Hyperfine Coupling Tensors Research Articles

Electric Field Dependence of EPR Hyperfine Coupling Constants.

In this article, we introduce a simple but reliable method to calculate the electric field dependence of the isotropic hyperfine coupling tensor Aiso for free radicals. This dependence, also referred to as the Bloembergen effect, can be of interest in analyzing EPR experiments for solid-state materials but is rarely studied for isolated radicals in the gaseous phase. The proposed method uses the numerical differentiation of the field-perturbed A tensor and, consequently, as a purely numerical method, does not depend on a quantum chemical method used to determine the hyperfine tensor A. To test the performance of the proposed method, we used a set of 28 systems, including seven organic radicals, the majority of which were taken from a recent benchmark study by Bartlett's group. We employed the well-tested and robust density functional theory (DFT) functional, namely CAM-B3LYP, and the variant of the CCSD method based on local pair natural orbitals, namely DLPNO-CCSD to calculate the Aiso tensor itself, and all first derivatives or Bloembergen effect constants ai(1).

A combined solid-state 1H, 13C, 17O NMR and periodic DFT study of hyperfine coupling tensors in paramagnetic copper(II) compounds

We report solid-state 1H, 13C, and 17O NMR determination of hyperfine coupling tensors (A-tensors) in several paramagnetic Cu(II) (d9, S = 1/2) complexes: trans-Cu(DL-Ala)2·H217O, Cu([1–13C]acetate)2·H2O, Cu([2–13C]acetate)2·H2O, and Cu(acetate)2·H217O. Using these new experimental results and some A-tensor data available in the literature for trans-Cu(L-Ala)2 and K2CuCl4·2H2O, we were able to examine the accuracy of A-tensor computation from a periodic DFT method implemented in the BAND program. We evaluated A-tensors on 1H (I = 1/2), 13C (I = 1/2), 14N (I = 1), 17O (I = 5/2), 39K (I = 3/2), 35Cl (I = 3/2), and 63Cu (I = 3/2) nuclei over a range spanning more than 3 orders of magnitude. We found that the BAND code can reproduce reasonably well the experimental results for both A-tensors and nuclear quadrupole coupling tensors.

Electron Spin Resonance Spin Probe Technique for Investigating Non‐TEMPO Radicals Dispersed in Nanospaces of a Crystalline Zn Complex

An ESR spin probe technique with non‐TEMPO radicals, such as nitronyl nitroxide (NN), benzonitronyl nitroxide (BzNN), and iminonitroxide (IN) radicals, was used for a porous metal‐organic framework (MOF), [(ZnI2)3(TPT)2] (ZnTPT; TPT = tris(4‐pyridyl)‐1,3,5‐triazine), at room temperature. The principal values of g and hyperfine coupling (A) tensors estimated from spectral reproduction were different from those for organic matrices for some of these radicals. These results indicate that host‐guest interactions occur between the ZnTPT matrix and guest radicals. Thus, when using NN, BzNN, and IN radicals as spin probes for a porous MOF, the interaction between the metal atoms or organic ligands in host materials and guest radicals should be considered. The experimental ESR spectra for the derivatives of NN or BzNN radicals were reproduced only by the rigid‐limit component in the ESR time scale. However, those for the derivatives of IN radicals were approximately reproduced only by rotational diffusion around the z‐axis perpendicular to the plane in the IN group. Interestingly, this reproduction was not around the y‐axis of the principal axes of the g tensors, parallel to the molecular long axis, as previously observed in a few organic matrices. The IN radicals dispersed in the ZnTPT matrix are expected to be accommodated in cylindrical or pseudocylindrical nanospaces sandwiched by the pyridyl or triazine rings of TPT in ZnTPT. These findings show that the ESR spin probe technique using non‐TEMPO radicals can be used to investigate the chemical and biological structures of nanosized materials.

Solid-state 35/37 Cl NMR detection of chlorine atoms directly bound to paramagnetic cobalt(II) ions in powder samples.

