Analysis of the Magnetic Exchange Interactions in Yttrium(III) Complexes Containing Nitronyl Nitroxide Radicals

HAL Id: hal-01544247 https://hal-univ-rennes1.archives-ouvertes.fr/hal-01544247 Submitted on 13 Sep 2017 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Analysis of the Magnetic Exchange Interactions in Yttrium(III) Complexes Containing Nitronyl Nitroxide Radicals Julie Jung, Marin Puget, Olivier Cador, Kevin Bernot, Carmen J. Calzado, Boris Le Guennic To cite this version: Julie Jung, Marin Puget, Olivier Cador, Kevin Bernot, Carmen J. Calzado, et al.. Analysis of the Magnetic Exchange Interactions in Yttrium(III) Complexes Containing Nitronyl Nitroxide Radicals. Inorganic Chemistry, American Chemical Society, 2017, 56 (12), pp.6788-6801. �10.1021/acs.inorgchem.6b02952�. �hal-01544247� Analysis of the Magnetic Exchange Interactions in Yttrium(III) Complexes Containing Nitronyl Nitroxide Radicals Julie Jung,†,‡Marin Puget,¶Olivier Cador,†Kevin Bernot,∗,¶Carmen J. Calzado,∗,§and Boris Le Guennic∗,† Institut des Sciences Chimiques de Rennes, UMR 6226 CNRS, Université de Rennes 1, 263 Avenue du Général Leclerc, 35042 Cedex Rennes, France, Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr, Germany, INSA, Institut des Sciences Chimiques de Rennes UMR CNRS 6226, 35708 Rennes, France, and Departamento de Química Física. Universidad de Sevilla. c/ Prof. García González, s/n. 41012 Sevilla, Spain E-mail: [email protected]; [email protected]; [email protected] Abstract We report a combined theoretical and experimental investigation of the exchange interactions governing the magnetic behavior of a series of nitronyl-nitroxide (NIT)- based Y(III) complexes, i.e. Y(hfac)3(NIT-R)2with R = PhOPh (1), PhOEt (2) and PhOMe (3a,3b). Even if some of these complexes or their Dy(III) parents were already described in the literature [Zhao et al. Trans. Met. Chem. 2006,31, 593; Bernot et ∗To whom correspondence should be addressed †Université de Rennes ‡Present address: Max Planck Institut für Chemische Energiekonversion ¶INSA de Rennes §Universidad de Sevilla 1 al. J. Am. Chem. Soc. 2009,131, 5573], their synthesis procedure as well as their structural and magnetic properties were completely reconsidered. Depending on the nature of R and of crystallization conditions, Y(hfac)3(NIT-R)2units can be organized as supramolecular dimers, linear or orthogonal chains. Such structural diversity within the series induces extremely different magnetic behaviors. The observed behaviors are rationalized by state-of-the-art wave-function-based quantum chemical approaches (CASSCF/DDCI) that demonstrate the existence of effective intra-molecular interactions between the NIT-R radical ligands of an isolated Y(hfac)3(NIT-R)2molecule, but also between NIT-R moieties belonging to different Y(hfac)3(NIT-R)2units. These results are supported by the use of spin Hamiltonian models going beyond the basic Bleaney-Bowers formalism to properly fit the experimental magnetic data. Finally, the microscopic mechanisms behind the evidenced intramolecular exchange interactions are elucidated through the inspection of the calculated wave-function. In particular, whereas the role of Y orbitals was already proposed, we herein demonstrate the contribution of the hfac−ancillary ligands in mediating the magnetic interaction between the NIT radicals. 2 1. Introduction Since the early 90’s the magnetic behavior of isolated molecules has caught much attention.1The discovery of molecules that present magnetic bistability of molecular origin2made molecular magnetism emerge as an intense field of research.3In particular, Single Molecule Magnets (SMMs) have been evidenced as particularly suitable entities for information storage and processing,4spintronic,5–8 or cryogenic9devices. Basically, SMM behavior is achieved in molecules having both a strongly axial magnetic anisotropy and a high energy barrier to the reversal of their magnetic moment.10,11 While the former property guarantees magnetic bistability by making the ground state a doublet and prevents fast relaxation in this doublet ground state by limiting the mixing between the two associated sub-states, the latter establishes the temperature window within which slow relaxation can be observed. Ultimately, the relaxation rate is only determined by the spin-phonon coupling mechanisms involved in the magnetic relaxation, which are completely system-dependent since correlated to the vibrations of both the molecule and the lattice. The optimization of the performance of SMMs, especially the temperature