Zero-field Splitting Research Articles

Exploring High-Spin Color Centers in Wide Band Gap Semiconductors SiC: A Comprehensive Magnetic Resonance Investigation (EPR and ENDOR Analysis).

High-spin defects (color centers) in wide-gap semiconductors are considered as a basis for the implementation of quantum technologies due to the unique combination of their spin, optical, charge, and coherent properties. A silicon carbide (SiC) crystal can act as a matrix for a wide variety of optically active vacancy-type defects, which manifest themselves as single-photon sources or spin qubits. Among the defects, the nitrogen-vacancy centers (NV) are of particular importance. This paper is devoted to the application of the photoinduced electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques at a high-frequency range (94 GHz) to obtain unique information about the nature and properties of NV defects in SiC crystal of the hexagonal 4H and 6H polytypes. Selective excitation by microwave and radio frequency pulses makes it possible to determine the microscopic structure of the color center, the zero-field splitting constant (D = 1.2-1.3 GHz), the phase coherence time (T2), and the values of hyperfine (≈1.1 MHz) and quadrupole (Cq ≈ 2.45 MHz) interactions and to define the isotropic (a = -1.2 MHz) and anisotropic (b = 10-20 kHz) contributions of the electron-nuclear interaction. The obtained data are essential for the implementation of the NV defects in SiC as quantum registers, enabling the optical initialization of the electron spin to establish spin-photon interfaces. Moreover, the combination of optical, microwave, and radio frequency resonant effects on spin centers within a SiC crystal shows the potential for employing pulse EPR and ENDOR sequences to implement protocols for quantum computing algorithms and gates.

High-field/high-frequency electron spin resonances of Fe-doped β−Ga2O3 by terahertz generalized ellipsometry: Monoclinic symmetry effects

We demonstrate detection and measurement of electron paramagnetic spin resonances (EPR) of iron defects in β−Ga2O3 utilizing generalized ellipsometry at frequencies between 110 and 170 GHz. The experiments are performed on an Fe-doped single crystal in a free-beam configuration in reflection at 45∘ and magnetic fields between 3 and 7 T. In contrast with low-field, low-frequency EPR measurements, we observe all five transitions of the s=5/2 high-spin state Fe3+ simultaneously. We confirm that ferric Fe3+ is predominantly found at octahedrally coordinated Ga sites. We obtain the full set of fourth-order monoclinic zero-field splitting parameters for both octahedrally and tetrahedrally coordinated sites by employing measurements at multiple sample azimuth rotations. The capability of high-field EPR allows us to demonstrate that simplified second-order orthorhombic spin Hamiltonians are insufficient, and fourth-order terms as well as consideration of the monoclinic symmetry are needed. These findings are supported by computational approaches based on density-functional theory for second-order and on ligand-field theory for fourth-order parameters of the spin Hamiltonian. Terahertz ellipsometry is a way to measure spin resonances in a cavity-free setup. Its possibility of varying the probe frequency arbitrarily without otherwise changing the experimental setup offers unique means of truly disentangling different components of highly anisotropic spin Hamiltonians. Published by the American Physical Society 2024

Cobalt(II) Single-Ion Magnet Coordinated by Double Deprotonation of 2,2'-Bipyridine-6,6'-diol Ligands.

In this study, we synthesized a new Co(II) complex, [NMe4]2[Co(bpyO2)2] (1), using deprotonated 2,2'-bipyridine-6,6'-diol ligands (bpyO2 2-). This compound exhibits a significant zero-field splitting (D) value. The far-infrared magneto spectroscopy and high-frequency and field electron paramagnetic resonance (HFEPR) measurements indicated that compound 1 possesses D = -54.8 cm-1 and E ∼ 0 cm-1. These findings were subsequently confirmed by other experimental data, including DC magnetic susceptibilities and variable temperature and variable magnetic field reduced magnetizations. Additionally, we conducted a series of AC magnetic susceptibility measurements to investigate the kinetics of magnetization relaxation. Below 6.6 K and under zero external magnetic field, fast quantum tunneling of magnetization (QTM) dominates (∼570 Hz), and temperature-independent out-of-phase signals are observed. Above 8.1 K, temperature-dependent behavior is observed. Furthermore, we examined the AC magnetic susceptibility behavior under external magnetic fields ranging from 300 to 4000 G. The effect of QTM is significantly reduced in the presence of an external magnetic field. Temperature-dependent behavior is primarily governed by Raman relaxation. Through structural analysis of compound 1 and a series of pure nitrogen-coordinated single-ion magnets (SIMs), we propose that the oxo substituents from the double-deprotonated form of the 2,2'-bipyridine-6,6'-diol ligands donate their negative charge to the pyridine ring, forming amido anion sites. This triggers a more pronounced out-of-phase signal than that observed in pure pyridine-coordinated compounds. Moreover, we observed intermolecular interactions, including intermolecular hydrogen bonding, which, to some extent, influenced the slow relaxation of molecules. Therefore, we speculate that the slow relaxation phenomenon of compound 1 may be attributed to the combination of oxo back-donating effects and intermolecular interactions.

