Zero-field Splitting Tensor Research Articles

Electrically Induced Crystal Field Distortion in a Ferroelectric Perovskite Revealed by Electron Paramagnetic Resonance.

The magnetoelectric material has attracted multidisciplinary interest in the past decade for its potential to accommodate various functions. Especially, the external electric field can drive the quantum behaviors of such materials via the spin-electric coupling effect, with the advantages of high spatial resolution and low energy cost. In this work, the spin-electric coupling effect of Mn2+-doped ferroelectric organic-inorganic hybrid perovskite [(CH3)3NCH2Cl]CdCl3 with a large piezoelectric effect was investigated. The electric field manipulation efficiency for the allowed transitions was determined by the pulsed electron paramagnetic resonance. The orientation-included Hamiltonian of the spin-electric coupling effect was obtained via simulating the angle-dependent electric field modulated continuous-wave electron paramagnetic resonance. The results demonstrate that the applied electric field affects not only the principal values of the zero-field splitting tensor but also its principal axis directions. This work proposes and exemplifies a route to understand the spin-electric coupling effect originating from the crystal field imposed on a spin ion being modified by the applied electric field, which may guide the rational screening and designing of hybrid perovskite ferroelectrics that satisfy the efficiency requirement of electric field manipulation of spins in quantum information applications.

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'.

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.

Magnetophotoselection in the Investigation of Excitonically Coupled Chromophores: The Case of the Water-Soluble Chlorophyll Protein.

A magnetophotoselection (MPS) investigation of the photoexcited triplet state of chlorophyll a both in a frozen organic solvent and in a protein environment, provided by the water-soluble chlorophyll protein (WSCP) of Lepidium virginicum, is reported. The MPS experiment combines the photoselection achieved by exciting with linearly polarized light with the magnetic selection of electron paramagnetic resonance (EPR) spectroscopy, allowing the determination of the relative orientation of the optical transition dipole moment and the zero-field splitting tensor axes in both environments. We demonstrate the robustness of the proposed methodology for a quantitative description of the excitonic interactions among pigments. The orientation of the optical transition dipole moments determined by the EPR analysis in WSCP, identified as an appropriate model system, are in excellent agreement with those calculated in the point-dipole approximation. In addition, MPS provides information on the electronic properties of the triplet state, localized on a single chlorophyll a pigment of the protein cluster, in terms of orientation of the zero-field splitting tensor axes in the molecular frame.

Spin\u2013spin interactions in defects in solids from mixed all-electron and pseudopotential first-principles calculations

Understanding the quantum dynamics of spin defects and their coherence properties requires an accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from first principles calculations. We present a real-space approach based on density functional theory for the calculation of spin-Hamiltonian parameters, where only selected atoms are treated at the all-electron level, while the rest of the system is described with the pseudopotential approximation. Our approach permits calculations for systems containing more than 1000 atoms, as demonstrated for defects in diamond and silicon carbide. We show that only a small number of atoms surrounding the defect needs to be treated at the all-electron level, in order to obtain an overall all-electron accuracy for hyperfine and zero-field splitting tensors. We also present results for coherence times, computed with the cluster correlation expansion method, highlighting the importance of accurate spin-Hamiltonian parameters for quantitative predictions of spin dynamics.

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.

PyZFS: A Python package for first-principles calculations of zero-field splitting tensors

PyZFS: A Python package for first-principles calculations of zero-field splitting tensors

Comprehensive investigation of the triplet state electronic structure of free-base 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin by a combined advanced EPR and theoretical approach.

The nature of the photoexcited triplet state of free-base 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin (H2TPPS4-) has been investigated by advanced Electron Paramagnetic Resonance (EPR) techniques combined with quantum chemical calculations. The zero-field splitting (ZFS) parameters, D and E, the orientation of the transition dipole moment in the ZFS tensor frame, and the proton hyperfine couplings have been determined by magnetophotoselection-EPR and pulse electron-nuclear double resonance spectroscopy. Both time-resolved and pulse experiments exploit the electron spin polarization of the photoexcited triplet state. Comparison of the magnetic observables with computational results, including CASSCF calculations of the ZFS interaction tensor, provides an accurate picture of the triplet-state electronic structure. The theoretical investigation has been integrated with a systematic analysis on the parent free-base porphyrin molecule to assess the effect of the sulfonatophenyl substituents on the magnetic tensors. Additionally, the magnetophotoselection effects are discussed in terms of tautomerization in the excited singlet state of H2TPPS4-.

