Calculating NMR Chemical Shifts for Paramagnetic Metal Complexes from First-Principles

Tris-Silanide f-Block Complexes: Insights into Paramagnetic Influence on NMR Chemical Shifts

The paramagnetism of f-block ions has been exploited in chiral shift reagents and magnetic resonance imaging, but these applications tend to focus on 1H NMR shifts as paramagnetic broadening makes less sensitive nuclei more difficult to study. Here we report a solution and solid-state (ss) 29Si NMR study of an isostructural series of locally D 3h -symmetric early f-block metal(III) tris-hypersilanide complexes, [M{Si(SiMe3)3}3(THF)2] (1-M; M = La, Ce, Pr, Nd, U); 1-M were also characterized by single crystal and powder X-ray diffraction, EPR, ATR-IR, and UV-vis-NIR spectroscopies, SQUID magnetometry, and elemental analysis. Only one SiMe3 signal was observed in the 29Si ssNMR spectra of 1-M, while two SiMe3 signals were seen in solution 29Si NMR spectra of 1-La and 1-Ce. This is attributed to dynamic averaging of the SiMe3 groups in 1-M in the solid state due to free rotation of the M-Si bonds and dissociation of THF from 1-M in solution to give the locally C 3v -symmetric complexes [M{Si(SiMe3)3}3(THF) n ] (n = 0 or 1), which show restricted rotation of M-Si bonds on the NMR time scale. Density functional theory and complete active space self-consistent field spin-orbit calculations were performed on 1-M and desolvated solution species to model paramagnetic NMR shifts. We find excellent agreement of experimental 29Si NMR data for diamagnetic 1-La, suggesting n = 1 in solution and reasonable agreement of calculated paramagnetic shifts of SiMe3 groups for 1-M (M = Pr and Nd); the NMR shifts for metal-bound 29Si nuclei could only be reproduced for diamagnetic 1-La, showing the current limitations of pNMR calculations for larger nuclei.

Paramagnetic Properties of [AnIV(NO3)6]2- Complexes (An = U, Np, Pu) Probed by NMR Spectroscopy and Quantum Chemical Calculations

Actinide +IV complexes with six nitrates [AnIV(NO3)6]2- (An = Th, U, Np, and Pu) have been studied by 15N and 17O NMR spectroscopy in solution and first-principles calculations. Magnetic susceptibilities were evaluated experimentally using the Evans method and are in good agreement with the ab initio values. The evolution in the series of the crystal field parameters deduced from ab initio calculations is discussed. The NMR paramagnetic shifts are analyzed based on ab initio calculations. Because the cubic symmetry of the complex quenches the dipolar contribution, they are only of Fermi contact origin. They are evaluated from first-principles based on a complete active space/density functional theory (DFT) strategy, in good accordance with the experimental one. The ligand hyperfine coupling constants are deduced from paramagnetic shifts and calculated using unrestricted DFT. The latter are decomposed in terms of the contribution of molecular orbitals. It highlights two pathways for the delocalization of the spin density from the metallic open-shell 5f orbitals to the NMR active nuclei, either through the valence 5f hybridized with 6d to the valence 2p molecular orbitals of the ligands, or by spin polarization of the metallic 6p orbitals which interact with the 2s-based molecular orbitals of the ligands.

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts

ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.

Mechanisms of Ligand Hyperfine Coupling in Transition-Metal Complexes: σ and π Transmission Pathways

Theoretical interpretation of hyperfine interactions was pioneered in the 1950s-1960s by the seminal works of McConnell, Karplus, and others for organic radicals and by Watson and Freeman for transition-metal (TM) complexes. In this work, we investigate a series of octahedral Ru(III) complexes with aromatic ligands to understand the mechanism of transmission of the spin density from the d-orbital of the metal to the s-orbitals of the ligand atoms. Spin densities and spin populations underlying ligand hyperfine couplings are analyzed in terms of π-conjugative or σ-hyperconjugative delocalization vs spin polarization based on symmetry considerations and restricted open-shell vs unrestricted wave function analysis. The transmission of spin density is shown to be most efficient in the case of symmetry-allowed π-conjugative delocalization, but when the π-conjugation is partially or fully symmetry-forbidden, it can be surpassed by σ-hyperconjugative delocalization. Despite a lower spin population of the ligand in σ-hyperconjugative transmission, the hyperfine couplings can be larger because of the direct involvement of the ligand s-orbitals in this delocalization pathway. We demonstrate a quantitative correlation between the hyperfine couplings of aromatic ligand atoms and the characteristics of the metal-ligand bond modulated by the trans substituent, a hyperfine trans effect.