We report high-quality solid-state 35/37 Cl NMR spectra for chlorine atoms directly bonded to paramagnetic cobalt(II) ions (high spin S = 3/2) in powered samples of CoCl2 , CoCl2 ·2H2 O, CoCl2 ·6H2 O, and CoCl2 (terpy) (terpy = 2,2':6',2″-terpyridine). Because solid-state 35/37 Cl NMR spectra for paramagnetic cobalt(II) compounds often cover an extremely wide spectral range, they were recorded in this work in the form of variable-offset cumulative spectra. Solid-state 35/37 Cl NMR measurements were performed at three magnetic fields (11.7, 14.1, and 16.5T) and analysis of data yielded information about 35/37 Cl quadrupole coupling and hyperfine coupling tensors in these paramagnetic cobalt(II) compounds. Experimental 35/37 Cl NMR tensors were found to be in reasonable agreement with quantum chemical calculations based on a periodic DFT method implemented in BAND.

High-Throughput Search for Triplet Point Defects with Narrow Emission Lines in 2D Materials.

We employ a first-principles computational workflow to screen for optically accessible, high-spin point defects in wide band gap, two-dimensional (2D) crystals. Starting from an initial set of 5388 point defects, comprising both native and extrinsic, single and double defects in ten previously synthesized 2D host materials, we identify 596 defects with a triplet ground state. For these defects, we calculate the defect formation energy, hyperfine (HF) coupling, and zero-field splitting (ZFS) tensors. For 39 triplet transitions exhibiting particularly low Huang-Rhys factors, we calculate the full photoluminescence (PL) spectrum. Our approach reveals many spin defects with narrow PL line shapes and emission frequencies covering a broad spectral range. Most of the defects are hosted in hexagonal BN (hBN), which we ascribe to its high stiffness, but some are also found in MgI2, MoS2, MgBr2 and CaI2. As specific examples, we propose the defects vSMoS0 and NiSMoS0 in MoS2 as interesting candidates with potential applications to magnetic field sensors and quantum information technology.

The electronic structure and dynamics of the excited triplet state of octaethylaluminum(III)-porphyrin investigated with advanced EPR methods

The photoexcited triplet state of octaethylaluminum(III)-porphyrin (AlOEP) was investigated by time-resolved Electron Paramagnetic Resonance, Electron Nuclear Double Resonance and Electron Spin Echo Envelope Modulation in an organic glass at 10 and 80 K. This main group element porphyrin is unusual because the metal has a small ionic radius and is six-coordinate with axial covalent and coordination bonds. It is not known whether triplet state dynamics influence its magnetic resonance properties as has been observed for some transition metal porphyrins. Together with density functional theory modelling, the magnetic resonance data of AlOEP allow the temperature dependence of the zero-field splitting (ZFS) parameters, D and E, and the proton AZZ hyperfine coupling (hfc) tensor components of the methine protons, in the zero-field splitting frame to be determined. The results provide evidence that the ZFS, hfc and spin–lattice relaxation are indeed influenced by the presence of a dynamic process that is discussed in terms of Jahn-Teller dynamic effects. Thus, these effects should be taken into account when interpreting EPR data from larger complexes containing AlOEP.

Characterization by ENDOR Spectroscopy of the Iron–Alkyl Bond in a Synthetic Counterpart of Organometallic Intermediates in Radical SAM Enzymes

Members of the radical S-adenosyl-l-methionine (SAM) enzyme superfamily initiate a broad spectrum of radical transformations through reductive cleavage of SAM by a [4Fe-4S]1+ cluster it coordinates to generate the reactive 5'-deoxyadenosyl radical (5'-dAdo•). However, 5'-dAdo• is not directly liberated for reaction and instead binds to the unique Fe of the cluster to create the catalytically competent S = 1/2 organometallic intermediate Ω. An alternative mode of reductive SAM cleavage, especially seen photochemically, instead liberates CH3•, which forms the analogous S = 1/2 organometallic intermediate with an Fe-CH3 bond, ΩM. The presence of a covalent Fe-C bond in both structures was established by the ENDOR observation of 13C and 1H hyperfine couplings to the alkyl groups that show isotropic components indicative of Fe-C bond covalency. The synthetic [Fe4S4]3+-CH3 cluster, M-CH3, is a crystallographically characterized analogue to ΩM that exhibits the same [Fe4S4]3+ cluster state as Ω and ΩM, and thus an analysis of its spectroscopic properties─and comparison with those of Ω and ΩM─can be grounded in its crystal structure. We report cryogenic (2 K) EPR and 13C/1/2H ENDOR measurements on isotopically labeled M-CH3. At low temperatures, the complex exhibits EPR spectra from two distinct conformers/subpopulations. ENDOR shows that at 2 K, one contains a static methyl, but in the other, the methyl undergoes rapid tunneling/hopping rotation about the Fe-CH3 bond. This generates an averaged hyperfine coupling tensor whose analysis requires an extended treatment of rotational averaging. The methyl group 13C/1/2H hyperfine couplings are compared with the corresponding values for Ω and ΩM.