Two competing acceptors: Electronic structure of PNDITBT probed by time-resolved electron paramagnetic resonance spectroscopy.

Balanced charge transport is particularly important for transistors. Hence, ambipolar organic semiconductors with comparable transport capabilities for both positive and negative charges are highly sought-after. Here, we report detailed insights into the electronic structure of PNDITBT, which is an alternating copolymer of naphthalene diimide (NDI), thiophene, benzothiodiazole (B), and thiophene (T) units, as gained by time-resolved electron paramagnetic resonance (TREPR) spectroscopy combined with quantum-chemical calculations. The results are compared to those obtained for PNDIT2 and PCDTBT, which are derivatives without B and NDI acceptor units, respectively. These two polymers show dominant n- and p-channel behavior in organic field-effect transistors. The TBT moiety clearly dominates the electronic structure of PNDITBT, although less so than in PCDTBT. Furthermore, the triplet exciton most probably delocalizes along the backbone, exhibits a highly homogeneous environment, and planarizes the polymer backbone. Obtaining the zero-field splitting tensors of these triplet states by means of quantum-chemical calculations reveals the triplet energy sublevel associated with the molecular axis parallel to the backbone to be preferentially populated, while the one perpendicular to the aromatic plane is not populated at all, consistent with the spin-density distribution. PNDITBT consisting of two acceptors (NDI and B) has a complex electronic structure, as evident from the two charge-transfer bands in its absorption spectrum. TREPR spectroscopy provides a detailed insight on a molecular level not available by and complementing other methods.

Density functional theory study on magnetically detecting positively charged nitrogen-vacancy center in diamond

A quantum-chemical study of the positive charge-state of the nitrogen-vacancy center in diamond is presented. Charge control of this promising qubit candidate is a focus of diamond quantum technology research, as currently charge stability relating to surfaces and nearby defects causes some difficulties for quantum applications. To demonstrate full charge control over the nitrogen vacancy, all three charge states should be identified and the processes that lead to charge state changes understood. However, experimental markers for the positive state remain elusive compared to the readily detectable zero-phonon lines of the neutral and negative. In this work we present predicted hyperfine and zero-field splitting tensors as clear signatures of the normally spinless ${\mathrm{NV}}^{+}\phantom{\rule{4pt}{0ex}}(^{1}\mathrm{A}_{1}$ ground state) by probing a long-lived spin-triplet excited-state $\ensuremath{\sim}0.7$ eV above the ${\mathrm{NV}}^{+}$ ground state. We find a relatively narrow excitation energy range of approximately 0.7--1.1 eV between excitation into an $^{3}\mathrm{E}$ state and conversion into the neutral charge state. To provide insight into the thermal stability of the positive charge state, we have calculated binding and diffusion energies for both charged and uncharged systems. We predict, given that the activation energies are only weakly charge state dependent, all three charge states would diffuse in the 1600--$1900{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\text{C}$ range, but the positive state has a significantly lower binding energy, suggesting that it will dissociate at temperatures around $1000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ rather than migrate.

Magic-angle effects in a trigonal Mn3III cluster: Deconstruction of a single-molecule magnet

We present angle-dependent high-frequency EPR studies on a single-crystal of a trigonal Mn3 cluster with an unusual structure in which the local magnetic easy-axes of the constituent Mn(III) ions are tilted significantly away from the molecular C3 axis towards the magic-angle of 54.7 degrees, resulting in an almost complete cancelation of the 2nd-order axial magnetic anisotropy associated with the ferromagnetically coupled total spin ST = 6 ground state. This contrasts the situation in many related Mn3 single-molecule magnets (SMMs) that have been studied intensively in the past, for which the local MnIII anisotropy tensors are reasonably parallel, resulting in substantial barriers to magnetization relaxation (Ueff = 30 to 35 cm 1) and magnetization blocking below about 2.5 K. The suppression of the 2nd-order anisotropy in the present case results in a situation in which the zero-field splitting (ZFS) of the ST = 6 ground state is dominated by 4th- and higher-order interactions. This provides a unique opportunity to study in depth how molecular geometry influences these interactions that are responsible for quantum tunneling of magnetization in high-symmetry SMMs. Angle-dependent EPR measurements provide a full mapping of the molecular magneto-anisotropy. Meanwhile, irreducible tensor operator (ITO) methods are employed in order to obtain analytic expressions that directly relate molecular anisotropy to the microscopic physics, i.e., the ZFS tensors associated with the individual MnIII ions, their orientations, and the exchange coupling between the three spins. We find that the magic-angle tilting leads to a massive compression of the ST = 6 ground state energy level diagram and strong mixing between spin projection states. Although these characteristics are antagonistic to SMM behavior, they provide important insights into the physics of polynuclear molecular nanomagnets.