Delving into theoretical and computational considerations for accurate calculation of chemical shifts in paramagnetic transition metal systems using quantum chemical methods

The chemical shielding tensor for a paramagnetic system has been derived from the macroscopically observed magnetization using the perturbation theory. An approach to calculate the paramagnetic chemical shifts in transition metal systems based on the spin-only magnetic susceptibility directly evaluated from the ab initio Hilbert space of the electronic Zeeman Hamiltonian has been discussed. Computationally, several advantages are associated with this approach: (a) it includes the state-specific paramagnetic Curie (first-order) and Van Vleck (second-order) contributions of the paramagnetic ion to the paramagnetic chemical shifts; (b) thus it avoids the system-specific modeling and evaluating effectively in terms of the electron paramagnetic resonance (EPR) spin Hamiltonian parameters of the magnetic moment of the paramagnetic ion formulated previously; (c) it can be utilized both in the point-dipole (PD) approximation (in the long-range) and with the quantum chemical (QC) method based the hyperfine tensors (in the short-range). Additionally, we have examined the predictive performance of various density functional theory (DFT) functionals of different families and commonly used core-augmented basis sets for nuclear magnetic resonance (NMR) chemical shifts. A selection of transition metal ion complexes with and without first-order orbital contributions, namely the [M(AcPyOx)3(BPh)]+ complexes of M = Mn2+, Ni2+ and Co2+ ions and CoTp2 complex and their reported NMR chemical shifts are studied from QC methods for illustration.

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

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

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Are Actinyl Cations Good Probes for Structure Determination in Solution by NMR?

We report on NMR spectroscopy, CAS-based method calculations, and X-ray diffraction of An^V and An^VI complexes with a neutral and slightly flexible TEDGA ligand. After checking that pNMR shifts mainly arise from pseudocontact interactions, we analyze pNMR shifts considering the axial and rhombic anisotropy of the actinyl magnetic susceptibilities. The results are compared to those of a previous study performed on [An^VIO₂]²⁺ complexes with dipicolinic acid. It is shown that 5f² cations (Pu^VI and Np^V) make very good candidates for determining the structure of actinyl complexes in solution by ¹H NMR spectroscopy as shown by the invariance of the magnetic properties to the equatorial ligands, as opposed to the Np^VI complexes with a 5f¹ configuration.

Nature of NMR Shifts in Paramagnetic Octahedral Ru(III) Complexes with Axial Pyridine-Based Ligands

In recent decades, transition-metal coordination compounds have been extensively studied for their antitumor and antimetastatic activities. In this work, we synthesized a set of symmetric and asymmetric Ru(III) and Rh(III) coordination compounds of the general structure (Na⁺/K⁺/PPh₄⁺/LH⁺) [trans-M^IIIL(eq)_nL(ax)₂]^- (M = Ru^III or Rh^III; L(eq) = Cl, n = 4; L(eq) = ox, n = 2; L(ax) = 4-R-pyridine, R = CH₃, H, C₆H₅, COOH, CF₃, CN; L(ax) = DMSO-S) and systematically investigated their structure, stability, and NMR properties. ¹H and ¹³C NMR spectra measured at various temperatures were used to break down the total NMR shifts into the orbital (temperature-independent) and hyperfine (temperature-dependent) contributions. The hyperfine NMR shifts for paramagnetic Ru(III) compounds were analyzed in detail using relativistic density functional theory (DFT). The effects of (i) the 4-R substituent of pyridine, (ii) the axial trans ligand L(ax), and (iii) the equatorial ligands L(eq) on the distribution of spin density reflected in the "through-bond" (contact) and the "through-space" (pseudocontact) contributions to the hyperfine NMR shifts of the individual atoms of the pyridine ligands are rationalized. Further, we demonstrate the large effects of the solvent on the hyperfine NMR shifts and discuss our observations in the general context of the paramagnetic NMR spectroscopy of transition-metal complexes.

