Hyperfine Coupling Tensors Research Articles

Room temperature Q-band electron magnetic resonance study of radicals in X-ray-irradiated l-threonine single crystals.

In the past, decennia radiation-induced radicals were successfully identified by electron magnetic resonance (EMR) in several solid-state amino acids and sugars. The authors present a room temperature (RT) EMR study of the stable radicals produced by X-ray-irradiation in the amino acid l-threonine (CH₃CH(OH)CH(NH₃ (+))COO(-)). Its chemical structure is similar to that of the well-known dosimetric material l-alanine (CH₃CH(NH₃(+))COO(-)), and radiation defects in l-threonine may straightforwardly be compared with the extensively studied l-alanine radicals. The hyperfine coupling tensors of three different radicals were determined at RT using electron nuclear double resonance. These results indicate that the two most abundant radicals share the same basic structure CH₃(•)C(OH)CH(NH₃(+))COO(-), obtained by H-abstraction, but are stabilised in slightly different conformations. The third radical is most probably obtained by deamination (CH₃CH(OH)(•)CHCOO(-)), similar in structure to the stable alanine radical.

Lithium Formate for EPR Dosimetry: Radiation-Induced Radical Trapping at Low Temperatures

Radiation-induced primary radicals in lithium formate. A material used in EPR dosimetry have been studied using electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR) and ENDOR-Induced EPR (EIE) techniques. In this study, single crystals were X irradiated at 6-8 K and radical formation at these and higher temperatures were investigated. Periodic density functional theory calculations were used to assist in assigning the radical structures. Mainly two radicals are present at 6 K, the well-known CO2(•-) radical and a protonated electron-gain product. Hyperfine coupling tensors for proton and lithium interactions were obtained for these two radicals and show that the latter radical exists in four conformations with various degrees of bending at the radical center. Pairs of CO2(•-) radicals were also observed and the tensor for the electron-electron dipolar coupling was determined for the strongest coupled pair, which exhibited the largest spectral intensity. Upon warming, both the radical pairs and the reduction product decay, the latter apparently by a transient species. Above 200 K the EPR spectrum was mainly due to the CO2(•-) (mono) radicals, which were previously characterized as the dominant species present at room temperature and which account for the dosimetric EPR signal.

On the Use of Locally Dense Basis Sets in the Calculation of EPR Hyperfine Couplings: A Study on Model Systems for Bio-Inorganic Fe and Co Complexes

The usage of locally dense basis sets in the calculation of Electron Paramagnetic Resonance (EPR) hyperfine coupling constants is investigated at the level of Density Functional Theory (DFT) for two model systems of biologically important transition metal complexes: One for the active site in the compound 0 intermediate of cytochrome P450cam, [Fe(OOH)(SH)(en)2]+, and one for the active site in coenzyme B12, [Co(NH3)(CN)(en)2]+. The Fermi contact, spin-dipolar and second order paramagnetic spin-orbit coupling contributions to the hyperfine coupling tensors of the metal and the ligating ethylenediamine N atoms are calculated, and their dependence on the basis set for the remaining atoms are investigated. Core property basis sets are employed for the metals (aug-cc-pVTZ-Juc) and their equatorially coordinating N atoms (aug-cc-pVTZ-J or 6-31G-Juc analogues to the Pople style basis sets used for the remaining atoms), while smaller correlation-consistent or Pople style basis sets are used for the remaining, so-called “non-coupled'', atoms. Most of the investigated basis set combinations are found to give results which differ by less than 1% from the results obtained with core property basis sets on all atoms. We find thus for the cytochrome model system that using the small 6-31G(d) basis set on the non-coupled atoms together with core property basis sets on the Fe and N atoms gives essentially converged results. It is found to be mostly the second order paramagnetic spin-orbit interaction that demands the use of larger basis sets on the non-coupled atoms. If, however, an error of less than 0.5MHz is sufficient any basis set can be used for the noncoupled atoms. For the cobalt containing model system the 6-31G(2d) basis set generally gives results within 1% of the reference value.

