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

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.

Dissecting the Molecular Origin of g-Tensor Heterogeneity and Strain in Nitroxide Radicals in Water: Electron Paramagnetic Resonance Experiment versus Theory

Nitroxides are common EPR sensors of microenvironmental properties such as polarity, numbers of H-bonds, pH, and so forth. Their solvation in an aqueous environment is facilitated by their high propensity to form H-bonds with the surrounding water molecules. Their g- and A-tensor elements are key parameters to extracting the properties of their microenvironment. In particular, the gxx value of nitroxides is rich in information. It is known to be characterized by discrete values representing nitroxide populations previously assigned to have different H-bonds with the surrounding waters. Additionally, there is a large g-strain, that is, a broadening of g-values associated with it, which is generally correlated with environmental and structural micro-heterogeneities. The g-strain is responsible for the frequency dependence of the apparent line width of the EPR spectra, which becomes evident at high field/frequency. Here, we address the molecular origin of the gxx heterogeneity and of the g-strain of a nitroxide moiety (HMI: 2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water. To treat the solvation effect on the g-strain, we combined a multi-frequency experimental approach with ab initio molecular dynamics simulations for structural sampling and quantum chemical EPR property calculations at the highest realistically affordable level, including an explicitly micro-solvated HMI ensemble and the embedded cluster reference interaction site model. We could clearly identify the distinct populations of the H-bonded nitroxides responsible for the gxx heterogeneity experimentally observed, and we dissected the role of the solvation shell, H-bond formation, and structural deformation of the nitroxide in the creation of the g-strain associated with each nitroxide subensemble. Two contributions to the g-strain were identified in this study. The first contribution depends on the number of hydrogen bonds formed between the nitroxide and the solvent because this has a large and well-understood effect on the gxx-shift. This contribution can only be resolved at high resonance frequencies, where it leads to distinct peaks in the gxx region. The second contribution arises from configurational fluctuations of the nitroxide that necessarily lead to g-shift heterogeneity. These contributions cannot be resolved experimentally as distinct resonances but add to the line broadening. They can be quantitatively analyzed by studying the apparent line width as a function of microwave frequency. Interestingly, both theory and experiment confirm that this contribution is independent of the number of H-bonds. Perhaps even more surprisingly, the theoretical analysis suggests that the configurational fluctuation broadening is not induced by the solvent but is inherently present even in the gas phase. Moreover, the calculations predict that this broadening decreases upon solvation of the nitroxide.

Elucidating the concentration-dependent effects of thiocyanate binding to carbonic anhydrase

Many proteins naturally carry metal centers, with a large share of them being in the active sites of several enzymes. Paramagnetic effects are a powerful source of structural information and, therefore, if the native metal is paramagnetic, or it can be functionally substituted with a paramagnetic one, paramagnetic effects can be used to study the metal sites, as well as the overall structure of the protein. One notable example is cobalt(II) substitution for zinc(II) in carbonic anhydrase. In this manuscript we investigate the effects of sodium thiocyanate on the chemical environment of the metal ion of the human carbonic anhydrase II. The electron paramagnetic resonance (EPR) titration of the cobalt(II) protein with thiocyanate shows that the EPR spectrum changes from A-type to C-type on passing from 1:1 to 1:1000-fold ligand excess. This indicates the occurrence of a change in the electronic structure, which may reflect a sizable change in the metal coordination environment in turn caused by a modification of the frozen solvent glass. However, paramagnetic nuclear magnetic resonance (NMR) data indicate that the metal coordination cage remains unperturbed even in 1:1000-fold ligand excess. This result proves that the C-type EPR spectrum observed at large ligand concentration should be ascribed to the low temperature at which EPR measurements are performed, which impacts on the structure of the protein when it is destabilized by a high concentration of a chaotropic agent.

The evolution of paramagnetic NMR as a tool in structural biology

Paramagnetic NMR data contain extremely accurate long-range information on metalloprotein structures and, when used in the frame of integrative structural biology approaches, they allow for the retrieval of structural details to a resolution that is not achievable using other techniques. Paramagnetic data thus represent an extremely powerful tool to refine protein models in solution, especially when coupled to X-ray or cryoelectron microscopy data, to monitor the formation of complexes and determine the relative arrangements of their components, and to highlight the presence of conformational heterogeneity. More recently, theoretical and computational advancements in quantum chemical calculations of paramagnetic NMR observables are progressively opening new routes in structural biology, because they allow for the determination of the structure within the coordination sphere of the metal center, thus acting as a loupe on sites that are difficult to observe but very important for protein function.

New-onset COVID-19-related diabetes: an early indicator of multi-organ injury and mortally of SARS-CoV-2 infection

Objective

The pandemic of 2019 coronavirus (SARS-CoV-2) disease (COVID-19) has imposed a severe public health burden worldwide. Most patients with COVID-19 were mild. Severe patients progressed rapidly to critical condition including acute respiratory distress syndrome (ARDS), multi-organ failure and even death. This study aims to find early multi-organ injury indicators and blood glucose for predicting mortality of COVID-19.

Methods

Fasting blood glucose (FBG) ≥7.0 mmol/L for two times during hospitalization and without a history of diabetes were defined as new-onset COVID-19-related diabetes (CRD). Indicators of injuries for multiple organs, including the lung, heart, kidney and liver, and glucose homeostasis were specifically analyzed for predicting death.

Results

A total of 120 patients with a severity equal to or greater than Moderate were hospitalized. After excluding patients with history of diabetes, chronic heart, kidney, and liver disease, 69 patients were included in the final analysis. Of the 69 patients, 23 were Moderate, 20 were Severe, and 26 were Critical (including 16 deceased patients). Univariable analysis indicated that CRD, lactate dehydrogenase (LDH), hydroxybutyrate dehydrogenase (HBDH), creatine kinase (CK) and creatinine (Cr) were associated with death. Multivariable analysis indicated that CRD was an independent predictor for death (HR = 3.75, 95% CI 1.26–11.15). Abnormal glucose homeostasis or CRD occurred earlier than other indicators for predicting poor outcomes. Indicators of multiple organ injury were in parallel with the expression patterns of ACE2 (the SARS-CoV-2 receptor) in different organs including pancreatic islet.

Conclusions

New-onset COVID-19-related diabetes is an early indicator of multi-organ injury and predictor for poor outcomes and death in COVID-19 patients. As it is easy to perform for clinical practices and self-monitoring, glucose testing will be helpful for predicting poor outcomes to facilitate appropriate intensive care.