Axial Coordinated Manganese(III) Porphyrin/Tetraazaporphyrin - 4-(10-phenylanthracen-9-yl)Pyridine Dyads: Self-Assembly, Structure and Spectral Properties in Ground and Excited States.

Self-assembly of new donor-acceptor systems based on (5,10,15,20-tetraphenylporphinato)manganese(III)/(5,10,15,20-tetra-4-tert-butylphenylporphinato)manganese(III)/(octakis(4-tert-butylphenyl)tetraazaporphinato)manganese(III) acetate ((AcO)MnTPP/(AcO)MnTBPP/(AcO)MnTAP) and 4-(10-phenylanthracen-9-yl)pyridine (PyAn) was studied using fluorescence spectroscopy and mass spectrometry. It was found that the coordination complexes of 1 : 1 composition (dyads) are formed in toluene. The spectral properties, the chemical structures and redox behavior of the dyads were described using 1H NMR, IR, ESR spectroscopy and cyclic voltammetry, respectively. The dynamic processes and the characteristics in the excited state of the dyads were obtained using the femtosecond transient absorption spectroscopy method. Density functional theory (DFT), time-dependent DFT methods were used to elucidate the dyad electronic structures and to establish the differences in their frontier molecular orbitals. The analysis of the lambda parameter and the distance of hole-pair interaction was indicated more favorable charge transfer between the macrocycle and the axial PyAn fragment in (AcO)(PyAn)MnTAP. The calculated values of the zero-field splitting parameters D and E/D, together with the g tensors of the lowest spin-orbit state for (AcO)MnTPP and (AcO)(PyAn)MnTPP were obtained using the combination of DFT and Multireference Perturbation Theory (CASSCF/NEVPT2) simulations. The data obtained develop the fundamental basis in the field of photovoltaics and show the prospects for the study of molecular systems of this class.

Uhlmann phase of a thermal spin-1 system with zero field splitting

We study the Uhlmann geometric phase of a spin-1 particle subjected to zero-field splitting (ZFS) interaction, modulated by a dimensionless parameter α, under the effect of an external magnetic field with a tilting angle θ. We show that the ZFS term induces a transition in the geometrical phase behavior, characterized by a critical parameter value, α=αc. For α<αc, this phase displays two critical temperatures at θ=π/2, similar to spin-1 systems without ZFS, but with a separation that varies with α. In contrast, for α>αc, the phase exhibits two singularities at a single critical temperature but at different field orientations θ≠π/2. The phase disappears for significantly large |α|, regardless of the values of the Hamiltonian parameters. This behavior clearly departs from the usual thermal Uhlmann phase observed in SU(2) systems. In addition, we analytically calculate the heat capacity, which, for θ=π/2 and nearby values, displays two different regimes according to the sign of α. For α<0, it develops two peaks associated to the multilevel nature of the system, while for α>0 only a single Schottky-anomaly like peak appears as in two level systems. Interestingly, when θ=π/2, the temperature centroids of the Uhlmann phase and the heat capacity coincide in the region between critical temperatures for a given value of α<αc. Furthermore, we demonstrate that when α=0, the Uhlmann phase, a global topological property of the system, can be expressed as a function of the thermal component of the Bures metric, a local geometric property related to the heat capacity.