ESR lineshape and 1H spin-lattice relaxation dispersion in propylene glycol solutions of nitroxide radicals – Joint analysis

Electron Spin Resonance (ESR) spectroscopy and Nuclear Magnetic Relaxation Dispersion (NMRD) experiments are reported for propylene glycol solutions of the nitroxide radical: 4-oxo-TEMPO-d16 containing (15)N and (14)N isotopes. The NMRD experiments refer to (1)H spin-lattice relaxation measurements in a broad frequency range (10 kHz-20 MHz). A joint analysis of the ESR and NMRD data is performed. The ESR lineshapes give access to the nitrogen hyperfine tensor components and the rotational correlation time of the paramagnetic molecule. The NMRD data are interpreted in terms of the theory of paramagnetic relaxation enhancement in solutions of nitroxide radicals, recently presented by Kruk et al. [J. Chem. Phys. 138, 124506 (2013)]. The theory includes the effect of the electron spin relaxation on the (1)H relaxation of the solvent. The (1)H relaxation is caused by dipole-dipole interactions between the electron spin of the radical and the proton spins of the solvent molecules. These interactions are modulated by three dynamic processes: relative translational dynamics of the involved molecules, molecular rotation, and electron spin relaxation. The sensitivity to rotation originates from the non-central positions of the interacting spin in the molecules. The electronic relaxation is assumed to stem from the electron spin-nitrogen spin hyperfine coupling, modulated by rotation of the radical molecule. For the interpretation of the NMRD data, we use the nitrogen hyperfine coupling tensor obtained from ESR and fit the other relevant parameters. The consistency of the unified analysis of ESR and NMRD, evaluated by the agreement between the rotational correlation times obtained from ESR and NMRD, respectively, and the agreement of the translation diffusion coefficients with literature values obtained for pure propylene glycol, is demonstrated to be satisfactory.

Four-Component Relativistic Density Functional Theory Calculations of NMR Shielding Tensors for Paramagnetic Systems

A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.

Massively parallel implementations of coupled-cluster methods for electron spin resonance spectra. I. Isotropic hyperfine coupling tensors in large radicals

Coupled cluster (CC) methods provide highly accurate predictions of molecular properties, but their high computational cost has precluded their routine application to large systems. Fortunately, recent computational developments in the ACES III program by the Bartlett group [the OED∕ERD atomic integral package, the super instruction processor, and the super instruction architecture language] permit overcoming that limitation by providing a framework for massively parallel CC implementations. In that scheme, we are further extending those parallel CC efforts to systematically predict the three main electron spin resonance (ESR) tensors (A-, g-, and D-tensors) to be reported in a series of papers. In this paper inaugurating that series, we report our new ACES III parallel capabilities that calculate isotropic hyperfine coupling constants in 38 neutral, cationic, and anionic radicals that include the (11)B, (17)O, (9)Be, (19)F, (1)H, (13)C, (35)Cl, (33)S,(14)N, (31)P, and (67)Zn nuclei. Present parallel calculations are conducted at the Hartree-Fock (HF), second-order many-body perturbation theory [MBPT(2)], CC singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] levels using Roos augmented double- and triple-zeta atomic natural orbitals basis sets. HF results consistently overestimate isotropic hyperfine coupling constants. However, inclusion of electron correlation effects in the simplest way via MBPT(2) provides significant improvements in the predictions, but not without occasional failures. In contrast, CCSD results are consistently in very good agreement with experimental results. Inclusion of perturbative triples to CCSD via CCSD(T) leads to small improvements in the predictions, which might not compensate for the extra computational effort at a non-iterative N(7)-scaling in CCSD(T). The importance of these accurate computations of isotropic hyperfine coupling constants to elucidate experimental ESR spectra, to interpret spin-density distributions, and to characterize and identify radical species is illustrated with our results from large organic radicals. Those include species relevant for organic chemistry, petroleum industry, and biochemistry, such as the cyclo-hexyl, 1-adamatyl, and Zn-porphycene anion radicals, inter alia.