Probing the orientation of porphyrin oligomers in a liquid crystal solvent – a triplet state electron paramagnetic resonance study

ABSTRACTLinear porphyrin oligomers have found various applications as synthetic molecular wires in the context of light harvesting, solar energy conversion and molecular electronics. In many of these applications a partial ordering of the molecules helps to improve the reaction efficiency or device performance. In this work we study the orientational properties of the building blocks of such porphyrin-based molecular wires, namely a porphyrin monomer and the corresponding butadiyne-bridged dimer. The porphyrins have been embedded in the nematic liquid crystal solvent 4-cyano-4'-pentylbiphenyl (5CB) and the anisotropic properties of their photogenerated triplet states were characterised by transient electron paramagnetic resonance (EPR) spectroscopy. When aligned in strong magnetic fields, the liquid crystal molecules impose their orientational anisotropy onto the solute guest molecules whose orientation-dependent magnetic properties can then be explored. The line shape analysis of the porphyrin triplet state EPR spectra – highly sensitive to small conformational changes – confirms the orientation of the zero-field-splitting (ZFS) tensors previously determined for these molecules by magnetophotoselection experiments. A biaxial distribution function is shown to be necessary to simulate the experimental EPR data. The biaxial behaviour, in conjunction with symmetry considerations, allows an unambiguous assignment of the three ZFS tensor axes to the molecular axes. From the determined orientational distributions of the porphyrins in 5CB, the biaxial order parameters for both molecules were calculated.

Fe-transferrins or their homologues in ex-vivo mushrooms as identified by ESR spectroscopy and quantum chemical calculations: A full spin-Hamiltonian approach for the ferric sextet state with intermediate zero-field splitting parameters

Fe-transferrins/their homologues in ex-vivo mushrooms were identified by ESR spectroscopy at liquid helium temperature, 4 K. The ESR fine-structure signals from Grifola frondosa were analyzed by spectral simulation with a full spin-Hamiltonian approach, determining the spin Hamiltonian parameters of the ferric iron species bound in the biological environment: S = 5/2, g = (2.045, 2.01, 2.235), |D| = 0.28 cm−1, |E/D| = 0.05. The zero-field splitting (ZFS) parameters, D- and E-values, are very close to the reported values, |D| = 0.25 cm−1 and |E/D| = 0.06, for an Fe-transferrin with oxalate anion, and to |D| = 0.25 cm−1 and |E/D| = 0.04 for one with malonate anion in human sera, suggesting that the Fe3+ species are from Fe-transferrins or their homologues. Quantum chemical calculations of the ZFS tensors for Fe-transferrins were carried out. Fe-transferrins/homologues have been identified for all the mushrooms under study, suggesting that such Fe3+ enzymes are widely distributed in mushrooms.

Calculation of spin-spin zero-field splitting within periodic boundary conditions: Towards all-electron accuracy

For high-spin centers, one of the key spectroscopic fingerprints is the zero-field splitting (ZFS) addressable by electron paramagnetic resonance. In this paper, an implementation of the spin-spin contribution to the ZFS tensor within the projector augmented-wave (PAW) formalism is reported. We use a single-determinant approach proposed by M. J. Rayson and P. R. Briddon [Phys. Rev. B 77, 035119 (2008)], and complete it by adding a PAW reconstruction term which has not been taken into account before. We benchmark the PAW approach against a well-established all-electron method for a series of diatomic radicals and defects in diamond and cubic silicon carbide. While for some of the defect centers the PAW reconstruction is found to be almost negligible, in agreement with the common assumption, we show that in general it significantly improves the calculated ZFS towards the all-electron results.

ESR analyses of picket fence MnII and 6th ligand coordinated FeIII porphyrins (S = 5/2) and a CoII(hfac) complex (S = 3/2) with sizable ZFS parameters revisited: a full spin Hamiltonian approach and quantum chemical calculations.