window where they depict magnetic slow relaxation, can be achieved through different strategies. The first and simplest one consists in synthesizing poly-nuclear complexes12 in order to increase the overall anisotropy of the molecule but the correlation between the anisotropy (D) and the total spin (S) of the molecule make this strategy hard to achieve13 provided that the respective arrangement of the ions is carefully controlled.14,15 A second approach is to use highly symmetrical and rigid ligands to carefully engineer ligand field and favor stabilization of ground-state magnetic moment along a defined axis.16 This approach is particularly suitable for SMMs that use highly anisotropic lanthanide ions as spin carriers.17 A third route is based on the use of isotopically-pure metal ion derivatives that avoid spontaneous loss of the magnetic bistability in zero-field.18,19 Finally, a last strategy relies on the use of radical ligands that can induce strong magnetic exchange between anisotropic spin carriers.20,21 One of the best examples of the latter strategy is given by the N3− 2radical-bridged terbium(III) 3 complex by J. R. Long and coworkers,22–24 which remains among the SMMs with the highest working temperature available to date. Among well-known organic radicals, nitronyl-nitroxides (NIT) are particularly appealing since they allow to obtain edifices of various dimensionalities. In these architectures, significant magnetic coupling can be observed that induces 0-, 1-, 2- or 3-dimensional overall magnetic behaviors.25–33 Such materials can also give rise to unique magnetic behavior such as next-nearest neighbor interactions,34 one-dimensional helimagnetism35–37 or Single Chain Magnets (SCMs) behavior.38–40 Among the latter class of compounds, SCMs of formula [Ln(hfac)3(NIT-PhOPh)]∞, where hfac−= hexafluoroacetylacetonate and NIT-PhOPh = 2,4’-benzoxo-4,4,5,5-tetramethyl-imi-dazoline-1-oxyl-3-oxide, were found to have a quite complex magnetic behavior41 and deep investigation of their monomeric constitutive units was necessary for its rationalization.42 From the pioneering work by Benelli, Caneschi and Gatteschi on the Ln(hfac)3(NIT-R)2compounds, it appears that the coupling interaction between the lanthanide ion and the radical ligand (Ln–NIT) can be either ferromagnetic (FM) or antiferromagnetic (AFM) depending on the nature of the lanthanide ion while magnetic interaction between the two radical ligands (NIT–NIT) is always found antiferromagnetic.25,34,43–48 Rationalization of these exchange interactions has been performed initially using angular overlap analysis.25,46 On the basis of Y(hfac)3(NIT-R)2investigations, three possible mechanisms for the NIT–NIT interaction have been proposed: (i) direct exchange, (ii) super-exchange through the metal ion and (iii) super-exchange through the non-radical hfacligands.45–47 However, definitive validation of the magnetic coupling mechanisms in these relatively simple units is still lacking. This is due, on the one hand, to the peculiar electronic structure of the lanthanide ions that induces great variety of magnetic coupling mechanisms (isotropic and anisotropic exchange, dipolar coupling...)49 and on the other hand, on the numerous exchange pathways potentially responsible for the overall magnetic behavior. Fundamentally, magnetic exchange is related to electronic repulsion and more precisely 4 to the Fermi hole surrounding the electrons. This interaction is thus mediated through electronic spin.49 From the computational point of view, as for magnetic anisotropy or ligand-field effects,50–54 procedures to investigate magnetic exchange rely on the use of a model Hamiltonian which is derived either from chemical intuition or using the effective Hamiltonian theory.55,56 In the simplest case, i.e. two half spins interacting isotropically, magnetic exchange can then be effectively described using the Heisenberg-Dirac-Van Vleck Hamiltonian. Yet, as soon as spin-orbit coupling (SOC) or local anisotropy arises, this Hamiltonian needs to be further refined,57 which can complicate greatly the physical picture of the system. As a consequence, ab initio calculations can become quite intricate, especially for lanthanidebased complexes, where SOC and magnetic anisotropy are rather strong. The approach is further complicated since lanthanide ions interact rather poorly through magnetic exchange with other spin-carriers such as transition metals or organic radicals, with coupling constants not exceeding 10 cm−1. This is mainly because the 4f shell of lanthanide trivalent