Hyperfine interactions in a gadolinium-based MRI contrast agent: High-frequency modulations from ab initio simulations

Hyperfine coupling tensors of the water molecule coordinated to the Prohance contrast agent in liquid water were calculated within and beyond the point dipole approximation along an ab initio molecular dynamics trajectory. We observe the non-equivalence at short time scales on structural as well as magnetodynamical properties of inner sphere water protons due to hydrogen bonds formation with the solvent. In addition, the influence of ultrafast internal motions on the anisotropic, dipolar, contribution to hyperfine couplings was probed thanks to a decomposition of its fluctuations in terms of a small set of meaningful collective variables.

Electron paramagnetic resonance study of gamma-irradiated phenidone single crystal

The electron paramagnetic resonance (EPR) spectra of gamma-irradiated single crystals of phenidone (fenidon C9H10N2O) have been studied for different orientations of crystals in a magnetic field. Phenidone single crystals have been irradiated with 60Co-γ rays at room temperature. The EPR spectra have been investigated at temperatures between 125 and 450 K. The spectra have been found to be temperature independent. The spin-Hamiltonian parameters have been obtained from the single-crystal EPR analysis. The principal values of the hyperfine coupling tensor of the unpaired electron and the principal values of the g-tensor have been determined.

Measuring the orientation of taurine in the active site of the non-heme Fe(II)/α-ketoglutarate-dependent taurine hydroxylase (TauD) using electron spin echo envelope modulation (ESEEM) spectroscopy.

The position and orientation of taurine near the non-heme Fe(II) center of the α-ketoglutarate (α-KG)-dependent taurine hydroxylase (TauD) was measured using Electron Spin Echo Envelope Modulation (ESEEM) spectroscopy. TauD solutions containing Fe(II), α-KG, and natural abundance taurine or specifically deuterated taurine were prepared anaerobically and treated with nitric oxide (NO) to make an S = 3/2 {FeNO}(7) complex that is suitable for robust analysis with EPR spectroscopy. Using ratios of ESEEM spectra collected for TauD samples having natural abundance taurine or deuterated taurine, (1)H and (14)N modulations were filtered out of the spectra and interactions with specific deuterons on taurine could be studied separately. The Hamiltonian parameters used to calculate the amplitudes and line shapes of frequency spectra containing isolated deuterium ESEEM were obtained with global optimization algorithms. Additional statistical analysis was performed to validate the interpretation of the optimized parameters. The strongest (2)H hyperfine coupling was to a deuteron on the C1 position of taurine and was characterized by an effective dipolar distance of 3.90 ± 0.25 Å from the {FeNO}(7) paramagnetic center. The principal axes of this C1-(2)H hyperfine coupling and nuclear quadrupole interaction tensors were found to make angles of 26 ± 5 and 52 ± 17°, respectively, with the principal axis of the {FeNO}(7) zero-field splitting tensor. These results are discussed within the context of the orientation of substrate taurine prior to the initiation of hydrogen abstraction.

Coupling of Li motion and structural distortions in olivine LiMnPO4from7Li and31P NMR

We present a detailed $^7$Li- and $^{31}$P-NMR study on single crystalline LiMnPO$_4$ in the paramagnetic and antiferromagnetic phase (AFM, $T_N \sim$ 34 K). This allows us to determine the spin directions in the field-induced spin-flop phase. In addition, the anisotropic dipolar hyperfine coupling tensor of the $^7$Li- and $^{31}$P-nuclei is also fully determined by orientation and temperature dependent NMR experiments and compared to the calculated values from crystal structure data. Deviations of the experimental values from the theoretical ones are discussed in terms of Mn disorder which is induced by Li-disorder. In fact, the disorder in the Mn-sublattice is directly revealed by our diffuse x-ray scattering data. The present results provide experimental evidence for the Li-diffusion strongly coupling to structural distortions within the MnPO$_4$ host, which is expected to significantly affect the Li-mobility as well as the performance of batteries based on this material.