Understanding the multiplet fine structures of MgO: Cr3+ with combination method of first−principles calculations and ligand field theory

The interpretative and predictive capabilities on the energy fine structures of transition metal ions in solids are explored by integrating the first -principles calculations with ligand-field (LF) theory. The charge-compensated site of MgO: Cr3+ is chosen as a case and the aim is to determine the energy-level fine structure and EPR g factor g// and g⊥. The approach involves initially computing all the required parameters for LF theory through first-principles calculations, and these parameters are subsequently fed into the LF model Hamiltonian, which fully incorporates interactions between different spectrum terms through the LF operator, spin-orbit coupling (SOC) operator and other relevant factors. The calculated zero-field splitting parameter D and g factors of the ground term A24(t23) are reasonably good agreement with the experimental observations. However, the energy levels of excited states are slightly underestimated compared to experimental values due to the underestimation of Racah parameters in the first-principles calculations, except the T24[t22(T13)e] term which is insensitive to Racah parameters for it is equal to 10Dq relative to ground term A24(t23) with possible minor corrections due to perturbations.

DFT investigation of [formula omitted]-split interstitial paramagnetic centers in diamond

The density functional theory (DFT) method, in combination with the cluster approach, has been utilized to investigate a series of paramagnetic interstitial defects in diamond with an electron spin of S = 1. A good correlation has been achieved between simulated and experimental zero-field splitting D-tensor eigenvalues and eigenvectors for the paramagnetic centers R2, R1, and O3, identified previously as 100-split interstitial, di-100-split interstitial, and planar three-100-split interstitial, respectively. Based on the calculations, two new configuration models have been proposed for the low-symmetry centers R13 and R3, as configurations of non-planar three- and five-100-split interstitial, respectively. The formation energies for the series of defects under study have been evaluated, suggesting that the aggregation of split interstitial fragments is energetically favored.

Assessment of Iron-Based Spin-Orbit Coupling Effects in Pt-Fe Heterobimetallic Lantern Complexes via 57Fe Mössbauer Spectroscopy.

A series of heterobimetallic lantern complexes, [PtFe(SOCR)4(pyX)] where R = Me, X = H (1), X = NH2 (2), X = SMe (3); R = Ph, X = H (4), X = NH2 (5), X = SMe (6), have been prepared and characterized spectroscopically. Compounds 1, 4, and 5 are reported herein for the first time. The high-spin iron(II) sites of 1-6 have been investigated using 57Fe Mössbauer spectroscopy. Although the isomer shift of these species is nearly identical, their quadrupole splitting exhibits a much larger variation. Moreover, the zero-field Mössbauer spectra of 3-5 show surprising changes over time which are likely indicative of small structural distortions. The field dependent Mössbauer study of 1 and 6 revealed a zero field splitting (ZFS) characterized by a relatively large and positive D value. The combined Density Functional Theory (DFT) and ab initio Complete Active Space Self-Consistent Field (CASSCF) investigation of 1-6 indicates that their ground state is best described using a linear combination of {|xz⟩, |yz⟩} states. Our theoretical analysis suggests that the ZFSs and magnitude of the quadrupole splitting of 1-6 are determined by the spin-orbit coupling of the three lowest orbital states which have a T2g parentage.

Exploring the Triplet State of Chlorophyll a in Mesoporous Silica Matrices by Time-Resolved EPR

Chlorophyll is a pivotal molecule in photosynthesis due to its ability to absorb solar light and start the photochemical process. The chlorophyll triplet state is easily populated from the light-induced singlet excited state via Intersystem Crossing (ISC) and can react with oxygen generating singlet oxygen, posing a threat to the stability of chlorophyll, but also an opportunity for photodynamic therapy. Here, we focus on the study of the photo-physical properties of chlorophyll a and WSCP (Water-Soluble Chlorophyll Protein, a protein binding the pigment), which have been adsorbed in mesoporous silica matrices. We adopt SBA-15, a silica matrix with well-ordered hexagonal structure with pores of 70 Å of diameter. The triplet formed upon illumination in these systems is studied by time-resolved EPR spectroscopy. Analysis of the EPR spectra shows that the triplet state is very sensitive to the inclusion in the pores of SBA-15 modifying its spin polarization. Chl a in SBA-15 loses its central metal ion, while its structure remains unchanged if the mesoporous silica is previously soaked into a basic solution before Chl a adsorption, as revealed by its zero-field splitting parameters of the triplet state. WSCP is readily included in the silica matrix, but its embedded pigments are no longer protected by the protein core.