ions is quite efficiently shielded by the outter 5s and 5d shells. This is the main reason why there are to date very few in-depth theoretical studies of magnetic exchange in lanthanide or more generally rare earth-based complexes.58,59 For all these reasons, and as highlighted by Benelli and coworkers, an alternative approach consists in studying first magnetic exchange in diamagnetic derivatives such as Y(III), La(III) or Lu(III). Consequently, to disentangle all the relative contributions to magnetic exchange in the Ln(hfac)3(NIT-R)2family, the complex Y(hfac)3(NIT-PhOPh)2has been chosen as target compound for the present study.42 The magnetic behavior is then dominated by intramolecular interactions between the radicals. However, uncoordinated NO groups are known to bear non-negligible electronic density60–62 and their respective geometric arrangement and distances in the crystal packing can give rise to sizeable intermolecular magnetic interactions (NIT· · · NIT interactions) that may compete with the intramolecular (NIT–NIT) ones. We have thus chosen to use different substituents on the aliphatic group of the nitronyl-nitroxide radical to afford structural diversity to our study. Three different substitutions in para position of the phenyl ring have 5 been explored affording three derivatives of formula Y(hfac)3(NIT-R)2with R = PhOPh (1), PhOEt (2)42 and PhOMe (3a,63 3b) (Scheme 1). They present very different supramolecular architectures, from dimers to linear or orthogonal chains, with a wide range of intermolecular distances (from 2.80 to 4.26 Å). Consequently, our study goes far beyond the investigation of SCM monomer’s and a simple description of these systems through HDVV Hamiltonian. In fact, high level ab initio calculations provide a reliable qualitative and quantitative picture of the magnetic behavior. Moreover, insights on the microscopic mechanisms responsible for the through-yttrium magnetic interactions in this series of complexes are provided. Scheme 1: Schematic representation of the nitronyl-nitroxide radical ligands used. Corresponding complexes of formula Y(hfac)3(NIT-R)2for R = PhOPh, PhOEt and PhOMe are named 1,2,3a and 3b, respectively. 2. Experimental section Synthesis and X-ray Crystallography Crystallization procedures for Y(hfac)3(NIT-R)2species vary drastically depending of both the nature of the -R substituent and the crystallization temperature (Tcrist). For R = PhOPh, crystals could be obtained only for the Dy derivative (1’, CCDC-1519869). Powders of 1 are found isostructural to 1’ by comparison with their powder X-ray diffraction patterns (Figure S1). For R = PhOEt, only one species, 2, is obtained whatever Tcrist.42 For R = PhOMe, if Tcrist < 5◦C, the already reported compound 3a is mainly obtained (CCDC- 178130),63 whereas for Tcrist = 20◦C a majority of crystals of 3b are found. Scanning of the 6 crystallization temperature conditions does not optimize the 3a/3b ratio. Single crystals of all derivatives were mounted on a APEXII AXS-Bruker diffractometer (150K) with Mo Kαradiation (λ= 0.71073 Å). Data reduction and cell refinement were performed with Denzo and Scalepack programs.64 The crystal structures have been solved by direct methods using SIR97 program,65 and refined with full matrix least-square methods based on F2(SHELX97)66 with WINGX program.67 All non-hydrogen atoms were refined anisotropically using SHELXL program. Hydrogen atoms bound to the organic ligand were located at ideal positions. Final structure refinement data of four derivatives are listed in Tables S1 and S2. Full details of the X-ray structure determination of the four crystal structures have been deposited at the Cambridge Crystallographic Data Center under the depository numbers CCDC-1519220 for 2and CCDC-1519219 for 3b. They can be obtained free of charge at http://www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cambridge Crystallographic Data Centre, 12, Union Road, Cambridge CB2 IEZ, UK; fax: (internat.) +44-1223/336-033; E mail: dep[email protected]), on request, from the authors and the reference to this publication. Powder X-ray diffraction diagram of 1has been collected at room temperature using a PanalyticalX’Pert Pro diffractometer equipped with an X’Celerator detector. Calculated pattern of 1’ was produced using Mercury 3.0 program. Magnetic measurements Magnetic measurements were performed on powder pellets with a MPMS Quantum Design magnetometer between 2 and 300K. All measurements have been corrected from sample holder contribution and from diamagnetic contributions as calculated by Pascal’s constants. 