Theoretical NMR spectroscopy

Nuclear magnetic resonance spectroscopy is one of the most widespread techniques for the characterization of molecules. From analyzing small organic molecules using 1D NMR spectroscopy in the undergraduate chemistry lab to the elucidation of full protein structures in solution, it can provide a wealth of information about chemical systems.

The physical principle of NMR is the splitting of the nuclear spin energy levels in the presence of a magnetic field. Radiowaves that are in resonance with this energy difference can then be absorbed, giving rise to an absorption spectrum. (To be precise, it should be mentioned that modern NMR experiments use radiofrequency pulses to excite all transitions simultaneously and use a Fourier transform to obtain spectral information). The energy splitting is proportional to the magnetic field, with the proportionality constant being called the gyromagnetic ratio, a constant that is specific to a given isotope. It might appear that the nuclear spin levels of all nuclei belonging to the same isotope should be identical, such that only a single peak should appear in the NMR spectrum. If this were the case, the scope of NMR spectroscopy would be quite limited.

In a molecule, nuclei do not exist in isolation, but are surrounded by electrons. The external applied magnetic field makes the electrons move and align their spins, which creates an additional induced magnetic field on top of the externally applied one. This induced magnetic field depends crucially on the chemical environment and is the source of the rich information provided by NMR spectroscopy.

In common diamagnetic molecules, like neutral organic molecules, the electronic state does not possess any spin or orbital angular momentum. The external field needs to induce the additional fields; hence, they are relatively weak. Paramagnetic molecules, on the contrary, have permanent magnetic moments that only need to be oriented in the external magnetic field. This leads to much stronger effects.

In my group, we employ theory in order to develop a better understanding of the NMR spectra of paramagnetic molecules. E.g., we clarified the status of the point-dipole approximation for the chemical shielding tensor, which is often employed to obtain structural information about lanthanoid complexes and paramagnetic metalloproteins. Furthermore, we are interested in novel behavior at very high field strengths (e.g. using state-of-the-art 1.2 GHz spectrometers, employing magnetic flux densities of 28.2 Tesla). At such large fields, it becomes apparent that chemical shifts are field-dependent, a phenomenon that is not yet understood in full detail.

Related publications:

  • Lucas Lang, Enrico Ravera, Giacomo Parigi, Claudio Luchinat and Frank Neese, Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory, J. Phys. Chem. Lett. 11, 8735 (2020).
  • Enrico Ravera, Lucia Gigli, Barbara Czarniecki, Lucas Lang, Rainer Kümmerle, Giacomo Parigi, Mario Piccioli, Frank Neese and Claudio Luchinat, A Quantum Chemistry View on Two Archetypical Paramagnetic Pentacoordinate Nickel(II) Complexes Offers a Fresh Look on Their NMR Spectra, Inorg. Chem. 60, 2068 (2021).
  • Lucas Lang, Enrico Ravera, Giacomo Parigi, Claudio Luchinat and Frank Neese, Theoretical analysis of the long-distance limit of NMR chemical shieldings, J. Chem. Phys. 156, 154115 (2022).
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