Spin–Electric Coupling in a Cobalt(II)‐Based Spin Triangle Revealed by Electric‐Field‐Modulated Electron Spin Resonance Spectroscopy

Abstract A cobalt(II)‐based spin triangle shows a significant spin–electric coupling. [Co3(pytag)(py)6Cl3]ClO4⋅3 py crystallizes in the acentric monoclinic space group P21. The intra‐triangle antiferromagnetic interaction, of the order of ca. −15 cm−1 (H=−JSaSb), leads to spin frustration. The two expected energy‐degenerate ground doublets are, however, separated by a few wavenumbers, as a consequence of magnetic anisotropy and deviations from threefold symmetry. The Co3 planes of symmetry‐related molecules are almost parallel, allowing for the determination of the spin–electric properties of single crystals by EFM‐ESR spectroscopy. The spin–electric effect detected when the electric field is applied in the Co3 plane was revealed by a shift in the resonance field. It was quantified as ΔgE/E=0.11×10−9 m V−1, which in terms of frequency corresponds to approximately 0.3 Hz m V−1. This value is comparable to what was determined for a Cu3 triangle despite the antiferromagnetic interaction being 20 times larger for the latter.

Dihedral angle ϑ (as defined in Figure S4) formed by the aromatic πplanes of the two pyridine coligands for all Co(II) centers in Co3P and Co3C (the latter are taken from ref. [1] ; see Figure S3 for an overlay of          Magnetic Susceptibility Measurements. A single crystal of Co3P was ground and placed in a gelatine capsule. Magnetic measurements were performed on a Quantum Design MPMS-5 SQUID magnetometer. Susceptibility data were obtained in the temperature range from 2 to 300 K at an applied dc field Hdc of 1000 Oe. The collected data were corrected for the diamagnetism of the sample holder, the capsule, and the diamagnetic contribution of the ligand. The fitting of the magnetic susceptibilty data with full matrix diagonalization was carried out using the program PHI in version 3.1.5. [2] Single Crystal and Powder CW X-Band ESR. A single crystal of Co3P was placed on a square acetate foil with Apiezon N vacuum grease and indexed with an SCD Oxford Xcalibu3 X-Ray diffractometer using a Cu source (Cu-Kα, λ = 1.54060 Å). Once the crystallographic orientations of the crystal were known, the crystal was mounted on an ESR support for single crystals and measured. For powder measurements, a single crystal of Co3P was ground and filled in an ESR tube. The measurements were performed on a Bruker E580 in an MS-5 resonator at 4.8 K with an exact microwave frequency of 9.4 GHz. Simulations of the obtained spectra were carried out using EasySpin. [3] Single Crystal Electric Field-Modulated X-Band ESR. For the experiments, a well-shaped single crystal of Co3P was picked and indexed on an X-ray diffractometer (same procedure as described for ESR measurements), so that the crystal could be positioned on the sample holder as described. The electric field modulated (EFM)-ESR measurements were performed with the setup as described in the literature. [4] EFM-ESR spectra were acquired with 100 times higher microwave power with respect to the ESR spectra. In order to improve the signal-to-noise ratio in the EFM-ESR measurements, several acquisitions were realized. The reported signal is the sum of all the acquisitions normalized to root square of the number of acquisition. All spectra were acquired at 20 K. The EFM-ESR measurements were acquired with the crystal axis � ⃗ parallel to the direction of Em and at 0° with respect to the direction of B0.
Computational Details. All computational structures for the theoretical studies are based on the atomic positions of the single crystal structure of Co3P. The positions of all hydrogen atoms were optimized with the Turbomole 7.2 package [5] of programs at RI-DFT [6] /BP86 [7,8] /def2-SVP [9] level of theory. Within these optimizations all cobalt(II) ions have been replaced by diamagnetic zinc(II) ions to reduce the computational effort. To study intra-molecular magnetic couplings broken-symmetry DFT (BSDFT) calculations have been performed on basis of the cationic dinuclear cobalt(II) model structures [Co2Zn(saltag)(Cl)3(py)6] + of Co3P (for computational models see Figure S7). BSDFT results are based on the B3LYP hybrid functional [7,10] in combination with the triple-ζ def2-TZVPP basis sets [9] and a tight SCF convergence criteria (10 −8 Hartree). The magnetic coupling constants were obtained by Yama- Single-ion anisotropies for the three crystallographically independent cobalt(II) ions in Co3P were calculated with the OpenMolcas package of programs in version 18.09 at CASSCF/CASPT2/SO-RASSI level of theory and the basis sets listed in Table S7. [12] For these calculations three mononuclear cobalt(II) model structures in which the two remaining paramagnetic ions have been replaced by diamagnetic zinc(II) ions. The mononuclear ab initio model structures are denoted as Co3P-Co1, Co3P-Co2, and Co3P-Co3, respectively, and visualized in Figure S9. State-average CASSCF calculations contained the 7 electrons of the 3d shell in 10 orbitals (3d and 4d shell) to adequately take the so-called 'double d-shell effect' into account [13] and were performed for 10 quartet ( 4 F, 4