Incommensurate Magnetic Order in Sm3BWO9 with Distorted Kagome Lattice

We investigate the magnetic ground state of Sm3BWO9 with a distorted kagome lattice. A magnetic phase transition is identified at T N = 0.75 K from the temperature dependence of specific heat. From 11B nuclear magnetic resonance measurements, an incommensurate magnetic order is shown by the double-horn type spectra under a c-axis magnetic field, and absence of line splitting is observed for field oriented within the ab-plane, indicating the incommensurate modulation of the internal field strictly along c-axis. From the spin dynamics, the critical slowing-down behavior is observed in the temperature dependence of 1/T 1 with μ 0 H⊥c-axis, which is completely absent in the case with μ 0 H||c-axis. Based on the local symmetry of 11B sites, we analyze the hyperfine coupling tensors and propose two constraints on the possible magnetic structure. The single ion anisotropy should play an important role in determination of contrasting ground states of Sm3BWO9 and Pr3BWO9.

Site-Dependent Local Spin Susceptibility and Low-Energy Excitation in a Weyl Semimetal WTe2

Site-dependent local spin susceptibility is investigated with $^{125}$Te nuclear magnetic resonance in a Weyl semimetal WTe$_2$. The nuclear spin-lattice relaxation rate $1/T_1T$ shows a dependence of the square of temperature $T$ at high temperatures, followed by a constant behavior below 50 K. The temperature dependence features Weyl fermions appearing around the linearly crossing bands. The Knight shift $K$ scales to the square root of $1/T_1T$, corroborating a predominant spin contribution in low-lying excitation. The observed dependence of $K$ and $1/T_1T$ on the four Te sites shows the site-dependent electron correlation and density of states. The angular profile of the NMR spectrum gives the anisotropic hyperfine coupling tensor, consistent with $5p$ hole occupations on Te sites.

Radicals in ammonium tartrate at 295 K by X-radiation: Revised radical structures by EMR and DFT analyses

The simple amino acid l-α-alanine (ala) in polycrystalline form was among the first substances to be proposed and subsequently developed for Electron Paramagnetic Resonance (EPR)-based solid state radiation dosimetry. One disadvantage with ala is a relatively low sensitivity for doses below a few gray (Gy) which is a dose range of particular interest in medical, accident and environmental applications. A number of other compounds have been screened and some of these have shown a better sensitivity to radiation exposure than ala, in some cases up to a factor of 7–8. In particular ammonium tartrate (AT) and lithium formate (LiFo) have been taken into practical use. The present work was initially aimed to investigate the low-temperature radical products in AT, and the reactions leading to the product of dosimetric interest at room temperature. As a part of these studies, the previously characterized major room temperature radical product was re-investigated using single crystal electron magnetic resonance (EMR) techniques combined with periodic density functional theory (DFT) -type quantum chemical calculations. Surprisingly, this study showed that the molecular structure of the dominant radical at room temperature is somewhat different from that previously proposed. Furthermore, a second room temperature radical, previously not well characterized, was carefully investigated and three hyperfine coupling tensors were determined. These three tensors were sufficient to simulate all experimental observations for the second radical but not alone sufficient to permit an unambiguous molecular structure of the defect to be determined. It appears that the EPR resonance from this radical does not influence the dosimetric potential of AT.