Relationship between Structure and Zero-Field Splitting of Octahedral Nickel(II) Complexes with a Low-Symmetric Tetradentate Ligand

Octahedral nickel(II) complexes are among the simplest systems that exhibit zero-field splitting by having two unpaired electrons. For the purpose of clarifying the relationship between structure and zero-field splitting in a low-symmetric system, distorted octahedral nickel(II) complexes were prepared with a tetradentate ligand, 2-[bis(2-methoxyethyl)aminomethyl]-4-nitrophenolate(1−) [(onp)−]. The complex [Ni(onp)(dmso)(H2O)][BPh4]·2dmso (1) (dmso = dimethyl sulfoxide) was characterized as a bulk sample by IR, elemental analysis, mass spectrometry, electronic spectra, and magnetic properties. The powder electronic spectral data were analyzed based on the angular overlap model to conclude that the spectra were typical of D4-symmetric octahedral coordination geometry with a weak axial ligand field. Simultaneous analysis of the temperature-dependent susceptibility and field-dependent magnetization data yielded the positive axial zero-field splitting parameter D (H = guβSuHu + D[Sz2 − S(S + 1)/3]), which was consistent with the weak axial ligand field. Single-crystal X-ray analysis revealed the crystal structures of [Ni(onp)(dmso)(H2O)][BPh4]·dmso (2) and [Ni(onp)(dmf)2][BPh4] (3) (dmf = N,N-dimethylformamide). The density functional theory (DFT) computations based on the crystal structures indicated the D4-symmetric octahedral coordination geometries with weak axial ligand fields. This study also showed the importance of considering g-anisotropy in magnetic analysis, even if g-anisotropy is small.

A novel non-adiabatic spin relaxation mechanism in molecular qubits.

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

Unravelling the Highest Magnetic Anisotropy Among all the nd-Shells in [WCp2]0 Metallocene.

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

Can Iron-Porphyrins Behave as Single-Molecule Magnets?

The study of magnetic properties, especially the magnetic anisotropy of iron-porphyrin complexes employing multiconfigurational methods, is quite challenging due to many strongly correlated electrons in nearly degenerate orbitals. However, a prerequisite for observing the magnetic anisotropy and slow magnetization relaxation, the zero-field splitting parameter, D, was experimentally observed decades ago for halide-based axially ligated penta-coordinate Fe(III)-porphyrins. In these complexes, the signs of D were reported mostly as positive; in a few cases, inconclusive signs of the D parameter were also mentioned. However, no ab initio calculations have been reported to shed light on this. Deciphering the electronic structure of these penta-coordinated complexes employing the complete active space self-consistent field method and N-electron valence second-order perturbation theory, we confirm the positive D values. However, a negative D value is highly desired to observe the single-molecule magnet properties without an external magnetic field, which we observed in the Fe(II)-porphyrin complexes with axial imidazole ligands instead of halide ligands. The detailed analysis of the multireference wave functions unravels the role of axial ligands in determining the sign and magnitude of the D parameters.

Zero-Field Splitting Tensor of the Triplet Excited States of Aromatic Molecules: A Valence Full-π Complete Active Space Self-Consistent Field Study.

A method to predict the D tensor in the molecular frame with multiconfigurational wave functions in large active space was proposed, and the spin properties of the lowest triplets of aromatic molecules were examined with full-π active space; such calculations were challenging because the size of active space grows exponentially with the number of π electrons. In this method, the exponential growth of complexity is resolved by the density matrix renormalization group (DMRG) algorithm. From the D tensor, we can directly determine the direction of the magnetic axes and the ZFS parameters, D- and E-values, of the phenomenological spin Hamiltonian with their signs, which are not usually obtained in ESR experiments. The method using the DMRG-CASSCF wave function can give correct results even when the sign of D- and E-values is sensitive to the accuracy of the prediction of the D tensor and existing methods fail to predict the correct magnetic axes.

Air-Stable Dinuclear Complexes of Four-Coordinate ZnII and NiII Ions with a Radical Bridge: A Detailed Look at Redox Activity and Antiferromagnetic Coupling.