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

Computational NMR of the iron pyrazolylborate complexes [Tp2Fe]+ and Tp2Fe including solvation and spin-crossover effects

Transition metal complexes have important roles in many biological processes as well as applications in fields such as pharmacy, chemistry and materials science. Paramagnetic nuclear magnetic resonance (pNMR) is a valuable tool in understanding such molecules, and theoretical computations are often advantageous or even necessary in the assignment of experimental pNMR signals. We have employed density functional theory (DFT) and the domain-based local pair natural orbital coupled-cluster method with single and double excitations (DLPNO-CCSD), as well as a number of model improvements, to determine the critical hyperfine part of the chemical shifts of the iron pyrazolylborate complexes [Tp₂Fe]⁺ and Tp₂Fe using a modern version of the Kurland-McGarvey theory, which is based on parameterising the hyperfine, electronic Zeeman and zero-field splitting interactions via the parameters of the electron paramagnetic resonance Hamiltonian. In the doublet [Tp₂Fe]⁺ system, the calculations suggest a re-assignment of the ¹³C signal shifts. Consideration of solvent via the conductor-like polarisable continuum model (C-PCM) versus explicit solvent molecules reveals C-PCM alone to be insufficient in capturing the most important solvation effects. Tp₂Fe exhibits a spin-crossover effect between a high-spin quintet (S = 2) and a low-spin singlet (S = 0) state, and its recorded temperature dependence can only be reproduced theoretically by accounting for the thermal Boltzmann distribution of the open-shell excited state and the closed-shell ground-state occupations. In these two cases, DLPNO-CCSD is found, in calculating the hyperfine couplings, to be a viable alternative to DFT, the demonstrated shortcomings of which have been a significant issue in the development of computational pNMR.

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

Quantum Chemical Approaches to the Calculation of NMR Parameters: From Fundamentals to Recent Advances

Quantum chemical methods for the calculation of indirect NMR spin–spin coupling constants and chemical shifts are always in progress. They never stay the same due to permanently developing computational facilities, which open new perspectives and create new challenges every now and then. This review starts from the fundamentals of the nonrelativistic and relativistic theory of nuclear magnetic resonance parameters, and gradually moves towards the discussion of the most popular common and newly developed methodologies for quantum chemical modeling of NMR spectra.

Theoretical analysis of the long-distance limit of NMR chemical shieldings

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

Covalency of Trivalent Actinide Ions with Different Donor Ligands: Do Density Functional and Multiconfigurational Wavefunction Calculations Corroborate the Observed "Breaks"?

A comprehensive ab initio study of periodic actinide-ligand bonding trends for trivalent actinides is performed. Relativistic density functional theory (DFT) and complete active-space (CAS) self-consistent field wavefunction calculations are used to dissect the chemical bonding in the [AnCl₆]^3-, [An(CN)₆]^3-, [An(NCS)₆]^3-, [An(S₂PMe₂)₃], [An(DPA)₃]^3-, and [An(HOPO)]^- series of actinide (An = U-Es) complexes. Except for some differences for the early actinide complexes with DPA, bond orders and excess 5f-shell populations from donation bonding show qualitatively similar trends in 5f ⁿ active-space CAS vs DFT calculations. The influence of spin-orbit coupling on donation bonding is small for the tested systems. Along the actinide series, chemically soft vs chemically harder ligands exhibit clear differences in bonding trends. There are pronounced changes in the 5f populations when moving from Pu to Am or Cm, which correlate with previously noted "breaks" in chemical trends. Bonding involving 5f becomes very weak beyond Cm/Bk. We propose that Cm(III) is a borderline case among the trivalent actinides that can be meaningfully considered to be involved in ground-state 5f covalent bonding.

Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding tensors and shifts in a nonrelativistic and scalar-relativistic density functional theory framework. For the latter, we make use of the scalar exact two-component Hamiltonian in its local approximation, and generally we apply the well established (multipole-accelerated) resolution of the identity approximation and the seminumerical exchange approximation. The perturbed density matrix of a paramagnetic NMR shielding calculation is further used to study the magnetically induced current density and ring currents of open-shell systems as illustrated for [U@Bi₁₂]^3-. [U@Bi₁₂]^3- features delocalized highest occupied molecular orbitals and sustains a net diatropic ring current of ca. 18 nA/T through the Bi₁₂ torus similar to the all-metal aromatic heavy-element cluster [Th@Bi₁₂]^4-.

Crystal and Substituent Effects on Paramagnetic NMR Shifts in Transition-Metal Complexes

Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed information about their molecular and electron-spin structure. The paramagnetic NMR spectrum is a very rich source of information about the hyperfine interaction between the atomic nuclei and the unpaired electron density. The Fermi-contact contribution to ligand hyperfine NMR shifts is particularly informative about the nature of the metal–ligand bonding and the structural arrangements of the ligands coordinated to the metal center. In this account, we provide a detailed experimental and theoretical NMR study of compounds of Cr(III) and Cu(II) coordinated with substituted acetylacetonate (acac) ligands in the solid state. For the first time, we report the experimental observation of extremely paramagnetically deshielded ¹³C NMR resonances for these compounds in the range of 900–1200 ppm. We demonstrate an excellent agreement between the experimental NMR shifts and those calculated using relativistic density-functional theory. Crystal packing is shown to significantly influence the NMR shifts in the solid state, as demonstrated by theoretical calculations of various supramolecular clusters. The resonances are assigned to individual atoms in octahedral Cr(acac)₃ and square-planar Cu(acac)₂ compounds and interpreted by different electron configurations and magnetizations at the central metal atoms resulting in different spin delocalizations and polarizations of the ligand atoms. Further, effects of substituents on the ¹³C NMR resonance of the ipso carbon atom reaching almost 700 ppm for Cr(acac)₃ compounds are interpreted based on the analysis of Fermi-contact hyperfine contributions.