7 Computational details Ab initio calculations All magnetic coupling constants have been evaluated by mean of Difference Dedicated Configuration Interaction (DDCI) calculations,68,69 as implemented in the CASDI suite of programs.70,71 The DDCI method is a multireference approach in which the wavefunction is defined by a combination of Slater determinants built from single and double excitations of the CASSCF wavefuntion. Contrary to the CASSCF approach only the wavefunction coefficients are optimised variationally in the DDCI method, making the calculation dependent on the initial set of orbitals. The excitations are organized according to the number of particles (p) and holes (h) they create in either the inactive or the virtual space, which gives rise to four different levels of calculation: (i) CASCI, which is the reference calculation with no excitations included, (ii) CAS+S, where only the 1h, 1p and 1h1p excitations are included, (iii) DDC2, where the 2h and 2p excitations are added, and (iv) DDCI, where the 2h1p and 1h2p excitations are also included.55 Since the same set of MOs is used to described the different spin states of the system, the 2h2p excitations are not included because they do not change the relative energies of the states that are considered.68,69 In the end, the DDCI method is a very accurate variational approach for dynamical correlation, which has already been shown to be effective in quantitatively computing magnetic coupling constants in transition metal compounds of various dimensionalities but also in organic crystals.55 In this work, the common set of MOs is generated at the CASSCF level of theory. The MOs are then classified as active, occupied inactive and virtual orbitals, following their occupation in the reference CASSCF wavefunction. To decrease the computational cost, the core orbitals are not included in the DDCI calculations. The size of the active space (CAS(n,m) including nelectrons in morbitals) and the nature of the active orbitals are discussed more deeply in the Results and Discussion section. The CASSCF calculations and 8 with Jspace the through-space coupling constant. We are then considering a linear tetramer of coupled spins. The magnetic susceptibility can be calculated and then compared to experiment by numerical diagonalization of the Hamiltonian matrix. The best fit is represented on Figure 3 with parameters given in Table 1. Interestingly, Jspace is still antiferromagnetic but one order of magnitude larger than Jbond, whereas the latter remains of the same order of magnitude than in the three previously discussed compounds. This strengthens our belief in the numerical approach we used. Furthermore, if one suppose that the role of the interactions should be inverted (the stronger within a dimer and the weaker between dimers), the blue curve on Figure 3 is obtained, that is far away from the experimental one. As for 3b, a relatively large amount of paramagnetic impurities must be included to properly reproduce the experiment (Table 1). Since crystals of 3a and 3b have been collected by hands, we cannot discard the possibility of pollution of one sample by the other, and thus the larger the amount of 3a in 3b (and vice et versa), the smaller the gvalue. Ab initio determination of the coupling constants for the NIT–NIT interactions in compound 1 Through-bond NIT–NIT interaction An isolated NIT radical possesses three electrons in its valence shell, two of them occupying the antibonding πorbitals of the NO groups, and one the 2pzorbital of the conjugated central C atom (Scheme 2). The combination of these local orbitals gives rise to three molecular orbitals (MOs), φb,φSOMO and φ∗ b, as represented in the right-hand side of Scheme 2. The distribution of the three valence electrons in these MOs gives a doublet ground state. As discussed elsewhere,62,83,84 the largest contribution to the doublet wavefunction corresponds to the determinant with two electrons in the φborbital and one unpaired electron occupying the φSOMO orbital. Hence, the study of the interaction between two NIT radicals can be attempted at first 15 Scheme 2: Schematic representation of the πorbitals for an isolated NIT unit.83 Figure 4: CAS(2/2)SCF MOs of the excited triplet state for the NIT-Y-NIT model in compound 1. 