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

Lang, Lucas; Ravera, Enrico; Parigi, Giacomo; Luchinat, Claudio; Neese, Frank

doi:10.1063/5.0088162

Cited by 9 publications

(17 citation statements)

References 62 publications

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“…The gauge contribution is necessary to preserve gauge invariance in the presence of spin–orbit coupling. 50,51 At the level of second-order degenerate perturbation theory, in the long-range limit, eventually it was shown thatin agreement with eqn (5) and (10), because and . This derivation confirms the validity of the classical equations for PCSs and thus paves the way for their predictions from the χ tensors which can possibly be calculated through QC tools.…”

Section: The Electron–nucleus Interaction: the Origin Of Relaxation A...supporting

confidence: 69%

“…34,39,40,42–48 Using the effective spin Hamiltonian framework, it was first clarified that if the contribution of the orbital angular momenta of electrons to the PCSs is not correctly included in the first-principles QC treatment, a different expression for the PCSs is obtained. 49 The validity of eqn (5) and (10) was finally demonstrated 50,51 using the QC formulation of hyperfine shifts to be proportional to the second derivative of the thermally averaged Helmholtz free energy F with respect to the magnetic field and the nuclear magnetic moment, calculated at zero magnetic field and zero magnetic moment. 52 In the effective spin Hamiltonian framework, the PCSs can in fact be written aswhere the hyperfine coupling tensor A is composed of the spin dipolar, paramagnetic spin–orbit and gauge contributions.…”

Section: The Electron–nucleus Interaction: the Origin Of Relaxation A...mentioning

confidence: 97%

“…The gauge contribution is necessary to preserve gauge invariance in the presence of spin-orbit coupling. 50,51 At the level of secondorder degenerate perturbation theory, in the long-range limit, eventually it was shown that…”

Section: The Hyperfine Shiftmentioning

confidence: 99%

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The evolution of paramagnetic NMR as a tool in structural biology

Ravera

Gigli

Fiorucci

et al. 2022

Phys. Chem. Chem. Phys.

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Section: The Electron–nucleus Interaction: the Origin Of Relaxation A...supporting

confidence: 69%

Section: The Electron–nucleus Interaction: the Origin Of Relaxation A...mentioning

confidence: 97%

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The evolution of paramagnetic NMR as a tool in structural biology

Ravera

Gigli

Fiorucci

et al. 2022

Phys. Chem. Chem. Phys.

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“…Recently, it has been shown from first-principles that the long-distance limit of the A-tensor within the perturbation theory (and linear SOC effects) has the following form: 32,33…”

Section: Long-distance (Ld) Limit Of the A-tensor And The Hyperfine N...mentioning

confidence: 99%

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

Novotny,

Komorovsky,

Marek

2024

Acc. Chem. Res.

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Metrics & More Article Recommendations CONSPECTUS: Magnetic 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 temperaturedependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δ HF ).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 πspace 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 demonstrat...

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“…The field of theoretical spectroscopy has been very active in recent years (for reviews, see refs –) The challenges under investigation are manifold and include the explicit treatment of solvent effects for systems of nontrivial size, ,− the development and validation of improved density functionals − and correlated ab initio methods, ,,− the treatment of relativistic- , and vibronic- ,, effects as well as conceptual and algorithmic advances ,,− ,,,− to name only a few. The characterizing parameters of a nitroxide’s EPR spectrum, namely, the g - and A -tensors, are accessible at different levels of theory .…”

Section: Introductionmentioning

confidence: 99%

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

Tran,

Teucher,

Galazzo

et al. 2023

J. Phys. Chem. A

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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 g xx 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 g xx 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 g xx 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 g xx -shift. This contribution can only be resolved at high resonance frequencies, where it leads to distinct peaks in the g xx 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.

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

Cited by 9 publications

References 62 publications

The evolution of paramagnetic NMR as a tool in structural biology

The evolution of paramagnetic NMR as a tool in structural biology

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

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

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