Primary donor triplet states of Photosystem I and II studied by Q-band pulse ENDOR spectroscopy

The photoexcited triplet state of the “primary donors” in the two photosystems of oxygenic photosynthesis has been investigated by means of electron-nuclear double resonance (ENDOR) at Q-band (34 GHz). The data obtained represent the first set of 1H hyperfine coupling tensors of the 3P700 triplet state in PSI and expand the existing data set for 3P680. We achieved an extensive assignment of the observed electron-nuclear hyperfine coupling constants (hfcs) corresponding to the methine α-protons and the methyl group β-protons of the chlorophyll (Chl) macrocycle. The data clearly confirm that in both photosystems the primary donor triplet is located on one specific monomeric Chl at cryogenic temperature. In comparison to previous transient ENDOR and pulse ENDOR experiments at standard X-band (9–10 GHz), the pulse Q-band ENDOR spectra demonstrate both improved signal-to-noise ratio and increased resolution. The observed ENDOR spectra for 3P700 and 3P680 differ in terms of the intensity loss of lines from specific methyl group protons, which is explained by hindered methyl group rotation produced by binding site effects. Contact analysis of the methyl groups in the PSI crystal structure in combination with the ENDOR analysis of 3P700 suggests that the triplet is located on the Chl aʹ (PA) in PSI. The results also provide additional evidence for the localization of 3P680 on the accessory ChlD1 in PSII.

Addressing Single Nuclear Spins Quantum Memories by a Central Electron Spin

Nuclei surrounding single electron spins are valuable resources for quantum technology. For application in this area, one is often interested in weakly coupled nuclei with coupling strength on the order of a few 10–100 kHz. In this paper, we compare methods to address single nuclear spins with this type of hyperfine coupling to a single electron spin. To achieve the required spectral resolution, we specifically focus on two methods, namely dynamical decoupling and correlation spectroscopy. We demonstrate spectroscopy of two single nuclear spins and present a method to derive components of their hyperfine coupling tensor from those measurements.

Characterization of a Triplet Vinylidene

Singlet vinylidenes (R2C=C:) are proposed as intermediates in a series of organic reactions, and very few have been studied by matrix isolation or gas-phase spectroscopy. Triplet vinylidenes, however, featuring two unpaired electrons at a monosubstituted carbon atom are thus far only predicted as electronically excited-state species and represent an unexplored class of carbon-centered diradicals. We report the photochemical generation and low-temperature EPR/ENDOR characterization of the first ground-state high-spin (triplet) vinylidene. The zero-field splitting parameters (D = 0.377 cm–1 and |E|/D = 0.028) were determined, and the 13C hyperfine coupling tensor was obtained by 13C-ENDOR measurements. Most strikingly, the isotropic 13C hyperfine coupling constant (50 MHz) is far smaller than the characteristic values of triplet carbenes, demonstrating a unique electronic structure which is supported by quantum chemical calculations.

Characterization of the negatively charged NV defect through the spin density distribution and the hyperfine coupling constants

The spin density function and hyperfine coupling constants of the NV− defect (a vacancy with one nitrogen atom as a first neighbor) in its triplet ground state, are computed by using hybrid functionals, a Gaussian type all electron basis set, the supercell scheme (216 atoms before the defect formation), and the CRYSTAL code. The charged defect has been simulated by using the charge compensated (CC) scheme, in which a background of positive charge is added to restore the neutrality of the unit cell. The local geometry, charge and spin distribution are also reported and discussed. The EPR constants (Fermi contact, the hyperfine coupling and electric field gradient tensors) of the N (both 14N and 15N) and of two C (for the 13C isotope) atoms around the vacancy are in excellent agreement with the recent experimental results by Felton et al. (Phys. Rev. B, 79,075 203, 2009). The comparison is extended to the many other experimental data collected in the last 30 years, to simpler functionals (LDA and PBE), larger supercells (512 atoms), and to recent simulations. It is shown that the present results are much closer to experiment than previous theoretical studies, with a quantitative, rather than qualitative, agreement.