Convergence of QM/MM and Cluster Models for the Spectroscopic Properties of the Oxygen-Evolving Complex in Photosystem II.

The latest crystal structure of photosystem II at 1.9 Å resolution, which resolves the topology of the Mn4CaO5 oxygen evolving complex (OEC) at atomistic detail, enables a better correlation between structural features and spectroscopic properties than ever before. Building on the refined crystallographic model of the OEC and the protein, we present combined quantum mechanical/molecular mechanical (QM/MM) studies of the spectroscopic properties of the natural catalyst embedded in the protein matrix. Focusing on the S2 state of the catalytic cycle, we examine the convergence of not only structural parameters but also of the intracluster magnetic interactions in terms of exchange coupling constants and of experimentally relevant (55)Mn, (17)O, and (14)N hyperfine coupling constants with respect to QM/MM partitioning using five QM regions of increasing size. This enables us to assess the performance of the method and to probe second sphere effects by identifying amino acid residues that principally affect the spectroscopic properties of the OEC. Comparison between QM-only and QM/MM treatments reveals that whereas QM/MM models converge quickly to stable values, the QM cluster models need to incorporate significantly larger parts of the second coordination sphere and surrounding water molecules to achieve convergence for certain properties. This is mainly due to the sensitivity of the QM-only models to fluctuations in the hydrogen bonding network and ligand acidity. Additionally, a hydrogen bond that is typically omitted in QM-only treatments is shown to determine the hyperfine coupling tensor of the unique Mn(III) ion by regulating the rotation plane of the ligated D1-His332 imidazole ring, the only N-donor ligand of the OEC.

Formation of New Non-oxido Vanadium(IV) Species in Aqueous Solution and in the Solid State by Tridentate (O, N, O) Ligands and Rationalization of Their EPR Behavior

The systems formed by the V(IV)O(2+) ion with tridentate ligands provided with the (O, N(imine), O) donor set were described. The ligands studied were 2,2'-dihydroxyazobenzene (Hdhab), α-(2-hydroxy-5-methylphenylimino)-o-cresol (Hhmpic), calmagite (H2calm), anthracene chrome red A (H3anth), calcon (H2calc), and calconcarboxylic acid (H3calc(C)). They can bind vanadium with the two deprotonated phenol groups and the imine nitrogen to give (5,6)-membered chelate rings. The systems were studied with EPR, UV-vis and IR spectroscopy, pH-potentiometry, and DFT methods. The ligands form unusual non-oxido V(IV) compounds both in aqueous solution and in the solid state. [V(anthH(-1))2](4-) and [V(calmH(-1))2](2-) (formed in water at the physiological pH) and [V(dhabH(-1))2] and [V(hmpicH(-1))2] (formed in the solid state in MeOH) are hexa-coordinated with geometry intermediate between the octahedron and the trigonal prism and an unsymmetric facial arrangement of the two ligand molecules. DFT calculations were used to predict the structure and (51)V hyperfine coupling tensor A of the non-oxido species. The EPR behavior of 13 non-oxido V(IV) species was put into relationship with the relevant geometrical parameters and was rationalized in terms of the spin density on the d(xy) orbital. Depending on the geometric isomer formed (meridional or facial), d(z)(2) mixes with the d(xy) orbital, and this effect causes the lowering of the highest (51)V A value.

