Electron Paramagnetic Resonance G-tensor Research Articles

Superstructure and Correlated Na+ Hopping in a Layered Mg-Substituted Sodium Manganate Battery Cathode are Driven by Local Electroneutrality.

In this work, we present a variable-temperature 23Na NMR and variable-temperature and variable-frequency electron paramagnetic resonance (EPR) analysis of the local structure of a layered P2 Na-ion battery cathode material, Na0.67[Mg0.28Mn0.72]O2 (NMMO). For the first time, we elucidate the superstructure in this material by using synchrotron X-ray diffraction and total neutron scattering and show that this superstructure is consistent with NMR and EPR spectra. To complement our experimental data, we carry out ab initio calculations of the quadrupolar and hyperfine 23Na NMR shifts, the Na+ ion hopping energy barriers, and the EPR g-tensors. We also describe an in-house simulation script for modeling the effects of ionic mobility on variable-temperature NMR spectra and use our simulations to interpret the experimental spectra, available upon request. We find long-zigzag-type Na ordering with two different types of Na sites, one with high mobility and the other with low mobility, and reconcile the tendency toward Na+/vacancy ordering to the preservation of local electroneutrality. The combined magnetic resonance methodology for studying local paramagnetic environments from the perspective of electron and nuclear spins will be useful for examining the local structures of materials for devices.

The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.

Calculation of the EPR g-tensor from auxiliary density functional theory.

The working equations for the calculation of the electron paramagnetic resonance (EPR) g-tensor within the framework of the auxiliary density functional theory (ADFT) are presented. The scheme known as gauge including atomic orbitals (GIAOs) is employed to treat the gauge origin problem. This ADFT-GIAO formulation possesses an inherent high computational performance, allowing for the calculation of the EPR g-tensor of molecules containing some hundreds of atoms in reasonable computational time employing moderate computational resources. The effect of the use of a gauge independent auxiliary density on the quality of the g-tensor calculation for the evaluation of the exchange-correlation contribution is analyzed in this work. The best agreement with the experiment is obtained with the BLYP functional (Becke 1988 exchange and Lee-Yang-Parr correlation) in combination with a double-ζ basis set, in particular aug-cc-pVDZ. Furthermore, models of endohedral fullerenes N@Cn, with n = {60, 70, 100, 180, 240}, were used for benchmarking its computational performance.

Investigation of room temperature ferromagnetism in transition metal doped BiFeO3

Spintronic functionality in ferromagnetic materials is a next-generation technique, to be used in data storage, high-frequency communications, and logic devices with minimum energy consumption. Ultra-low energy consumption in high-speed logic devices can be envisioned by inducing ferromagnetic behavior into room temperature multiferroic materials. However, there is a scarcity of room temperature multiferroic materials which have a definite spin degree of freedom. To fully exploit these technological challenges, we introduce the induced ferromagnetism in bismuth ferrite (BiFeO3, BFO) by doping transition metal (Cr, Ni, Co) elements. Our investigation initiates with the experimental study on chemically synthesized BiFe(1−x)MxO3 samples where x = 0.0625 (6.25%) and M = Cr, Ni and Co. Experimental findings are verified by theoretical simulation using density functional theory (DFT + U) and gauge including projector augmented wave (GIPAW) based calculation. All the experimental studies are done at room temperature while the theoretical verification using DFT is carried to understand the underlying mechanism behind the magnetic behavior of doped BiFeO3. It is done by optimizing the structural parameters comparable to the room temperature values. Microstructural and magnetic properties are studied using x-ray diffraction (XRD), transmission electron microscopy (TEM) and Vibrating sample magnetometer (VSM). All these experimental studies confirm the structural changes and induced ferromagnetism with doping. X-ray photoelectron spectroscopy (XPS) verified the reason behind this ferromagnetic property on the basis of oxygen vacancy content. Electron paramagnetic resonance (EPR) spectroscopy shows the tuning of Δg values due to enhanced magnetization.The density of states (DOS) calculations were performed on BFO (band-gap 1.89 eV) after structural optimization using DFT + U method, confirm our experimental findings. Magnetic moment values change drastically with doping elements (M), i.e. almost negligible for BFO (antiferromagnetic) to maximum (2.85 μB/f.u.) for Ni-doped sample. We also compute the EPR g-tensor using GIPAW method to confirm the tuning of Δg values due to enhanced magnetization. These results can highlight the impact and importance of suitable transition element doping to induce the room temperature ferromagnetism in BiFeO3.