The fictitious spin-1/2 (effective spin-1/2) Hamiltonian approach has been the putative method to analyze the conventional fine-structure/hyperfine ESR spectra of high spin metallocomplexes with sizable zero-field splitting (ZFS) tensors since the early 1950s, and the approach gives salient principal geff-values far from g = 2 without explicitly affording their ZFS values in most cases. The experimental geff-values thus determined, however, never agree with those (gtrue-values) of the true principal g-tensors, which are obtainable from reliable quantum chemical calculations. We have recently derived exact or extremely accurate analytical expressions for the geff/gtrue relationships for the spin quantum number S's up to S = 7/2 (T. Yamane et al., Phys. Chem. Chem. Phys., 2017, 19, 24769-24791). In this work, we have removed the limitation of the collinearity between g- and ZFS tensors and derived the generalized geff/gtrue relationships. To illustrate the usefulness of the present approach, we have revisited important typical high spin systems with large ZFS values such as picket fence metalloporphyrins with MnII (S = 5/2) (Q. Yu et al., Dalton Trans., 2015, 44, 9382-9390), a 6th ligand coordinated porphyrin with FeIII (S = 5/2) (Y. Ide et al., Dalton Trans., 2017, 46, 242-249) and a pseudo-octahedral CoII (S = 3/2)(hfac)2 complex (D. V. Korchagin et al., Dalton Trans., 2017, 46, 7540-7548), completing the ESR spectral and magnetic susceptibility analyses and gaining significant physical insights into their electronic structures. The off-principal axis extra peaks overlooked in the documented spectra of the picket fence MnII porphyrins have fully been assigned, affording their accurate true g-, hyperfine and ZFS tensors, for the first time. For the CoII complex, the occurrence of the non-collinearity between the g- and ZFS tensors has been discussed by using the generalized geff/gtrue relationships. We have attempted to carry out reliable DFT-based and ab initio quantum chemical calculations of their magnetic tensors, in which spin-orbit couplings are incorporated, reproducing the experimental true tensors. We emphasize that the incorporation of multi-reference nature in the electron configuration is important to interpret the magnetic tensors for the CoII complex.

An ab initio CASSCF study of zero field splitting fluctuations in the octet ground state of aqueous [Gd(iii)(HPDO3A)(H2O)

In this work, we present ab initio calculations of the zero-field splitting (ZFS) of a gadolinium complex [Gd(iii)(HPDO3A)(H2O)] sampled from an ab initio molecular dynamics (AIMD) simulation. We perform both post-Hartree-Fock (complete active space self-consistent field-CASSCF) and density functional theory (DFT) calculations of the ZFS and compare and contrast the methods with experimental data. Two different density functional approximations (TPSS and LC-BLYP) were investigated. The magnitude of the ZFS from the CASSCF calculations is in good agreement with experiment, whereas the DFT results in varying degrees overestimate the magnitude of the ZFS for both functionals and exhibit a strong functional dependence. It was found in the sampling over the AIMD trajectory that the fluctuations in the transient ZFS tensor derived from DFT are not correlated with those of CASSCF nor does the magnitude of the ZFS from CASSCF and DFT correlate. From the fluctuations in the ZFS tensor, we extract a correlation time of the transient ZFS which is on the sub-picosecond time scale, showing a faster decay than experimental estimates.

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor ( $$D^{\mathrm{SO}})$$ of the axial ZFS parameter D. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of $$\hbox {Mn}^{2+}$$ ion in the host matrix.

Structural, Spectroscopic, and Theoretical Investigation of a T-Shaped [Fe3(μ3-O)] Cluster.