Hyperfine interactions and electron distribution in FeIIFeI and FeIFeI models for the active site of the [FeFe] hydrogenases: Mössbauer spectroscopy studies of low-spin FeI

Mössbauer studies of [{μ-S(CH2C(CH3)2CH2S}(μ-CO)Fe(II)Fe(I)(PMe3)2(CO)3]PF6 (1 OX ), a model complex for the oxidized state of the [FeFe]hydrogenases, and the parent Fe(I)Fe(I) derivative are reported. The paramagnetic 1 OX is part of a series featuring a dimethylpropanedithiolate bridge, introducing steric hindrance with profound impact on the electronic structure of the diiron complex. Well-resolved spectra of 1 OX allow determination of the magnetic hyperfine couplings for the low-spin distal Fe(I) ([Formula: see text]) site, A x,y,z = [-24(6),-12(2), 20(2)]MHz, and the detection of significant internal fields (approximately 2.3T) at the low-spin ferrous site, confirmed by density functional theory (DFT) calculations. Mössbauer spectra of 1 OX show nonequivalent sites and no evidence of delocalization up to 200K. Insight from the experimental hyperfine tensors of the Fe(I) site is used in correlation with DFT to reveal the spatial distribution of metal orbitals. The Fe-Fe bond in [Fe2{μ-S(CH2C(CH3)2CH2S}(PMe3)2(CO)4] (1) involving two [Formula: see text]-type orbitals is crucial in keeping the structure intact in the presence of strain. On oxidation, the distal iron site is not restricted by the Fe-Fe bond, and thus the more stable isomer results from inversion of the square pyramid, rotating the [Formula: see text] orbital of [Formula: see text]. DFT calculations imply that the Mössbauer properties can be traced to this [Formula: see text] orbital. The structure of the magnetic hyperfine coupling tensor, A, of the low-spin Fe(I) in 1 OX is discussed in the context of the known Atensors for the oxidized states of the [FeFe]hydrogenases.

H, D and HD adsorption upon the metal-organic framework [CuZn(btc)] studied by pulsed ENDOR and HYSCORE spectroscopy

The adsorption of hydrogen has become interesting in terms of gas separation as well as safe and reversible storage of hydrogen as an energy carrier. In this regard, metal-organic framework compounds are potential candidates. The metal-organic framework [CuZn(btc)] as a partially Zn-substituted analogue of the well known compound HKUST-1 is well suited for studying adsorption geometries at cupric ions by electron paramagnetic resonance (EPR) methods due to the formation of few mixed Cu/Zn paddle wheel units with isolated S = 1/2 electron spins. The adsorption of hydrogen (H2) as well as the deuterium (D2) and HD molecules were investigated by continuous wave EPR and pulsed ENDOR and HYSCORE spectroscopy. The principal values of the proton and deuterium hyperfine coupling tensors and were determined by spectral simulations as well as of the deuterium nuclear quadrupole tensor for adsorbed HD and D2. The results show a side-on coordination of HD and D2 with identical Cu–H and Cu–D distances rCuX = 2.8 Å with the tensors and aligned parallel to the C4 symmetry axis of the paddle wheel unit. A thermodynamic non-equilibrium state with J = 1, mJ = ±1 is indicated by the experimental data with and averaged by rotation around C4.

Formula omitted] radicals for EPR dosimetry: X- and Q band EPR study and LET dependency of crystalline potassium dithionate

The structures of the free radicals formed by the irradiation of potassium dithionate (K2S2O6) with 60Co γ-rays and 14N7+ ions were investigated by EPR to further examine a recently proposed LET effect in this material. Two types of SO3− radical ions were identified in X-irradiated single crystals by measurements at X- and Q bands. One of these (S1) exhibited 33S hyperfine couplings A⊥ = 12.49, A|| = 15.60 mT, the other (S2) A⊥ = 11.29, A|| = 13.92 mT. The g-factors were nearly isotropic, g⊥ = 2.0010, g|| = 2.0003; and g⊥ = 2.0026, g|| = 2.0008, respectively. The 33S hyperfine coupling tensors and g-tensors were axially symmetric about the trigonal <c>-axis, coinciding with the direction of the S–S bonds of the two non-equivalent S2O62− ions in the crystal. A model for the radiation damage was proposed in which the SO3− radical ions retain the orientation of the SO3 groups, aligned along the trigonal axis. The structure of a third main radical species (S3) with g⊥ = 2.0026, g|| = 2.0052 could not be unambiguously assigned, due to undetected 33S features. The relative integrated intensities of S1, S2 and S3 depended on the radiation quality and were approximately estimated as 0.18: 0.65:0.17 for 60Co γ-rays and 0.47: 0.38: 0.15 for 14N7+ ions. Additional weak lines on the low field side of the main signal were tentatively attributed to SO2− radical ions. An even weaker strongly anisotropic pair of lines was attributed to SO3− radical pairs separated by 0.93–0.95 nm along the trigonal axis.