Air-stable dinuclear complexes [(bmsab)NiII(tmsab)NiII(bmsab)]3- and [(bmsab)ZnII(tmsab)ZnII(bmsab)]3- (bmsab = bis(methanesulfoneamido)benzene, tmsab = tetra(methanesulfonamido)benzene) were prepared via a synthetic route based on heteroleptic precursor complexes. The new complexes combine a distorted tetrahedral coordination environment with an open-shell bridging ligand. The ZnII species was subjected to a detailed investigation of the (spectro-)electrochemical processes. The NiII species is a rare example of a complex that combines strong exchange coupling (J > 440 cm-1) with pronounced positive zero-field splitting (D = +72 cm-1). Combining SQUID magnetometry and (HF)EPR spectroscopy with ab initio calculations allowed for accurate quantification of the exchange interaction.

Oxygen-Donor Metalloligands Induce Slow Magnetization Relaxation in Zero Field for a Cobalt(II) Complex with {CoO4} Motif.

Most 3d metal-based single-molecule magnets (SMMs) use N-ligands or ligands with even softer donors to impart a particular coordination geometry and increase the zero-field splitting parameter |D|, while complexes with hard O-donor ligands showing slow magnetization relaxation are rare. Here, we report that a diamagnetic NiII complex of a tetradentate ligand featuring two N-heterocyclic carbene and two alkoxide-O donors, [LO,ONi], can serve as a {O,O'}-chelating metalloligand to give a trinuclear complex [(LO,ONi)Co(LO,ONi)](OTf)2 (2) with an elongated tetrahedral {CoIIO4} core, D = -74.3 cm-1, and a spin reversal barrier Ueff = 86.9 cm-1 in the absence of an external dc field. The influence of diamagnetic NiII on the electronic structure of the {CoO4} unit in comparison to [Co(OPh)4]2- (A) has been probed with multireference ab initio calculations. These reveal a contrapolarizing effect of the NiII, which forms stronger metal-alkoxide bonds than the central CoII, inducing a change in ligand field splitting and a 5-fold increase in the magnetic anisotropy in 2 compared to A, with an easy magnetization axis along the Ni-Co-Ni vector. This demonstrates a strategy to enhance the SMM properties of 3d metal complexes with hard O-donors by modulating the ligand field character via the coordination of diamagnetic ions and the benefit of robust metalloligands in that regard.

Coordination complexes of reduced organic dye isoviolanthrone with transition metals and lanthanides [Mn(II), Dy(III), Gd(III), Nd(III)

The reduction of a vat dye isoviolanthrone to the dianion state in the presence of metal-containing compounds yields binuclear coordination complexes. Two manganese(II) acetylacetonate units coordinate to isoviolanthrone2− (L) in {(K+)cryptand}2{[MnII(acac)2]2⋅L}2– (1) with an average Mn–O bond length of 2.022(2) Å. Dysprosium(III)- or gadolinium(III)-2,2,6,6-tetramethyl-3,5-heptanedionate (TMHD) units form {(K+)cryptand}2{[MIII(TMHD)3]2⋅L}2− (M = DyIII for 2 and GdIII for 3) with the length of the M−O bonds of 2.193(3) and 2.254(4) Å, respectively. Tris(cyclopentadienyl)neodymium(III) forms {(Cs+)cryptand}2{[Cp3NdIII]2⋅L}2–⋅C6H4Cl2 (4) with the Nd–O bonds of 2.264(2) and 2.308(2) Å length. The formation of isoviolanthrone2− is supported by their optical spectra, disappearance of the bands of the CO vibrations in the IR-spectra as well as elongation of the CO bonds in 1–4. High-spin (S = 5/2) MnII atoms in 1 have exchange interaction of J = − 0.122 cm−1 at g = 1.98. Lanthanides have weaker coupling through isoviolanthrone2− in 2 and 3 with J = − 0.029 and D = − 0.004 cm−1 for DyIII and J = 0.0019 cm−1 for GdIII. Complex 4 with two Cp3NdIII species demonstrates the χMT value of 2.33 emu⋅K/mol at 300 K, and this value is lower than the theoretically calculated value of 3.39 emu⋅K/mol. The decrease of χMT is observed in the whole 300–1.9 K range providing negative Weiss temperatures of –32 K. That is explained by magnetic behavior of Cp3NdIII similar to pristine Cp3NdIII. Complexes comprising MnII, GdIII, and NdIII show electron paramagnetic resonance (EPR) signals. Zero-field splitting (ZFS) is observed from MnII and GdIII allowing the estimation of zero-field splitting parameter D as − 0.047 and E close to 0 cm−1 for 1 and − 0.033 and − 0.020 cm−1 for 3. Complex 4 with NdIII manifests an asymmetric two-component EPR signal without ZFS. Weak antiferromagnetic couplings are explained by diamagnetism of isoviolanthrone2− and rather long distances between the metal centers of 15.47–16.25 Å. This study shows that the dianions of organic dyes are promising bidentate ligands for preparation of coordination complexes with d- and f-block metal ions.