The ligand NMR shifts in paramagnetic acetylacetonato Cr(III) and Cu(II) complexes have been predicted and measured in the solid state and interpreted by relativistic DFT calculations. The effects of the metal atom, ligand, and crystal packing on the spin delocalization and polarization reflected in the Fermi-contact contribution to the hyperfine interaction are rationalized.

Temperature Dependence of 1 H Paramagnetic Chemical Shifts in Actinide Complexes, Beyond Bleaney's Theory: The AnVI O2 2+ -Dipicolinic Acid Complexes (An=Np, Pu) as an Example

Actinide +VI complexes ( A n V I = U V I , N p V I and P u V I ) with dipicolinic acid derivatives were synthesized and characterized by powder XRD, SQUID magnetometry and NMR spectroscopy. In addition, N p V I and P u V I complexes were described by first principles CAS based and two-component spin-restricted DFT methods. The analysis of the ¹ H paramagnetic NMR chemical shifts for all protons of the ligands according to the X-rays structures shows that the Fermi contact contribution is negligible in agreement with spin density determined by unrestricted DFT. The magnetic susceptibility tensor is determined by combining SQUID, pNMR shifts and Evans' method. The SO-RASPT2 results fit well the experimental magnetic susceptibility and pNMR chemical shifts. The role of the counterions in the solid phase is pointed out; their presence impacts the magnetic properties of the N p V I complex. The temperature dependence of the pNMR chemical shifts has a strong 1 / T contribution, contrarily to Bleaney's theory for lanthanide complexes. The fitting of the temperature dependence of the pNMR chemical shifts and SQUID magnetic susceptibility by a two-Kramers-doublet model for the N p V I complex and a non-Kramers-doublet model for the P u V I complex allows for the experimental evaluation of energy gaps and magnetic moments of the paramagnetic center.

A Quantum Chemistry View on Two Archetypical Paramagnetic Pentacoordinate Nickel(II) Complexes Offers a Fresh Look on Their NMR Spectra

Quantum chemical methods for calculating paramagnetic NMR observables are becoming increasingly accessible and are being included in the inorganic chemistry practice. Here, we test the performance of these methods in the prediction of proton hyperfine shifts of two archetypical high-spin pentacoordinate nickel(II) complexes (NiSAL-MeDPT and NiSAL-HDPT), which, for a variety of reasons, turned out to be perfectly suited to challenge the predictions to the finest level of detail. For NiSAL-MeDPT, new NMR experiments yield an assignment that perfectly matches the calculations. The slightly different hyperfine shifts from the two “halves” of the molecules related by a pseudo-C₂ axis, which are experimentally divided into two well-defined spin systems, are also straightforwardly distinguished by the calculations. In the case of NiSAL-HDPT, for which no X-ray structure is available, the quality of the calculations allowed us to refine its structure using as a starting template the structure of NiSAL-MeDPT.

State-of-the-art quantum chemical methods and paramagnetism-tailored NMR experiments provide a deep insight on the relation between the spectra and the electronic structure for two paramagnetic pentacoordinate nickel(II) complexes.

Electron-Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab initio wavefunction calculations at the multireference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron-nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on nonrelativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538-549] and therefore had limited applicability. Results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic "semiempirical" equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn-Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS.

Paramagnetic Pyrazolylborate Complexes Tp2M and Tp*2M: 1H, 13C, 11B, and 14N NMR Spectra and First-Principles Studies of Chemical Shifts

The paramagnetic pyrazolylborates Tp₂M and Tp*₂M (M = Cu, Ni, Co, Fe, Mn, Cr, V) as well as [Tp₂M]⁺ and [Tp*₂M]⁺ (M = Fe, Cr, V) have been synthesized and their NMR spectra recorded. The ¹H signal shift ranges vary from ∼30 ppm (Cu(II) and V(III)) to ∼220 ppm (Co(II)), and the ¹³C signal shift ranges from ∼180 ppm (Fe(III)) to ∼1150 ppm (Cr(II)). The ¹¹B and ¹⁴N shifts are ∼360 and ∼730 ppm, respectively. Both negative and positive shifts have been observed for all nuclei. The narrow NMR signals of the Co(II), Fe(II), Fe(III), and V(III) derivatives provide resolved ¹³C,¹H couplings. All chemical shifts have been calculated from first-principles on a modern version of Kurland-McGarvey theory which includes optimized structures, zero-field splitting, and g tensors, as well as signal shift contributions. Temperature dependence in the Fe(II) spin-crossover complex results from the equilibrium of the ground singlet and the excited quintet. We illustrate both the assignment and analysis capabilities, as well as the shortcomings of the current computational methodology.