The synthesis, X-ray crystal and electronic structures of [Fe3(μ3-O)(mpmae)2(OAc)2 Cl3], 1, where mpmae-H = 2-(N-methyl-N-((pyridine-2-yl)methyl)amino)ethanol, are described. This cluster comprises three high-spin ferric ions and exhibits a T-shaped site topology. Variable-frequency electron paramagnetic resonance measurements performed on single crystals of 1 demonstrate a total spin ST = 5/2 ground state, characterized by a small, negative, and nearly axial zero-field splitting tensor D = -0.49 cm-1, E/D ≈ 0.055. Analysis of magnetic susceptibility, magnetization, and magneto-structural correlations further corroborate the presence of a sextet ground-spin state. The observed ground state originates from the strong anti-ferromagnetic interaction of two iron(III) spins, with J = 115(5) cm-1, that, in turn, are only weakly coupled to the spin of the third site, with j = 7(1) cm-1. These exchange interactions lead to a ground state with magnetic properties that are essentially entirely determined by the weakly coupled site. The contributions of the individual spins to the total ground state of the cluster were monitored using variable-field 57Fe Mössbauer spectroscopy. Field-dependent spectra reveal that, while one of the iron sites exhibits a large negative internal field, typical of ferric ions, the other two sites exhibit small, but not null, negative and positive internal fields. A theoretical analysis reveals that these small internal fields originate from the mixing of the lowest ST = 5/2 excited state into the ground state which, in turn, is induced by a minute structural distortion.

Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems.

We apply approximate relativistic methods to calculate the magnetic property tensors, i.e., the g-tensor, zero-field splitting (ZFS) tensor (D), and hyperfine coupling (HFC) tensors, for the purpose of constructing paramagnetic nuclear magnetic resonance (pNMR) shielding tensors. The chemical shift and shielding anisotropy are calculated by applying a modern implementation of the classic Kurland-McGarvey theory ( J. Magn. Reson. 1970 , 2 , 286 ), which formulates the shielding tensor in terms of the g- and HFC tensors obtained for the ground multiplet, in the case of higher than doublet multiplicity defined by the ZFS interaction. The g- and ZFS tensors are calculated by ab initio complete active space self-consistent field and N-electron valence-state perturbation theory methods with spin-orbit (SO) effects treated via quasidegenerate perturbation theory. Results obtained with the scalar relativistic (SR) Douglas-Kroll-Hess Hamiltonian used for the g- and ZFS tensor calculations are compared with nonrelativistically based computations. The HFC tensors computed using the fully relativistic four-component matrix Dirac-Kohn-Sham approach are contrasted against perturbationally SO-corrected nonrelativistic results in the density functional theory framework. These approximations are applied on paramagnetic metallocenes (MCp2) (M = Ni, Cr, V, Mn, Co, Rh, Ir), a Co(II) pyrazolylborate complex, and a Cr(III) complex. SR effects are found to be small for g and D in these systems. The HFCs are found to be more influenced by relativistic effects for the 3d systems. However, for some of the 3d complexes, nonrelativistic calculations give a reasonable agreement with the experimental chemical shift and shielding anisotropy. The influence of scalar relativity is strong for the 5d IrCp2 system. This mixed ab initio/DFT technique, with a fully relativistic method used for the critical HFC tensor, should be useful for the treatment of both electron correlation and relativistic effects at a reasonable computational cost to compute the pNMR shielding tensors in transition metal systems.

Paramagnetic Enhancement of Nuclear Spin-Spin Coupling.

We present a derivation and computations of the paramagnetic enhancement of the nuclear magnetic resonance (NMR) spin-spin coupling, which may be expressed in terms of the hyperfine coupling (HFC) and (for systems with multiple unpaired electrons) zero-field splitting (ZFS) tensors. This enhancement is formally analogous to the hyperfine contributions to the NMR shielding tensor as formulated by Kurland and McGarvey. The significance of the spin-spin coupling enhancement is demonstrated by using a combination of density-functional theory and correlated ab initio calculations, to determine the HFC and ZFS tensors, respectively, for two paramagnetic 3d metallocenes, a CrII(acac)2 complex, a Co(II) pyrazolylborate complex, and a lanthanide system, Gd-DOTA. Particular attention is paid to relativistic effects in HFC tensors, which are calculated using two methods: a nonrelativistic method supplemented by perturbational spin-orbit coupling corrections, and a fully relativistic, four-component matrix-Dirac-Kohn-Sham approach. The paramagnetic enhancement lacks a direct dependence on the distance between the coupled nuclei, and represents more the strength and orientation of the individual hyperfine couplings of the two nuclei to the spin density distribution. Therefore, the enhancement gains relative importance as compared to conventional coupling as the distance between the nuclei increases, or generally in the cases where the conventional coupling mechanisms result in a small value. With the development of the experimental techniques of paramagnetic NMR, the more significant enhancements, e.g., of the 13C13C couplings in the Gd-DOTA complex (as large as 9.4 Hz), may eventually become important.