The NV0 defects in diamond: A quantum mechanical characterization through its vibrational and Electron Paramagnetic Resonance spectroscopies

The NV0 defect in diamond has been investigated quantum-mechanically, by analyzing its structural, electronic, vibrational and magnetic properties. The possible spin states for NV0 are a quartet NVq0 (4A2 symmetry) and a doublet (2E symmetry). In the latter state a single electron occupies a double degenerate level producing a Jahn Teller distortion that removes the degeneracy and lowers the total energy. The symmetry reduces from C3v to CS and two local minima are indeed identified, to be indicated as NVd10 (2A′ symmetry) and NVd20 (2A″ symmetry). NVd10 is the ground state, and is more stable than NVq0 by ~ 0.5 eV, and than NVd20 by ~ 0.2 eV, irrespective of the functional or basis set adopted.The EPR hyperfine coupling tensor has been computed for NVq0 and has been found to be in excellent agreement with available experimental data. The IR spectra of the NV defects (the three neutral cases and also the negatively charged one, for comparison) show specific peaks and shape that characterize each system and differentiate the spectra according to the spin and charge state. The Raman spectra of the NV0 defects shows a single peak, redshifted with respect to the single peak of pristine diamond by 2 cm−1 only, but in turn well separated from the negatively charged form of the defect.

Molecular Optimization for Nuclear Spin State Control via a Single Electron Spin Qubit by Optimal Microwave Pulses: Quantum Control of Molecular Spin Qubits

Quantum state control is one of the most important concepts in advanced quantum technology, emerging quantum cybernetics and related fields. Molecular open shell entities can be a testing ground for implementing quantum control technology enabling us to manipulate molecular spin quantum bits (molecular spin qubits). In well-designed molecular spins consisting of unpaired electron and nuclear spins, the electrons and nuclear spins can be bus and client qubits, respectively. Full control of molecular spin qubits, in which client spins interact via hyperfine coupling, is a key issue for implementing quantum computers (QCs). In solid-state QCs, there are two approaches to the control of nuclear client qubits, namely, direct control of nuclear spins by radio-wave (RF) pulses and indirect control via hyperfine interactions by microwave pulses applied to electron spin qubits. Although the latter is less popular in the literature, the indirectness has advantage of greatly reducing unnecessary interactions between a qubit system and its environment. In this work, we investigate molecular spin optimization to find optimal experimental conditions which can afford to achieve the high fidelity of quantum gates by the indirect control scheme. In the present quantum systems, one electron is directly controlled by pulsed ESR techniques without manipulating individual hyperfine resonance, but the states of two nuclear client spins are indirectly steered via hyperfine interactions. Single crystals of potassium hydrogen maleate (KHM) radical and 13C-labeled malonyl radical are chosen as typical molecular spin qubits which exemplify the importance of the symmetry of hyperfine tensors and their collinear properties. We have found that both the non-collinearity of the principal axes of hyperfine coupling tensors and the non-distinguishability/non-equivalency between nuclear spins are key issues which extremely reduce the gate fidelity.

Experimental and Theoretical Evidence for an Unusual Almost Triply Degenerate Electronic Ground State of Ferrous Tetraphenylporphyrin.