Remarkable reversal of 13C-NMR assignment in d1, d2 compared to d8, d9 acetylacetonate complexes: analysis and explanation based on solid-state MAS NMR and computations

13C solid-state MAS NMR spectra of a series of paramagnetic metal acetylacetonate complexes; [VO(acac)2] (d1, S = ½), [V(acac)3] (d2, S = 1), [Ni(acac)2(H2O)2] (d8, S = 1), and [Cu(acac)2] (d9, S = ½), were assigned using modern NMR shielding calculations. This provided a reliable assignment of the chemical shifts and a qualitative insight into the hyperfine couplings. Our results show a reversal of the isotropic 13C shifts, δiso(13C), for CH3 and CO between the d1 and d2versus the d8 and d9 acetylacetonate complexes. The CH3 shifts change from about -150 ppm (d1,2) to roughly 1000 ppm (d8,9), whereas the CO shifts decrease from 800 ppm to about 150 ppm for d1,2 and d8,9, respectively. This was rationalized by comparison of total spin-density plots and computed contact couplings to those corresponding to singly occupied molecular orbitals (SOMOs). This revealed the interplay between spin delocalization of the SOMOs and spin polarization of the lower-energy MOs, influenced by both the molecular symmetry and the d-electron configuration. A large positive chemical shift results from spin delocalization and spin polarization acting in the same direction, whereas their cancellation corresponds to a small shift. The SOMO(s) for the d8 and d9 complexes are σ-like, implying spin-delocalization on the CH3 and CO groups of the acac ligand, cancelled only for CO by spin polarization. In contrast, the SOMOs of the d1 and d2 systems are π-like and a large CO-shift results from spin polarization, which accounts for the reversed assignment of δiso(13C) for CH3 and CO.

31P MAS NMR and DFT study of crystalline phosphate matrices

We present the study of the phosphorus local environment by using ³¹P MAS NMR in a series of seven double monophosphates M^IIM^IV(PO₄)₂ (M^II and M^IV being divalent and tetravalent cations, respectively) of yavapaiite and low-yavapaiite type crystal structures. Solid-state and cluster DFT calculations were found to be efficient for predicting the ³¹P isotropic chemical shift and chemical shift anisotropy. To achieve this performance, however, a proper computational optimisation of the experimental structural data was required. From the three optimisation methods tested, the full optimisation provided the best reference structure for the calculation of the NMR parameters of the studied phosphates. Also, a better prediction of the chemical shifts was possible by using a correction to the GIPAW calculated shielding.

Magnetic susceptibility and paramagnetism-based NMR

The magnetic interactions between the nuclear magnetic moment and the magnetic moment of unpaired electron(s) depend on the structure and dynamics of the molecules where the paramagnetic center is located and of their partners. The long-range nature of the magnetic interactions is thus a reporter of invaluable information for structural biology studies, when other techniques often do not provide enough data for the atomic-level characterization of the system. This precious information explains the flourishing of paramagnetism-assisted NMR studies in recent years. Many paramagnetic effects are related to the magnetic susceptibility of the paramagnetic metal. Although these effects have been known for more than half a century, different theoretical models and new approaches have been proposed in the last decade. In this review, we have summarized the consequences for NMR spectroscopy of magnetic interactions between nuclear and electron magnetic moments, and thus of the presence of a magnetic susceptibility due to metals, and we do so using a unified notation.