Molecular structures of nickel adducts in zeolites – Interpretation of experimental EPR g-tensors guided by DFT calculations

Computational electron paramagnetic resonance (EPR) spectroscopy is a combination of robust simulation techniques of complex spectra with density functional theory (DFT) calculations of spin-Hamiltonian parameters for the adopted models of the investigated paramagnetic species. This approach was used for guiding interpretation of the experimental EPR data of selected adducts of nickel(I) and nickel (II) centers in high-silica zeolites with gas-phase small molecules of environmental significance (CO, NO, C2H2, NH3, O2). As a result, a quantitative connection between the spectroscopic fingerprints, in particular g-tensors, and structure of the molecular clusters mimicking the real intrazeolitic species was obtained. Possible calculation schemes for assessing g-tensor values were explored. Various levels of relativistic effects (including relativistic corrections to the composition of electronic ground state and spin-orbit approximations) were studied. Selection of a proper exchange-correlation functional was also discussed underlying its influence for the systems for which spin density is delocalized over a metal core and a ligand. The conformation analysis of g-tensor anisotropy for amine adducts in assessing its structure was shown. Finally, molecular interpretation of electronic g-tensor in terms of the magnetic field-induced transitions between involved orbitals was shown taking as an example a diamine Ni(I) adduct.

Influence of Ring-Expanded N-Heterocyclic Carbenes on the Structures of Half-Sandwich Ni(I) Complexes: An X-ray, Electron Paramagnetic Resonance (EPR), and Electron Nuclear Double Resonance (ENDOR) Study.

Potassium graphite reduction of the half-sandwich Ni(II) ring-expanded diamino/diamidocarbene complexes CpNi(RE-NHC)Br gave the Ni(I) derivatives CpNi(RE-NHC) (where RE-NHC = 6-Mes (1), 7-Mes (2), 6-MesDAC (3)) in yields of 40%-50%. The electronic structures of paramagnetic 1-3 were investigated by CW X-/Q-band electron paramagnetic resonance (EPR) and Q-band 1H electron nuclear double resonance (ENDOR) spectroscopy. While small variations in the g-values were observed between the diaminocarbene complexes 1 and 2, pronounced changes in the g-values were detected between the almost isostructural species (1) and diamidocarbene species (3). These results highlight the sensitivity of the EPR g-tensor to changes in the electronic structure of the Ni(I) centers generated by incorporation of heteroatom substituents onto the backbone ring positions. Variable-temperature EPR analysis also revealed the presence of a second Ni(I) site in 3. The experimental g-values for these two Ni(I) sites detected by EPR in frozen solutions of 3 are consistent with resolution on the EPR time scale of the disordered components evident in the X-ray crystallographically determined structure and the corresponding density functional theory (DFT)-calculated g-tensor. Q-band 1H ENDOR measurements revealed a small amount of unpaired electron spin density on the Cp rings, consistent with the calculated SOMO of complexes 1-3. The magnitude of the 1H A values for 3 were also notably larger, compared to 1 and 2, again highlighting the influence of the diamidocarbene on the electronic properties of 3.

Probe the Heme Iron Ligand and Conformational Change of Misfolded States of Cytochrome C through EPR Spectroscopy