Crystal Structure Description
Intermolecular π•••π stacking interactions can be observed in Co3P and are formed by the 2-pyridyl moiety of the chelate ligand, as is illustrated in Figure S2. This interconnects the trinuclear complex cations along the crystallographic ⃗ axis in a layered staircase-like manner. The respective distances between the π-planes show an average value of approximately 360 pm, which is a reasonable magnitude for π•••π stacking interactions. As a consequence, the closest intermolecular Co•••Co distance is found to be 815.1 pm.
The π-plane of the tritopic ligand pytag 2− features a minor bowl-shaped distortion, the terminal 2-pyridyl moieties protrude from the central triaminoguanidine plane. Therefore, the three pyridine co-ligands 'in the bowl' (the ones with donor atoms N10-N12) are packed closer than the ones on the opposite site of tritopic ligand (co-ligands with donor atoms N13-N15). Interestingly, the aromatic planes of the pyridine co-ligands 'in the bowl' in all three cases align along the direction of the respective Co-Cl bond, while the remaining other ones do not appear to have a preferential alignment.
Selected bond lengths and angles of the coordination environment for the three crystallographically independent cobalt(II) centers in Co3P are listed in Overall, the bond lengths and angles within the coordination spheres of the cobalt(II) centers are comparable to the ones in the structure of Co3C. [1] To further characterize and compare the distortion of the coordination geometry of the distinct cobalt(II) centers, continuous shape measures for Co3P have been undertaken. [16][17][18] The latter reveal deviation parameters from an ideal octahedron of S(Oh) = 2.514, 2.230, and 2.256 for Co1, Co2, and Co3, respectively (S(Oh) = 0 refers to an ideal octahedron). Those are by far the smallest deviation parameters in comparison to any other ideal coordination geometry given in Table S3. Hence, all three coordination polyhedra in Co3P can be regarded as moderately distorted octahedra, although atom Co1 shows a slightly higher distortion   Table S3.
An overlay representation of the complex cation [Co3(pytag)(py)6Cl3] + with the one found in Co3C is presented in Figure S3. It reveals only minor differences between the cationic complex molecules in Co3P and Co3C, for which the orientation of the axial pyridine coligands can be determined as the largest structural difference.

SUPPORTING INFORMATION
S14 Figure S2. Illustration of the π•••π stacking interactions in Co3P, which are emphasized by orange dashed bonds between the centroids of the involved aromatic rings. A staircase-like structure is formed along the crystallographic � �⃗ axis. Top: View along the crystallographic -� �⃗ axis, the cationic complex molecules including two unit cells along the a axis. Bottom: View along the crystallographic -�⃗ axis of the same ensemble of molecules. Hydrogen atoms, perchlorate anions, cocrystallized solvent molecules, and the axial pyridine co-ligands have been omitted for clarity. The color code of the molecules represents their relative position along the crystallographic �⃗ axis.  Table S3. Continuous shape measures for the metal ions in the two complexes Co3P and Co3C (a value S = 0 describes an ideal polyhedron; OC−6 = octahedron; TPR−6 = trigonal prism; PPY−6 = pentagonal pyramid; JPPY−6 = Johnson pentagonal pyramid; HP−6 = Hexagon) [16][17][18] OC-6 S(Oh)

SUPPORTING INFORMATION
S16 Figure S3. Overlay of the cationic complex structure [Co3(pytag)(py)6Cl3] + as found in Co3P (blue) and Co3C (red). The figure on the left-hand side shows a topview perspective and the right-hand side displays the triaminoguanidine-based ligand backbone with the axial pyridine co-ligands removed. Hydrogen atoms have been omitted for clarity.