Probing Jahn-Teller distortions in Mn(acac)3 through paramagnetic interactions in solid-state MAS NMR

The structural and electronic properties of solid coordination compounds are of great interest in a wide variety of applications. The sensitivity of solid-state NMR to local structural environments in the presence of a transition metal with unpaired spins is demonstrated through ¹³C and ¹H MAS NMR spectra of tris(acetylacetonato)manganese (III), Mn(acac)₃. The spectral assignment is established using a combination of density-functional theory and experimental NMR methods. An analysis of the spin-density distribution throughout the ligands as probed by NMR provides an understanding of the molecular electronic structure. The paramagnetic interaction enhances the spectral resolution and offers the possibility of using these spectra as structural fingerprints. The unique character of Mn(acac)₃ to manifest various degrees of Jahn-Teller distortions allows for a discussion of the relation between the electron occupancy, crystal structure, and ¹³C NMR peak shifts.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Insight of the Metal-Ligand Interaction in f-Element Complexes by Paramagnetic NMR Spectroscopy

The magnetic properties of Ln^III and An^III complexes formed with dipicolinate ligands have been studied by NMR spectroscopy. To know precisely the geometries of these complexes, a crystallographic study by single-crystal X-ray diffraction (XRD) and extended X-ray absorption fine structure (EXAFS) in solution was performed. Several methods to separate the paramagnetic shifts observed in the NMR spectra were applied to these complexes. Methods using a number of nuclei of the dipicolinate ligands revealed an abrupt change in the geometries of the complexes and a metal-ligand interaction in the middle of the lanthanide series. A study of the variation of the paramagnetic shifts with temperature demonstrated that higher-order terms of the dipolar and contact contributions are required, especially for the lightest Ln^III and almost all the studied An^III . Bleaney's parameters <S_z >_a and C a D relating to the contact and dipolar terms, respectively, were deduced from experimental data and compared with the results of ab initio calculations. Quite a good agreement was found for the temperature dependencies of <S_z >_a and C a D . However, the C a D values obtained from cation magnetic anisotropy calculations showed some discrepancies with the values derived from Bleaney's equation defined for Ln^III . Other parameters, such as the crystal field parameter and the hyperfine constants F_i obtained from the experimental data of the [An(ethyl-dpa)₃ ]^3- complexes (ethyl-dpa=4-ethyl-2,6-dipicolinic acid), are at odds with the assumptions underlying Bleaney's theory.

Similar ligand-metal bonding for transition metals and actinides? 5f1 U(C7H7)2-versus 3d n metallocenes

U(C7H7)2- is a fascinating 5f1 complex whose metal-ligand bonding was assigned in the literature as being very similar to 3d7 cobaltocene, based on a crystal-field theoretical interpretation of the experimental magnetic resonance data. The present work provides an in-depth theoretical study of the electronic structure, bonding, and magnetic properties of the 5f1 U(C7H7)2-vs. 3d metallocenes with V, Co, and Ni, performed with relativistic wavefunction and density functional methods. The ligand to metal donation bonding in U(C7H7)2- is strong and in fact similar to that in vanadocene, in the sense that the highest occupied arene orbitals donate electron density into empty metal orbitals of the same symmetry with respect to the rotational axis (3dπ for V, 5fδ for U), but selectively with α spin (↑). For Co and Ni, the dative bonding from the ligands is β spin (↓) selective into partially filled 3dπ orbitals. In all systems, this spin delocalization triggers spin polarization in the arene σ bonding framework, causing proton spin densities opposite to those of the carbons. As a consequence, the proton spin densities and hyperfine coupling constants are negative for the Co and Ni complex, but positive for vanadocene. The of U(C7H7)2- is negative and similar to that of cobaltocene, but only because of the strong spin-orbit coupling in the actinocene, which causes to be opposite to the sign of the proton spin density. The study contributes to a better understanding of actinide 5f vs. transition metal 3d covalency, and highlights potential pitfalls when interpreting experimental magnetic resonance data in terms of covalent bonding for actinide complexes.

Interplay of Through-Bond Hyperfine and Substituent Effects on the NMR Chemical Shifts in Ru(III) Complexes

The links between the molecular structure and nuclear magnetic resonance (NMR) parameters of paramagnetic transition-metal complexes are still relatively unexplored. This applies particularly to the contact term of the hyperfine contribution to the NMR chemical shift. We report combining experimental NMR with relativistic density functional theory (DFT) to study a series of Ru(III) complexes with 2-substituted β-diketones. A series of complexes with systematically varied substituents was synthesized and analyzed using ¹H and ¹³C NMR spectroscopy. The NMR spectra recorded at several temperatures were used to construct Curie plots and estimate the temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the NMR shift. Relativistic DFT calculations of electron paramagnetic resonance and NMR parameters were performed to interpret the experimental observations. The effects of individual factors such as basis set, density functional, exact-exchange admixture, and relativity are analyzed and discussed. Based on the calibration study in this work, the fully relativistic Dirac-Kohn-Sham (DKS) method, the GIAO approach (orbital shift), the PBE0 functional with the triple-ζ valence basis sets, and the polarizable continuum model for describing solvent effects were selected to calculate the NMR parameters. The hyperfine contribution to the total paramagnetic NMR (pNMR) chemical shift is shown to be governed by the Fermi-contact (FC) term, and the substituent effect (H vs Br) on the through-bond FC shifts is analyzed, interpreted, and discussed in terms of spin-density distribution, atomic spin populations, and molecular-orbital theory. In contrast to the closed-shell systems of Rh(III), the presence of a single unpaired electron in the open-shell Ru(III) analogs significantly alters the NMR resonances of the ligand atoms distant from the metal center in synergy with the substituent effect.