Cytochrome c is a heme-protein existing in the membrane of mitochrondria which plays a pivotal role in apoptosis. Besides its important biological functions, it is a model system for protein folding and unfolding studies. Recently, Soffer et al. [Soffer et al. Biochemistry 2013, 52, 1397−1408] claimed that a meta-stable misfolded state of horse heart ferricytochreome c could be obtained after exposing the protein to the ferricyanide solution at very alkaline pH for an extended period of time, and it did not undergo any remarkable change in its secondary and tertiary structures upon adjusting the solution to folding promoting conditions at neutral pH. Yet the axial coordination of the heme iron as well as the electronic structures for the misfolded protein remained undetermined. For this purpose, in this work, electron paramagnetic resonance (EPR) spectra of the misfolded protein in the solution at different pH values were recorded, and DFT calculation was conducted to predict the EPR g-tensor at different axial ligand configurations. Our EPR data indicate that the misfolded protein at very alkaline condition exhibits a hexacoordinated low spin state, while at pH 5 the protein adapt the configuration similar to the native-like low-spin ferric heme complex which possesses a histidine/methionine coordination environment. For pH value between 6 and 7, the EPR spectra appear to be the superposition of the two species. With the aid of DFT calculation, also checked by the EPR and other spectroscopic data, the possible hexacoordinated low spin state with a hydroxyl ion as the proximal ligand and the pentacoordinated quantum mixed state of the heme iron for misfolded protein at different folding conditions were discussed. This work was partially supported by Hundred Talents Program of Chinese Academy of Sciences.

Correlated four-component EPR g-tensors for doublet molecules

The first correlated ab initio four-component calculations of electron paramagnetic resonance (EPR) g-tensors for doublet radicals are reported. We have implemented a first-order degenerate perturbation theory approach based on the four-component Dirac-Coulomb Hamiltonian and fully relativistic configuration interaction wave functions in the DIRAC program package. We find that the correlation effects on the g-tensors can be sufficiently well described with manageable basis sets of triple-zeta quality and manageable configuration spaces. The new fully relativistic EPR module in DIRAC should be useful for benchmarking density functional theory approaches, however, with future optimization of the code we believe it will also be useful for applications.

A fully variational spin-orbit coupled complete active space self-consistent field approach: Application to electron paramagnetic resonance g-tensors

In this work, a relativistic version of the state-averaged complete active space self-consistent field method is developed (spin-orbit coupled state-averaged complete active space self-consistent field; CAS-SOC). The program follows a "one-step strategy" and treats the spin-orbit interaction (SOC) on the same footing as the electron-electron interaction. As opposed to other existing approaches, the program employs an intermediate coupling scheme in which spin and space symmetry adapted configuration space functions are allowed to interact via SOC. This adds to the transparency and computational efficiency of the procedure. The approach requires the utilization of complex-valued configuration interaction coefficients, but the molecular orbital coefficients can be kept real-valued without loss of generality. Hence, expensive arithmetic associated with evaluation of complex-valued transformed molecular integrals is completely avoided. In order to investigate the quality of the calculated wave function, we extended the method to the calculation of electronic g-tensors. As the SOC is already treated to all orders in the SA-CASSCF process, first order perturbation theory with the Zeeman operator is sufficient to accomplish this task. As a test-set, we calculated g-tensors of a set of diatomics, a set of d(1) transition metal complexes MOX4(n-), and a set of 5f(1) actinide complexes AnX6(n-). These calculations reveal that the effect of the wavefunction relaxation due to variation inclusion of SOC is of the same order of magnitude as the effect of inclusion of dynamic correlation and hence cannot be neglected for the accurate prediction of electronic g-tensors.

THEORY OF ORBITAL MAGNETIZATION IN SOLIDS

In this review article, we survey the relatively new theory of orbital magnetization in solids — often referred to as the "modern theory of orbital magnetization" — and its applications. Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact that the position operator is ill-defined in such a context. Approaches that overcome this problem were first developed in 2005 and in the first part of this review we present the main ideas reaching from a Wannier function approach to semi-classical and finite-temperature formalisms. In the second part, we describe practical aspects of calculating the orbital magnetization, such as taking k-space derivatives, a formalism for pseudopotentials, a single k-point derivation, a Wannier interpolation scheme, and DFT specific aspects. We then show results of recent calculations on Fe, Co, and Ni. In the last part of this review, we focus on direct applications of the orbital magnetization. In particular, we will review how properties such as the nuclear magnetic resonance shielding tensor and the electron paramagnetic resonance g-tensor can be elegantly calculated in terms of a derivative of the orbital magnetization.