16 using the minimal active space, with two unpaired electrons in the two φSOMO orbitals, i.e. a CAS(2/2). The active MOs are obtained from a CAS(2/2)SCF calculation on either the ground singlet state (S) or on the excited triplet state (T). As shown in Figures 4 and S3, the active MOs correspond to the bonding (φ1) and antibonding (φ2) combinations of the φSOMO orbitals of each NIT group. They are almost identical for the (S) and (T) states, since in both cases, the electronic density is mostly localized on the external NO groups. The Jbond values computed for the through-bond interaction with these two sets of orbitals are shown in Table 2. Even at the best level of calculation, the ab initio Jbond values are significantly smaller than that obtained from the fitting procedure. Such strong underestimation is particularly surprising at the DDCI level, where the key effects of dynamical correlation are taken into account and thus leading to Jvalues in good agreement with the experimental values, at least in transition metal complexes.55 However, this underestimation correlates well with the strong localization of the electron density on the external NO groups. Previous calculations on organic biradicals presented also this unusual behavior ,62,83,85,86 and two different strategies have been adopted in the literature to overcome this problem: (i) to extend the active space by including all the valence πelectrons and orbitals for each NIT radical, i.e. to use a CAS(6/6),62,83,84 and (ii) to still rely on the minimal active space, but using an optimized set of MOs instead of the CASSCF ones which are excessively localized on the external NO moieties.85,87–89 Here one should mention that increasing the quality of the basis sets, i.e. [4s3p1d] contraction for all C and O atoms (see Computational details), induces only a variation of ∼5% of the calculated values. Table 2 shows the results obtained when using the CAS(6/6) extended active space. As previously, the MOs employed in the CI calculations come from CAS(6/6)SCF calculations on either the singlet ground state or the triplet excited state. The six active MOs of the triplet state are shown in Figure 5. Similar shapes are found for the singlet MOs. Comparing with Figure 4, a larger electron delocalization on the central NO groups is observed, which 17 Table 2: Calculated magnetic coupling constants Jbond (cm−1) for the NIT–Y–NIT model. In parenthesis, the values obtained with a CAS(2/2) using the CAS(6/6)SCF MOs. DDCI(6/6) values were not obtained due to computational limitations. CAS Singlet MOs Triplet MOs SA-7:3 singlet MOs Natural DDCI MOs (2/2) CASCI -0.4 -0.4 -1.8 -1.4 CAS+S -1.1 -1.1 -3.8 -4.4 DDC2 -1.4 -1.2 -5.3 -5.9 DDCI -2.6 -2.4 -8.8 -7.9 (6/6) CASCI -0.7 (-1.3) -1.0 (-1.3) CAS+S -1.7 (-1.8) -2.1 (-2.6) DDC2 -2.5 (-2.4) -2.3 (-3.0) DDCI – (-4.2) – (-4.0) Jexp -15.6 can be directly related to the improvement – with respect to the experimental value – of the calculated Jbond values. Nonetheless, the best estimate (i.e. -4.2 cm−1) is still far of being quantitative since it only represents 25%of the experimental value. It is worth mention that this slight improvement is not related directly to the CAS extension itself but to the larger delocalization of the density observed in the two singly occupied MOs (φ3and φ4in the top of Figure 5), as demonstrated by the Jbond values in parenthesis in Table 2. It is also supported by the comparison between the spin density associated to the CAS(2/2) and CAS(6/6) triplet calculations (Figure S4). These Jbond values have been obtained on the basis of the CAS(6/6)SCF MOs, but including in the CI active space only the two singly occupied orbitals (i.e. orbitals φ3and φ4). The present results strongly suggest that the failure of the CI calculation is not related to the size of the active space but to the quality of the MOs. Thus, we decided to focus on optimizing the MOs within the frame of the minimal CAS. To this end, two options have been explored, both providing quite similar active MOs and hence close Jbond values (see Table 2). First, averaged natural orbitals were built from the density matrices of the singlet and triplet states at the DDCI(2/2) level. The resulting MOs are employed in subsequent DDCI calculations until convergence (iterative DDCI or IDDCI 18 (a) CAS(6/6)SCF singlet MOs (b) Natural IDDCI(2/2) MOs (c) CAS(2/2)SCF SA 7:3 singlet MOs Figure 5: (a) CAS(6/6)SCF MOs of the triplet state for the NIT–Y–NIT model in compound 1with occupations 1.89 (φ1), 1.88 (φ2), 1.00 (φ3), 1.00 (φ4), 0.11 (φ5) and 0.12 (φ6). φ3 and φ4MOs correspond to the symmetric and antisymmetric combinations of the SOMO of each NIT radical. (b) Averaged natural orbitals from the density matrices of the singlet and triplet states at DDCI(2/2) level. (c) CAS(2/2)SCF MOs of the SA 7:3 singlet wavefunction for the NIT–Y–NIT model in compound 1. 