Validating and Analyzing EPR Hyperfine Coupling Constants with Density Functional Theory.

This paper focuses on the calculation of the (isotropic) hyperfine coupling tensor, AisoK, which consists of the Fermi contact term (AFCK) and a spin orbit correction, the pseudocontact term (APCK). Using the aug-cc-pVTZ-J basis set, we test a range of correlation exchange functionals against experimental values for a series of first row transition metal complexes. This has been done both with (AisoK = AFCK + APCK) and without (AisoK = AFCK) spin orbit coupling included. Overall, hybrid functionals perform best, although some exceptions are found. Furthermore, we analyze molecular orbital contributions to the Fermi contact term. We find a great difference in the relative magnitude of contributions from frontier orbitals and inner or outer-core orbitals. Complexes, where the frontier orbital contribution exceeds the core-orbital contributions, are always small, ionic complexes (“class 1”). For these complexes, the computational requirements with respect to the one-electron basis set are not severe, and reg...

A Combined Pulsed Electron Paramagnetic Resonance Spectroscopic and DFT Analysis of the13CO2and13CO Adsorption on the Metal–Organic Framework Cu2.97Zn0.03(btc)2

Cu3(btc)2 (btc = 1,3,5-benzenetricarboxylate), also called HKUST-1, is one of the well-known representatives of the metal–organic framework (MOF) compounds. It exhibits a large surface area and a high pore volume. Due to the coordinatively unsaturated metal centers as preferential adsorption sites, Cu3(btc)2 is particularly interesting for the separation of CO2 and CO in gaseous mixtures. We studied the interactions of 13C-enriched carbon dioxide (13CO2) and carbon monoxide (13CO) with the Cu2+ centers in the zinc-substituted homologue Cu2.97Zn0.03(btc)2 using continuous wave (cw) and pulsed electron paramagnetic resonance (EPR) spectroscopy (Davies or Mims electron nuclear double resonance (ENDOR) and hyperfine sublevel correlation (HYSCORE)). Upon adsorption of 13CO2 and 13CO, the coordination geometry of the Cu2+ centers changed from square planar to square pyramidal. The cupric ion g-tensor and the 63/65Cu hyperfine coupling tensor ACu show the changes in the ligand field of Cu2+. Moreover, the interaction with the 13C nuclei of the gas molecules is reflected in the isotropic coupling constant AisoC and the dipolar coupling parameter T⊥C which are derived from the 13C hyperfine coupling tensor AC obtained by the pulsed EPR experiments. From the experimentally obtained parameters, we derived a geometrical model for the adsorption of 13CO2 and 13CO at the Cu2+ ions that is consistent with our DFT calculations. The 13CO molecule is found to coordinate linearly at the Cu2+ center via the 13C atom and perpendicular to the CuO4 plane with a Cu–C distance of rCuC = 2.57(10) Å (DFT, 2.42 Å). The 13CO2 molecule is coordinated slightly tilted via the O atom with a Cu–C distance of rCuC = 3.34(10) Å (DFT, 3.27 Å). The Cu–O distance for adsorbed 13CO2 is not directly accessible to EPR measurements but could be estimated from geometrical considerations in the range of rCuO = 2.53–2.73 Å (DFT, 2.39 Å). The results provide detailed insight into the geometry of adsorbed CO2 and CO in porous materials and show the potential of EPR spectroscopy for analyzing adsorption complexes.