The Inhibitor DBMIB Provides Insight into the Functional Architecture of the QoSite in the Cytochromeb6fComplex

Previously [Roberts, A. G., and Kramer, D. M. (2001) Biochemistry 40, 13407-13412], we showed that 2 equiv of the quinone analogue 2,5-dibromo-3-methyl-6-isopropylbenzoquinone (DBMIB) could occupy the Q(o) site of the cytochrome (cyt) b(6)f complex simultaneously. In this work, a study of electron paramagnetic resonance (EPR) spectra from the oriented cyt b(6)f complex shows that the Rieske iron-sulfur protein (ISP) is in distinct orientations, depending on the stoichiometry of the inhibitor at the Q(o) site. With a single DBMIB at the Q(o) site, the ISP is oriented with the 2Fe-2S cluster toward cyt f, which is similar to the orientation of the ISP in the X-ray crystal structure of the cyt b(6)f complex from thermophilic cyanobacterium Mastigocladus laminosus in the presence of DBMIB, as well as that of the chicken mitochondrial cyt bc(1) complex in the presence of the class II inhibitor myxothiazol, which binds in the so-called "proximal niche", near the cyt b(L) heme. These data suggest that the high-affinity DBMIB site is at the proximal niche Q(o) pocket. With >or=2 equiv of DBMIB bound, the Rieske ISP is in a position that resembles the ISP(B) position of the chicken mitochondrial cyt bc(1) complex in the presence of stigmatellin and the Chlamydomonas reinhardtii cyt b(6)f complex in the presence of tridecylstigmatellin (TDS), which suggests that the low-affinity DBMIB site is at the distal niche. The close interaction of DBMIB bound at the distal niche with the ISP induced the well-known effects on the 2Fe-2S EPR spectrum and redox potential. To further test the effects of DBMIB on the ISP, the extents of cyt f oxidation after flash excitation in the presence of photosystem II inhibitor DCMU were measured as a function of DBMIB concentration in thylakoids. Addition of DBMIB concentrations at which a single binding was expected did not markedly affect the extent of cyt f oxidation, whereas higher concentrations, at which double occupancy was expected, increased the extent of cyt f oxidation to levels similar to that of cyt f oxidation in the presence of a saturating concentration of stigmatellin. Simulations of the EPR g-tensor orientations of the 2Fe-2S cluster versus the physical orientations based on single-crystal studies of the cyt bc(1) complex suggest that the soluble ISP domain of the spinach cyt b(6)f complex can rotate by at least 53 degrees, which is consistent with long-range ISP domain movement. Implications of these results are discussed in the context of the X-ray crystal structures of the chicken mitochondrial cyt bc(1) complex and the M. laminosus and C. reinhardtii cyt b(6)f complexes.

Efficient calculation of electron paramagnetic resonance g-tensors by multireference configuration interaction sum-over-state expansions, using the atomic mean-field spin–orbit method

Using the multireference configuration interaction method due to Grimme and Waletzke, combined with the atomic mean-field approximations for the efficient calculation of spin–orbit matrix elements, the g-tensors in second-order perturbation theory have been calculated for the main group radicals CO+, CN, BO, BS, MgF, AlO, O2, HCO, H2O+, NO2, CO2−, NF2, NO22−, O3−, ClO2, and H2CO+, and for the transition metal compounds ZnH, ZnF, and TiF3, using explicit sum-over-state expansions for up to 20 excited states. In most cases, a valence triple-zeta basis set with polarization functions has been employed. It is shown that the addition of diffuse functions to this basis set does not improve the g-tensor results, and in several instances leads to slower convergence of the sum-over-state expansion. The calculated g-tensors are in good agreement with experimental values, and with our previous multireference configuration interaction results available for 9 of the 19 radicals. Our results are shown to be equivalent to, or better than, values obtained by other theoretical methods. Examples of radicals for which g-tensor calculations presented problems in the past are AlO and TiF3. For AlO, we obtain Δg⊥=−1530 ppm (parts per million), compared with an experimental value of −1900 ppm in Ne matrix. Using the SVP (valence double-zeta plus polarization) basis set, Δg⊥ of TiF3 is calculated to be −115.3 ppt (parts per thousand), compared with experimental values of −111.9 and −123.7 ppt.