19 calculations).90 This procedure has been shown to be efficient in eliminating any dependence of the DDCI results on the starting MOs, taking into account the orbital relaxation induced by the electron correlation. The shape of the so-obtained MOs is represented in Figure 5, the most relevant feature being the enhancement of the electron density on the central NO groups, which is in line with the increase of the calculated Jbond value at DDCI(2/2) level (Table 2). Alternatively, Angeli and Calzado have shown recently that it is possible to reproduce the natural DDCI magnetic orbitals with a simple state average CAS(2/2)SCF calculation, that mixes the singlet ground state (essentially represented by the neutral configuration, i.e. with one electron per magnetic site) and the excited ionic singlet states (the two active electrons on the same magnetic site).87 This mixing induces the stabilization of the ionic states, which are usually too high in energy at the CASSCF level, allowing for the relaxation of the active orbitals, and thus providing a nice improvement of the calculated J values at MRPT2 level. In this previous work,87,91 a 7:3 mixture of the neutral:ionic singlet states gave magnetic orbitals showing a large overlap with the DDCI natural MOs. The same mixture was used here and the so-obtained active orbitals are shown in Figure 5, with very similar features to those obtained from the IDDCI approach. The DDCI Jbond value with these SA-7:3 MOs (i.e. -8.8 cm−1) is then closely similar to that obtained with the natural MOs (i.e. -7.9 cm−1). Unfortunately, there are no experimental data available with respect to the spin density in compound 1or any other of the compounds investigated in the present work, which could validate the shape of the optimized magnetic MOs. Tentative polarized neutron diffraction (PND) measurements were carried out with no concluding results to date. However, for the free NIT radical and for Cu(hfac)2(NIT-Ph)2compound, which can be seen as a Cu(II) analogue of compound 1, such data are available.60,61 In the former case, the spin density is equally delocalized on the two -NO groups of each NIT radical, while in the latter case, it is more delocalized on the outer -NO group of each NIT radical, with only a small contribution on the nitrogen atom of the -NO moiety linked to the Cu(II) ion. Since the Cu(II) 20 ion interacts rather strongly, i.e. covalently, with the NIT radical61 while the Y(III)–NIT interaction is mainly electrostatic, one may expect that the spin density distribution in 1is somewhere in between the two extreme pictures from the free NIT radical on one side and the Cu(hfac)2(NIT-Ph)2compound on the other side. Thus, one may be confident in the distribution obtained either with natural or SA MOs (Figure 5b,c). In the end, compared to the fitted Jvalue (-15.6 cm−1), our best ab initio estimate (-8.8 cm−1) represents only 55% of this value, a notably larger deviation than expected for this method, which as already stated, cannot be attributed to the structural simplifications associated to the NIT–Y–NIT model (see Supporting Information). Through-space NIT· · · NIT interactions The unexpected disagreement between the calculated and the fitted Jvalues for 1impels us to look for additional exchange interaction pathways able to explain the experimental thermal dependence of the susceptibility curve (Figure 3). Looking at the X-ray structure, three different through-space pathways are explored. They are illustrated in Figure 6. All of them involve two NIT radical groups coordinated to different but close Y(hfac)3moieties. In these three pathways, the NIT radical ligands are separated by 3.74 Å, 8.56 Å and 8.90 Å, respectively. In the particular case of Pathway #2, to rule out any important contribution of the phenyl rings directly bound to the imidazole backbones to the exchange interaction through π-stacking interactions or electronic delocalization, two NIT–NIT models are considered: (i) the one classically used in this study (as described in Computational details) and (ii) a second one including explicitly these phenyl rings (one for each NIT radical ligand). The through-space NIT· · · NIT interactions are evaluated using the approach that was most satisfactorily in the previous section, i.e. DDCI(2/2) on the basis of CASSCF SA-7:3 singlet MOs. For all pathways, the active orbitals correspond to the symmetric and antisymmetric combinations of the SOMOs of each NIT radical (Figure S5). As