Electron Paramagnetic Resonance Spectroscopic Study of Copper Hopping in Doped Bis(l-histidinato)cadmium Dihydrate

Electron paramagnetic resonance (EPR) spectroscopy was used to study Cu(II) dynamic behavior in a doped biological model crystal, bis(L-histidinato)cadmium dihydrate, in order to gain better insight into copper site stability in metalloproteins. Temperature-dependent changes in the low temperature X-band EPR spectra became visible around 100 K and continued up to room temperature. The measured 298 K g-tensor (principal values: 2.17, 2.16, 2.07) and copper hyperfine coupling tensor (principal values: -260, -190, -37 MHz) were similar to the average of the 77 K tensor values pertaining to two neighboring histidine binding sites. The observed temperature dependence was interpreted using Anderson's theory of motional narrowing, where the magnetic parameters for the different states are averaged as the copper rapidly hops between sites. The EPR pattern was also found to undergo a sharp sigmoidal-shaped, temperature-dependent conversion between two species with a critical temperature T(c) ≈ 160 K. The species below T(c) hops between the two low temperature site patterns, and the one above T(c) represents an average of the molecular spin Hamiltonian coupling tensors of the two 77 K sites. In addition, the low and high temperature species hop between one another, contributing to the dynamic averaging. Spectral simulations using this 4-state model determined a hop rate between the two low temperature sites ν(h4) = 4.5 × 10(8) s(-1) and between the low and high temperature states ν(h2) = 1.7 × 10(8) s(-1) at 160 K. An Arrhenius relationship of hop rate and temperature gave energy barriers of ΔE4 = 389 cm(-1) and ΔE2 = 656 cm(-1) between the two low temperature sites and between the low and high temperature states, respectively.

Derivation and assessment of relativistic hyperfine-coupling tensors on the basis of orbital-optimized second-order Møller–Plesset perturbation theory and the second-order Douglas–Kroll–Hess transformation

The accurate calculation of hyperfine-coupling tensors requires a good description of the electronic spin density, especially close to and at the nucleus. Thus, dynamic correlation as well as relativistic effects have to be included in the quantum-chemical calculation of this quantity. In this paper, orbital-optimized second-order Møller-Plesset perturbation theory (MP2) is combined with the second-order Douglas-Kroll-Hess (DKH) transformation to yield an efficient and accurate ab initio method for the calculation of hyperfine couplings for larger molecules including heavy elements. Particular attention is paid to the derivation of the hyperfine-coupling tensor in the DKH framework. In the presence of a magnetic field, the DKH-transformation is not unique. Two different versions can be found in the literature. In this paper, a detailed derivation of one-electron contributions to the hyperfine-coupling tensor as they arise in linear-response theory is given for both DKH-transformations. It turns out that one of the two variants produces divergent hyperfine-coupling constants. The possibility to remove this divergence through a physically motivated finite-nucleus model taking into account the different extent of charge and magnetization distribution is discussed. Hyperfine-coupling values obtained at the orbital-optimized MP2 level with second-order DKH corrections for the non-divergent variant are presented. The influence of a Gaussian nucleus model is studied. The method is compared to four-component, high-accuracy calculations for a number of cations and atoms. Comparison to B3LYP and B2PLYP is made for a set of transition-metal complexes of moderate size.

Electron correlation and nuclear charge dependence of parity-violating properties in open-shell diatomic molecules

The scaling of nuclear spin-dependent parity violating effects with increasing nuclear charge $Z$ is discussed in two series of isovalent open-shell diatomic molecules. The parameter $W_\mathrm{a}$ characterising the strength of parity violation in diatomic molecules is calculated in the framework of the zeroth-order regular approximation (ZORA) and found to be in good agreement with the $R(Z) Z^k$ scaling law derived for atoms in which $R(Z)$ represents a relativistic enhancement factor. The influence of electron correlation is studied on the molecular level, with spin-polarisation effects being conveniently accounted for by a previously established approximate relation between the hyperfine coupling tensor and $W_\mathrm{a}$. For high accuracy predictions of parity violating effects in radium fluoride the necessity for systematically improvable correlation calculations is emphasised.