Structural origin of two paramagnetic species in six-coordinated nitrosoiron(II) porphyrins revealed by density functional theory analysis of the g tensors.

Potential energy and electron paramagnetic resonance (EPR) g tensor surfaces of model five- and six-coordinated porphyrins were examined. For both types of complexes, the NO ligand is preferably coordinated end-on, with a Fe-N-O bond angle of approximately 140 degrees. In the free five-coordinated structure, NO undergoes free rotation around the axial Fe-N(NO) bond. This motion is strongly coupled to the saddle-type distortion of the porphyrin ligand. Coordination by the second axial ligand (imidazole) raises the calculated barrier for NO rotation to about 1 kcal/mol, which is further increased by displacements of imidazole from the ideal axial position. The potential energy surface for the dissociation of the weakly coordinated imidazole ligand is exceptionally flat, with variation of the Fe-N(Im) bond length between 2.1 and 2.5 A changing the energy by less than 1 kcal/mol. Experimental orientations of both axial ligands, as well as the Fe-N(Im) bond length, are therefore likely to be determined by the environment of the complex. In contrast to the total energy, calculated EPR g-tensors are sensitive to the orientation of the NO ligand and to the Fe-N(Im) bond length. Contrary to a common assumption, the g tensor component closest to the free-electron value does not coincide with the direction of the Fe-N(NO) bond. From comparison of the calculated and experimental g-tensor components for a range of structures, the rhombic ("type I") EPR signal is assigned to a static structure with NO oriented toward the meso-C atom of the prophyrin ring, and RFe-N(Im) approximately 2.1 A (calcd g1 = 1.95, g2 = 2.00, g3 = 2.04; exptl g1 = 1.96-1.98, g2 = 2.00, g3 = 2.06-2.08). The axial ("type II") EPR signal cannot correspond to any of the static structures studied presently. It is tentatively assigned to a partially dissociated six-coordinated complex (RFe-N(Im) > 2.5 A), with a freely rotating NO ligand (calcd g parallel = 2.00, g perpendicular = 2.03; exptl g parallel = 1.99-2.00, g perpendicular = 2.02-2.03).

Prediction of electron paramagnetic resonance g-tensors of transition metal complexes using density functional theory: First applications to some axial d1MEX4 systems

We applied the recently developed density-functional (DFT) formulation of the electron paramagnetic resonance (EPR) g-tensor to a series of axially symmetric d1 transition metal complexes (MEX4z−, where M=V, Cr, Mo, W, Tc, and Re; E=O and N; X=F, Cl, and Br). Values for the g-tensor components are determined by an interplay between three contributions arising due to magnetic field-induced coupling between the following orbitals: (a) The singly occupied α b2 (“dxy”) molecular orbital (α-SOMO) and a metal-based vacant d orbital [either b1 (“dx2−y2”) or e1 (“dxz”,“dyz”) depending on the tensor component]; (b) the bonding counterparts of the metal’s b1/e1-type d orbitals and the vacant β-SOMO; and (c) ligand-based occupied MOs (molecular orbitals) of the appropriate symmetry and the β-SOMO. The first contribution (which is the only term accounted for in the simple ligand field theory) is usually negative, and decreases the g-tensor components relative to the free electron value, while contributions (b) and (c) are positive. Either of the three terms may dominate, so that values both below and above the free electron are obtained naturally. Calculated g tensors exhibit only a moderate dependence on the molecular geometry. Quasi-relativistic VWN (Vosko–Wilk–Nusair) LDA (local density approximation) geometries are in a good agreement with the available experimental data, and are satisfactory for calculation of g tensors. Tensor components obtained with VWN LDA and gradient-corrected BP86 functionals are essentially identical, and always too positive compared to experiment. The residual errors in both components exhibit strong correlation with the position of the transition metal center in the periodic table. Trends in g-tensor components within the same transition row are correctly reproduced by both functionals, so that a simple additive correction brings g∥ and g⊥ results into a good agreement with experiment. The deficiencies in the calculated g values may be traced back to the overestimation of the covalent character of bonds formed by metal d orbitals in popular approximate functionals. Calculations of EPR g-tensor thus provide a very stringent quality test for approximate density functionals.