for the through-bond 21 (a) Pathway #1 (b) Pathway #2 (c) Pathway #3 Figure 6: Through-space exchange pathways for 1. Same color code as in Figure 1. NIT–NIT interaction, using the CASSCF SA-7:3 singlet MOs allows for a better description of the magnetic orbitals, with almost equal electron delocalization over the two -NO groups of each NIT radical. For Pathways #2 (with and without the phenyl rings) and #3 the computed coupling constants are almost null (-0.0 cm−1and +0.1 cm−1, respectively), while for Pathway #1 the computed coupling constant results in a small but non-negligible antiferromagnetic interaction, with a Jvalue of -3.6 cm−1. First of all, these results prove the effectiveness of the through-space interactions pathways in the overall magnetic behavior of 1 since the intensity of the through-space NIT· · · NIT interaction is more than 2/5 that of the through-bond NIT–NIT interaction. Though, the strength of the through-space NIT· · · NIT interaction seems to decrease quite fast with increasing distance, since going from -3.6 cm−1 to zero while the NIT· · · NIT distance goes from about 3.5 Å to about 8.5 Å. Fitting of the susceptibility curves The presence of a magnetic pathway (Pathway #1) connecting two neighbor NIT-Y(hfac)3- NIT units questions the suitability of the Bleaney-Bowers model to fully represent the mag- 22 netic interactions in 1, despite the high quality of the fitting based on this model (Figure 3). Indeed, in this model the magnetic behavior can only be attributed to isolated NIT-Y(hfac)3- NIT units where the two NIT radicals are coupled antiferromagnetically, i.e. taking only into account the through-bond NIT–NIT interaction with J= -15.6 cm−1. On the other hand, the Hatfield model corresponds to a 1D magnetic chain with alternating exchange interactions decribed by two parameters J1and J2, such as J2=αJ1(see Supporting Information).1The green curve in Figure 7 is obtained with this model using the calculated through-bond and through-space Jvalues, i.e. Jbond = -8.8 cm−1and Jspace = -3.6 cm−1, respectively, and α = 0.409. The fact that this curve predicts a larger χvalue than the experimental one indicates that the magnetic interactions are underestimated in our computational protocol. By increasing these values by a factor of 1.5 (i.e. with Jbond and Jspace raised to -13.2 cm−1and -5.4 cm−1, respectively) a better agreement with the experimental χvs T curve is obtained (blue curve in Figure 7). This result suggests that, even at the DDCI level of calculation, the computed Jvalues are underestimated by about 35%. 23 Figure 7: Plots of χMand χMTas a function of temperature for compound 1with simulated curves using the Hatfield model and the calculated Jvalues (green curve; Jbond = -8.8 cm−1, Jspace = -3.6 cm−1) and J∗1.5values (blue curve; Jbond = -13.2 cm−1and Jspace = -5.4 cm−1). Both curves have been simulated using the experimental gvalue (g= 1.98). To summarize, this result indicates that (i) for both the through-bond and through-space NIT–NIT interactions, the computed Jvalues are underestimated; (ii) once the calculated Jvalues are corrected, a model based on an alternating 1D chain can accurately reproduce the experimental dependence of the magnetic response with temperature; (iii) the Bleaney- Bowers model has to be considered as an effective model, able to reproduce the overall experimental behavior, but not as a realistic picture of the different interactions operating in 1. 24 (a) (b) (c) Figure 8: Through-space pathways (O· · · O distances in blue) for 2(a), 3a (b) and 3b (c). distances are 4.261 Å and 2.805 Å for 2and 3a, respectively. For 2, the calculated coupling is very weak (Jspace = -0.5 cm−1), as expected for such a large separation between the NIT units. From this, the Bleaney-Bowers model used experimentally seems to be appropriate to analyse the magnetic behavior of compound 2. However, as for 1, the magnetic curves can also be simulated by taking into account all the calculated magnetic interactions using the Hatfield model (Figure S8). Here again, the calculated Jvalues have to be slightly corrected for a better agreement with experiment. For 3a, on the other hand, the through-space NIT· · · NIT interaction is far from negligible since a strong antiferromagnetic interaction is found (Jspace = -144 cm−1, Table 4). This is undoubtedly related to the very short distance and the 180◦between the planes containing the NIT radicals, that favors an efficient overlap between the πorbitals (Figure 9). Importantly, these results well support the experimental interpretation with a much larger through-space than through-bond interaction (Table 4). 