Comparison of the Magnetic Anisotropy and Spin Relaxation Phenomenon of Dinuclear Terbium(III) Phthalocyaninato Single-Molecule Magnets Using the Geometric Spin Arrangement

Herein we report the synthesis and characterization of a dinuclear Tb^III single-molecule magnet (SMM) with two [TbPc₂]⁰ units connected via a fused-phthalocyaninato ligand. The stable and robust complex [(obPc)Tb(Fused-Pc)Tb(obPc)] (1) was characterized by using synchrotron radiation measurements and other spectroscopic techniques (ESI-MS, FT-IR, UV). The magnetic couplings between the Tb^III ions and the two π radicals present in 1 were explored by means of density functional theory (DFT). Direct and alternating current magnetic susceptibility measurements were conducted on magnetically diluted and nondiluted samples of 1, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc₂]^-/0/+ and the axially symmetric dinuclear Tb^III phthalocyaninato triple-decker complex (Tb₂(obPc)₃). Assuming that the probability of quantum tunneling of the magnetization (QTM) occurring in one TbPc₂ unit is P_QTM, the probability of QTM simultaneously occurring in 1 is P_QTM², meaning that QTM is effectively suppressed. Furthermore, nondiluted samples of 1 underwent slow magnetic relaxation times (τ ≈ 1000 s at 0.1 K), and the blocking temperature (T_B) was determined to be ca. 16 K with an energy barrier for spin reversal (U_eff) of 588 cm^-1 (847 K) due to D_4d geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (H_bias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamic) were done on 1, which led to the determination of the high rotation barrier (83 ± 10 kJ/mol) of the obPc ligand. A comparison with previously reported Tb^III triple-decker compounds shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large U_eff causes strong uniaxial magnetic anisotropy in 1, leading to a χ_ax value (1.39 × 10^-30 m³) that is larger than that for Tb₂(obPc)₃ (0.86 × 10^-30 m³). Controlling the coordination environment and spin arrangement is an effective technique for suppressing QTM in TbPc₂-based SMMs.

Pseudocontact shifts from mobile spin labels

This paper presents a detailed analysis of the pseudocontact shift (PCS) field induced by a mobile spin label that is viewed as a probability density distribution with an associated effective magnetic susceptibility anisotropy. It is demonstrated that non-spherically symmetric density can lead to significant deviations from the commonly used point dipole approximation for the PCS. Analytical and numerical solutions are presented for the general partial differential equation that describes the non-point case. It is also demonstrated that it is possible, with some reasonable approximations, to reconstruct paramagnetic centre probability distributions from the experimental PCS data.

Assignment of solid-state 13C and 1H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations

Recent advances in computational methodology allowed for first-principles calculations of the nuclear shielding tensor for a series of paramagnetic nickel(II) acetylacetonate complexes, [Ni(acac)₂L₂] with L = H₂O, D₂O, NH₃, ND₃, and PMe₂Ph have provided detailed insight into the origin of the paramagnetic contributions to the total shift tensor. This was employed for the assignment of the solid-state ^1,2H and ¹³C MAS NMR spectra of these compounds. The two major contributions to the isotropic shifts are by orbital (diamagnetic-like) and contact mechanism. The orbital shielding, contact, as well as dipolar terms all contribute to the anisotropic component. The calculations suggest reassignment of the ¹³C methyl and carbonyl resonances in the acac ligand [Inorg. Chem.53, 2014, 399] leading to isotropic paramagnetic shifts of δ(¹³C) ≈ 800-1100 ppm and ≈180-300 ppm for ¹³C for the methyl and carbonyl carbons located three and two bonds away from the paramagnetic Ni(II) ion, respectively. Assignment using three different empirical correlations, i.e., paramagnetic shifts, shift anisotropy, and relaxation (T₁) were ambiguous, however the latter two support the computational results. Thus, solid-state NMR spectroscopy in combination with modern quantum-chemical calculations of paramagnetic shifts constitutes a promising tool for structural investigations of metal complexes and materials.

