, Tm. Dalton Trans. 41, 1352–1362 (2012). relaxation in field-induced single-molecule magnets. Chem. Sci. 3, 2158–2164 (2012). Acknowledgements 17. Boulon, M. E. et al. Magnetic anisotropy and spin-parity effect along the series of This work was supported by the EPSRC (UK). N.F.C. thanks the University of Man- lanthanide complexes with DOTA. Angew. Chem. Int. Ed. 125, 368–372 (2013). chester for a President’s Doctoral Scholarship and Mr. J.P.S. Walsh for assistance with 18. Sorace, L., Benelli, C. & Gatteschi, D. Lanthanides in molecular magnetism: old figures. R.E.P.W. thanks The Royal Society for a Wolfson research merit award. tools in a new field. Chem. Soc. Rev. 40, 3092–3104 (2011). 19. Sessoli, R. & Luzo´n, J. Lanthanides in molecular magnetism: so fascinating so challenging. Dalton Trans. 41, 13556–13567 (2012). Author contributions 20. Chilton, N. F. et al. Single molecule magnetism in a family of mononuclear N.F.C. and A.S. designed the research and performed the calculations. E.J.L.M., D.C. and b-diketonate lanthanide(III) complexes: rationalization of magnetic anisotropy R.E.P.W. provided detailed critique of the approach. N.F.C. and A.S. wrote the manu- in complexes of low symmetry. Chem. Sci. 4, 1719–1730 (2013). script with input from the other authors. 21. Sievers, J. Asphericity of 4f-shells in their Hund’s rule ground states. Z. Phys. B Con. Mat. 45, 289–296 (1982). 22. Rinehart, J. D. & Long, J. R. Exploiting single-ion anisotropy in the design of Additional information Supplementary Information accompanies this paper at http://www.nature.com/ f-element single-molecule magnets. Chem. Sci. 2, 2078–2085 (2011). naturecommunications 23. Jiang, S.-D. et al. Series of lanthanide organometallic single-ion magnets. Inorg. Chem. 51, 3079–3087 (2012). Competing financial interests: The authors declare no competing financial interests. 24. Yamashita, K. et al. A luminescent single-molecule magnet: observation of magnetic anisotropy using emission as a probe. Dalton Trans. 42, 1987–1990 Reprints and permission information is available online at http://npg.nature.com/ (2013). reprintsandpermissions/ 25. Pointillart, F. et al. A series of tetrathiafulvalene-based lanthanide complexes displaying either single molecule magnet or luminescence—direct magnetic and How to cite this article: Chilton, N.F. et al. An electrostatic model for the determination photo-physical correlations in the ytterbium analogue. Inorg. Chem. 52, of magnetic anisotropy in dysprosium complexes. Nat. Commun. 4:2551 doi: 10.1038/ 5978–5990 (2013). ncomms3551 (2013). NATURE COMMUNICATIONS | 4:2551 | DOI: 10.1038/ncomms3551 | www.nature.com/naturecommunications 7 & 2013 Macmillan Publishers Limited. All rights reserved.

Journal

Nature Communications – Springer Journals

Published: Oct 7, 2013

There are no references for this article.