31 (a) (b) (c) Figure 9: CAS(2,2)SCF SA-7:3 singlet MOs (φ1and φ2) for the through-space NIT· · · NIT interaction in 2(a), 3a (b) and 3b (c). For 3b, as shown in Figure 8, the two interacting NIT radicals lie perpendicularly and the shortest inter-molecular NIT· · ·NIT distance is 3.309 Å. Here, the calculated interaction is found ferromagnetic with a Jspace value of 19.6 cm−1(Table 4). This quite large ferromagnetic interaction is induced by the orthogonality of the magnetic orbitals (Figure 9). Remarkably, this through-space NIT· · · NIT interaction is of the same order of magnitude as the throughbond NIT–NIT interaction (Jbond = -10.2 cm−1). Similarly to 1, from the magnetic point of view, 3b can thus be seen as a magnetic 1D chain with alternating interactions, but this time, with both ferromagnetic (intermolecular) and antiferromagnetic (intramolecular) interactions.107 The curve simulated with these calculated Jvalues (Figure S9) does not reproduce the experimental one as good as for 1and 2. However, this behavior was certainly expected for two well-separated reasons. From the computational point of view, it is well recognized that ferromagnetic interactions are often overestimated,55 while experimentally, it has been evidenced (See Magnetic properties Section) that both 3b and 3a are always present in the samples. 32 4. Conclusions and perspectives To conclude, through a combined theoretical and experimental investigation of a series of yttrium-based complexes containing NIT radicals, we show that through-bond and throughspace NIT–NIT interactions can both be effective as soon as the inter-molecular NIT· · · NIT distance remains smaller than 4-5 Å. This second interaction pathway strongly questions the up-to-now systematic use of the Bleaney-Bowers model to analyse the magnetic interactions in such complexes through fitting of the experimental data. Indeed, even if this model leads to a good quality fit, it does not give a realistic physical picture of the magnetic system. In this, state-of-the-art ab initio calculations, even if not fully quantitative, are the best tools to avoid loss of information but also potential over-parametrization. Thanks to orbital localization procedures, we elucidate the microscopic mechanisms behind the through-bond NIT–NIT interaction, for which a predominant role is played by the π orbitals of the hfac−ligand orthogonal to the O1-O2direction. Though, one should keep in mind that this mechanism might not hold similarly for the isostructural lanthanide derivatives of the Y(hfac)3(NIT-R)2compounds studied here. Indeed, in other trivalent lanthanide ions, contrary to the Y(III) ion and even if shielded by the outer shells, the 4f orbitals are not empty and could be involved in the NIT–NIT interaction mechanisms, maybe through spin-polarization effects, as suggested by Benelli and Gatteschi,46 but also through the empty 6s, 6p and 5d shells which have a larger radical expansion than the 4f shell. To support this hypothesis of non-transferability, one could refer to the work by Sutter and Kahn.92–95 Using the HDVV Hamiltonian, they extract the coupling constant in isostructural Y(III), La(III) and Lu(III) complexes, which are all diamagnetic but with different electronic structures (empty 4f shell in Y(III) and La(III) while completely filled in Lu(III)). Surprisingly, the coupling constants are not identical for all complexes, suggesting different operating mechanisms. In addition, contrary to the mechanism evidenced here, most of the mechanisms discussed in the litterature for Ln(hfac)3(NITR)2complexes involve either the half-filled 4f orbitals or the virtual 5d and 6s orbitals of the lanthanide ion.25,27,34,43,46,47,92–95 To get a 33 clearer picture of the through-bond NIT–NIT interaction in these lanthanide derivatives, and clarify whether or not the lanthanide orbitals are involved in the exchange mechanism, we are currently investigating the Gd(III) analogue of 1. 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Chem. 1994,33, 5171–5175. 47 Graphical TOC Entry Combined theoretical (CASSCF/DDCI) and experimental investigations of a series of yttrium-based complexes containing nitronyl-nitroxide radicals (NIT) demonstrate that through-bond and through-space interactions can be effective for intermolecular distances as high as 5 Å. Orbital localization procedure highlights that πorbitals of hfac−ligands play a predominant role in mediating the through-bond NIT-NIT interaction. 48