Electronic Structure of Three-Coordinate FeII and CoII β-Diketiminate Complexes.

The β-diketiminate supporting group, [ArNCRCHCRNAr]-, stabilizes low coordination number complexes. Four such complexes, where R = tert-butyl, Ar = 2,6-diisopropylphenyl, are studied: (nacnactBu)ML, where M = FeII, CoII and L = Cl, CH3. These are denoted FeCl, FeCH3, CoCl, and CoCH3 and have been previously reported and structurally characterized. The two FeII complexes (S = 2) have also been previously characterized by Mössbauer spectroscopy, but only indirect assessment of the ligand-field splitting and zero-field splitting (zfs) parameters was available. Here, EPR spectroscopy is used, both conventional field-domain for the CoII complexes (with S = 3/2) and frequency-domain, far-infrared magnetic resonance spectroscopy (FIRMS) for all four complexes. The CoII complexes were also studied by magnetometry. These studies allow accurate determination of the zfs parameters. The two FeII complexes are similar with nearly axial zfs and large magnitude zfs given by D = -37 ± 1 cm-1 for both. The two CoII complexes likewise exhibit large and nearly axial zfs, but surprisingly, CoCl has positive D = +55 cm-1 while CoCH3 has negative D = -49 cm-1. Theoretical methods were used to probe the electronic structures of the four complexes, which explain the experimental spectra and the zfs parameters.

Spectroscopic and Theoretical Investigation of High-Spin Square-Planar and Trigonal Fe(II) Complexes Supported by Fluorinated Alkoxides.

The electronic structures and spectroscopic behavior of three high-spin FeII complexes of fluorinated alkoxides were studied: square-planar {K(DME)2}2[Fe(pinF)2] (S) and quasi square-planar {K(C222)}2[Fe(pinF)2] (S') and trigonal-planar {K(18C6)}[Fe(OC4F9)3] (T) where pinF = perfluoropinacolate and OC4F9 = tris-perfluoro-t-butoxide. The zero-field splitting (ZFS) and hyperfine structure parameters of the S = 2 ground states were determined using field-dependent 57Fe Mössbauer and high-field and -frequency electron paramagnetic resonance (HFEPR) spectroscopies. The spin Hamiltonian parameters were analyzed with crystal field theory and corroborated by density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) calculations. Whereas the ZFS tensor of S has a small rhombicity, E/D = 0.082, and a positive D = 15.17 cm-1, T exhibits a negative D = -9.16 cm-1 and a large rhombicity, E/D = 0.246. Computational investigation of the structural factors suggests that the ground-state electronic configuration and geometry of T's Fe site are determined by the interaction of [Fe(OC4F9)3]- with {K(18C6)}+. In contrast, two distinct countercations of S/S' have a negligible influence on their [Fe(pinF)2]2- moieties. Instead, the distortions in S' are likely induced by the chelate ring conformation change from δλ, observed for S, to the δδ conformation, determined for S'.

Paramagnetic Nuclear Magnetic Resonance Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods.

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals (LHFs) is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes zero-field splitting (ZFS), hyperfine coupling (HFC), and the g-tensor. For consistency, we calculate these three tensors at the same level of theory, i.e., using scalar-relativistic X2C augmented with spin-orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the HFC constant is large. For small HFC constants, the relative error is often large, and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with a very large ZFS and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows use of large basis sets for converged HFCs. Overall, current-dependent meta-generalized gradient approximations and LHFs show some potential; however, the currently available functionals leave a lot to be desired, and the predictive power is limited.