Iron porphyrins exhibit unrivalled catalytic activity for electrochemical CO2-to-CO conversion. Despite intensive experimental and computational studies in the last 4 decades, the exact nature of the prototypical square-planar [FeII(TPP)] complex (1; TPP2- = tetraphenylporphyrinate dianion) remained highly debated. Specifically, its intermediate-spin (S = 1) ground state was contradictorily assigned to either a nondegenerate 3A2g state with a (dxy)2(dz2)2(dxz,yz)2 configuration or a degenerate 3Egθ state with a (dxy)2(dxz,yz)3(dz2)1/(dz2)2(dxy)1(dxz,yz)3 configuration. To address this question, we present herein a comprehensive, spectroscopy-based theoretical and experimental electronic-structure investigation on complex 1. Highly correlated wave-function-based computations predicted that 3A2g and 3Egθ are well-isolated from other triplet states by ca. 4000 cm-1, whereas their splitting ΔA-E is on par with the effective spin-orbit coupling (SOC) constant of iron(II) (≈400 cm-1). Therfore, we invoked an effective Hamiltonian (EH) operating on the nine magnetic sublevels arising from SOC between the 3A2g and 3Egθ states. This approach enabled us to successfully simulate all spectroscopic data of 1 obtained by variable-temperature and variable-field magnetization, applied-field 57Fe Mössbauer, and terahertz electron paramagnetic resonance measurements. Remarkably, the EH contains only three adjustable parameters, namely, the energy gap without SOC, ΔA-E, an angle θ that describes the mixing of (dxy)2(dxz,yz)3(dz2)1 and (dz2)2(dxy)1(dxz,yz)3 configurations, and the ⟨rd-3⟩ expectation value of the iron d orbitals that is necessary to estimate the 57Fe magnetic hyperfine coupling tensor. The EH simulations revealed that the triplet ground state of 1 is genuinely multiconfigurational with substantial parentages of both 3A2g (<88%) and 3Eg (>12%), owing to their accidental near-triple degeneracy with ΔA-E = +950 cm-1. As a consequence of this peculiar electronic structure, 1 exhibits a huge effective magnetic moment (4.2 μB at 300 K), large temperature-independent paramagnetism, a large and positive axial zero-field splitting, strong easy-plane magnetization (g⊥ ≈ 3 and g∥ ≈ 1.7) and a large and positive internal field at the 57Fe nucleus aligned in the xy plane. Further in-depth analyses suggested that g⊥ ≫ g∥ is a general spectroscopic signature of near-triple orbital degeneracy with more than half-filled pseudodegenerate orbital sets. Implications of the unusual electronic structure of 1 for CO2 reduction are discussed.

Determination of the g-, hyperfine coupling- and zero-field splitting tensors in EPR and ENDOR using extended Matlab codes

The analysis of single crystal electron magnetic resonance (EMR) data has traditionally been performed using software in programming languages that are difficult to update, are not easily available, or are obsolete. By using a modern script-language with tools for the analysis and graphical display of the data, three MatLab® codes were prepared to compute the g, zero-field splitting (zfs) and hyperfine coupling (hfc) tensors from roadmaps obtained by EPR or ENDOR measurements in three crystal planes. Schonland’s original method was used to compute the g- and hfc -tensors by a least-squares fit to the experimental data in each plane. The modifications required for the analysis of the zfs of radical pairs with S = 1 were accounted for. A non-linear fit was employed in a second code to obtain the hfc -tensor from EPR measurements, taking the nuclear Zeeman interaction of an I = ½ nucleus into account. A previously developed method to calculate the g- and hfc -tensors by a simultaneous linear fit to all data was used in the third code. The validity of the methods was examined by comparison with results obtained experimentally, and by roadmaps computed by exact diagonalization. The probable errors were estimated using functions for regression analysis available in MatLab. The software will be published at https://doi.org/10.17632/ps24sw95gz.1, Input and output examples presented in this work can also be downloaded from https://old.liu.se/simarc/downloads?l=en.

Microscopic Characterization of Oxygen Defects in Diamond as Models for N3 and OK1 Defects: A Comparison of Calculated and Experimental Electron Paramagnetic Resonance Data.

The local structure and composition of the diamond paramagnetic defects labelled N3 and OK1 in which two heteroatoms (one of them is nitrogen) occupy vicinal substitutional positions are still a matter of debate. The electron paramagnetic resonance (EPR) is the technique adopted experimentally to characterize these defects, whose ground state is a doublet. In the present study, two models suggested in literature that contain N and O impurities are investigated at the quantum mechanical level by using the supercell model, a local Gaussian-type basis set, and the hybrid B3LYP functional as implemented in the CRYSTAL code. The computed EPR results (the Fermi contact and the available elements of the hyperfine coupling and electric field gradient tensors) are in good agreement (much better than in all previous, in some cases recently, studies) with an experiment. The two defects are further characterized in terms of local geometry, charge and spin density distributions, and IR and Raman spectra.

Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory.

We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO+, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving Sz symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.