SUPPORTING INFORMATION
S17 Figure S4. Schematic definition of the dihedral angle ϑ formed by the aromatic π-planes of the two pyridine co-ligands connected to a cobalt center (depiction: ϑ for Co1 in Co3P). Table S4. Dihedral angle ϑ (as defined in Figure S4) formed by the aromatic π-planes of the two pyridine co-ligands for all Co(II) centers in Co3P and Co3C (the latter are taken from ref. [1] ; see Figure S3 for an overlay of both cationic complex structures)

Description of the Hamiltonian used for fitting and simulation of the magnetic susceptibility
In the following part the single terms of the used Hamiltonian given in the main manuscript are shown and described in detail. In case of the magnetic exchange as defined in Equation (S2), a single isotropic coupling constant −Jex has been used in the model to avoid a potential overparametrization, which assumes an equilateral triangle spin topology for Co3P.
The spin-orbit contribution as represented by Equation (S3) includes the spin-orbit coupling constant for an octahedrally coordinated cobalt(II) ion in a weak ligand-field (λ = −171.5 cm −1 ). [19] The orbital-reduction parameter λ is a fit parameter (2/3 < λ < 1) and due to the structural similarity between all three cobalt(II) centers, again, has been condensed to a single parameter for all three ions.
The ligand-field splitting (LFS) of the three individual cobalt(II) centers in Co3P has been described by two extended Stevens opera- ) and the corresponding LFS parameters 2 0 and 2 2 , respectively (Equation (S4)).
[20] Based on the first LFS parameter, different types of magnetic anisotropy in the ground state KD can be described ( 2 0 < 0: easy axis; 2 0 > 0: easy plane; 2 0 = 0: isotropic). The second LF parameter 2 2 introduces a rhombic distortion of the magnetic anisotropy ( 2 2 ≠ 0). In addition, an Euler rotation (zxz' convention) as represented by the rotation matrix R � ( , ) is included to take the local magnetic anisotropy into account. The Euler angles of rotation αi are pre-determined due to an assumed C3 pseudo-symmetry in the fitting model (α1 = 0°; α2 = 120°; α3 = 240°). The Euler angle of rotation β describes the angle of intersection between the local magnetic z axis and the main rotational axis of the C3 pseudo-symmetry. A third Euler angle of rotation γ has not been applied, i.e. no rotation about the z' axis (γ = 0°).
The Zeeman effect for Co3P was taken into account by Equation (S5), in which µB is the Bohr magneton. The spin contribution includes the Landé factor of the free electron (g0 = 2.0023) and the orbital contribution is influenced by the orbital reduction factor κ.
Single-ion properties in terms of the relative ligand-field splitting of the 4 T1g[ 4 F] multiplet for the three cobalt(II) centers can be described by the combination of spin-orbit contribution and ligand-field splitting as given in Equation (S6).

SUPPORTING INFORMATION
S19 Figure S5. Experimental magnetic susceptibility (•) of Co3P in the low temperature regime between 2 and 30 K at an applied dc magnetic field of 1000 Oe. The solid red line shows the best-fit according to the Hamiltonian given in Equation (1) from the main manuscript, fitting parameter values are given in Table S55.  (1)        in Co3P (see also Table S11). Hydrogen atoms have been omitted for clarity.

SUPPORTING INFORMATION
S29 Figure Table S13. Overview of parameters used for simulations of the powder CW X-band ESR spectra of Co3P measured at T = 4.8 K for a pseudospin Seff = ½ formalism to represent the coupled ground state of the whole molecule with one set of g values (isotropic Voigtian (lwpp: Gaussian, Lorentzian [mT]) as well as anisotropic line broadening (Hstrain) were used; for information on the implementation of the parameters see the EasySpin documentation) [3] Seff ½

SUPPORTING INFORMATION
S30 Figure S14. Temperature dependence of normalized CW X-band ESR spectra of Co3P. The shape of the spectra does not show further change above 10 K, which is indicative for a nearly equal population of the two lowest lying molecular magnetic states KD1 and KD2. The resonance positions of ab initio (POLY_ANISO) calculated Cartesian components of the g values (see Table S12  (black line), � �⃗ at an angle of 10° with respect to B0 (blue line) and � �⃗ at an angle of 20° with respect to B0 (red line).