Uranyl Carbonate Complexes in Aqueous Solution and Their Ligand NMR Chemical Shifts and 17O Quadrupolar Relaxation Studied by ab Initio Molecular Dynamics

Dynamic structural effects, NMR ligand chemical shifts, and ¹⁷O NMR quadrupolar relaxation rates are investigated in the series of complexes UO₂²⁺, UO₂(CO₃)₃^4-, and (UO₂)₃(CO₃)₆^6-. Car-Parrinello molecular dynamics (CPMD) is used to simulate the dynamics of the complexes in water. NMR properties are computed on clusters extracted from the CPMD trajectories. In the UO₂²⁺ complex, coordination at the uranium center by water molecules causes a decrease of around 300 ppm for the uranyl ¹⁷O chemical shift. The final value of this chemical shift is within 40 ppm of the experimental range. The UO₂(CO₃)₃^4- and (UO₂)₃(CO₃)₆^6- complexes show a solvent dependence of the terminal carbonate ¹⁷O and ¹³C chemical shifts that is less pronounced than that for the uranyl oxygen atom. Corrections to the chemical shift from hybrid functionals and spin-orbit coupling improve the accuracy of chemical shifts if the sensitivity of the uranyl chemical shift to the uranyl bond length (estimated at 140 ppm per 0.1 Å from trajectory data) is taken into consideration. The experimentally reported trend in the two unique ¹³C chemical shifts is correctly reproduced for (UO₂)₃(CO₃)₆^6-. NMR relaxation rate data support large ¹⁷O peak widths, but remain below those noted in the experimental literature. Comparison of relaxation data for solvent-including versus solvent-free models suggest that carbonate ligand motion overshadows explicit solvent effects.

Model-free extraction of spin label position distributions from pseudocontact shift data

Not a point, but a cloud: advanced PCS data analysis using 3D probability density reconstruction provides more information.

A significant problem with paramagnetic tags attached to proteins and nucleic acids is their conformational mobility. Each tag is statistically distributed within a volume between 5 and 10 Angstroms across; structural biology conclusions from NMR and EPR work are necessarily diluted by this uncertainty. The problem is solved in electron spin resonance, but remains open in the other major branch of paramagnetic resonance – pseudocontact shift (PCS) NMR spectroscopy, where structural biologists have so far been reluctantly using the point paramagnetic centre approximation. Here we describe a new method for extracting probability densities of lanthanide tags from PCS data. The method relies on Tikhonov-regularised 3D reconstruction and opens a new window into biomolecular structure and dynamics because it explores a very different range of conditions from those accessible to double electron resonance work on paramagnetic tags: a room-temperature solution rather than a glass at cryogenic temperatures. The method is illustrated using four different Tm³⁺ DOTA-M8 tagged mutants of human carbonic anhydrase II; the results are in good agreement with rotamer library and DEER data. The wealth of high-quality pseudocontact shift data accumulated by the biological magnetic resonance community over the last 30 years, and so far only processed using point models, could now become a major source of useful information on conformational distributions of paramagnetic tags in biomolecules.

NMR analysis of an Fe(i)–carbene complex with strong magnetic anisotropy

A paramagnetic, easy-plane anisotropic Fe^I complex, bearing cyclic-alkyl(amino) carbene (cAAC) ligands, is studied by means of NMR and DFT.

Synthesis, structure and paramagnetic NMR analysis of a series of lanthanide-containing [LnTi6O3(OiPr)9(salicylate)6] cages

The influence of paramagnetic Ln³⁺ ions on the NMR behaviour is investigated via a series of new isostructural lanthanide-containing cages with the general formula [LnTi₆O₃(OⁱPr)₉(salicylate)₆] (Ln = La–Er).

Solution and solid state structures and magnetism of a series of linear trinuclear compounds with a hexacoordinate LnIII and two terminal NiII centers

Reported are the syntheses, structures and magnetic properties, also by NMR spectroscopy in solution, of a series of 13 linear trinuclear 3d-4f compounds with a lanthanide(iii) surrounded by two Ni^II ions, NiLn^III, where the central Ln^III is hexacoordinate. For three of the crystal structures, an additional H₂O molecule is coordinated to the central Ln^III ion, leading to a monocapped trigonal prismatic structure. However, NMR spectroscopy indicates that in solution, these complexes also have a hexacoordinate Ln^III center. The solution magnetic anisotropies, determined by NMR spectroscopy, indicate that the axial components of the anisotropies are relatively small and that the Dy^III derivative might therefore not exhibit single molecule magnetism. The axial anisotropies determined by NMR spectroscopy are in good agreement with the expectations based on the distorted trigonal prismatic ligand field.