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# EPR and paramagnetic NMR of solids from relativistic two- and four-component density-functional theory

**Alternative title:** EPR og paramagnetisk NMR av faste stoffer fra relativistisk to- og firekomponents tetthetsfunksjonalteori

#### Awarded: NOK 12.3 mill.

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Project Number:

315822

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Project Period:

2021 - 2026

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When an external magnetic field is applied to a molecular or solid sample, the spin sub-levels of nuclei possessing a spin is split. The energy splitting is unique to the nucleus and to the local chemical environment, and these nuclei are very sensitive probes of the molecular structure. This forms the basis for Nuclear Magnetic Resonance (NMR) spectroscopy, one of the most important methods for structural determinations in chemistry. In a similar manner, the spin sublevels of unpaired electrons are split by an external magnetic fields, and these splittings can give detailed insight into where the unpaired electron density is located in a molecule, which in term can provide valuable insight into chemical reactivity. This forms the basis for electron paramagnetic resonance (EPR), an important technique for studying radicals and chemical reactivity. Finally, the presence of any unpaired electrons will also directly affect the splitting of the nuclear spin levels, coupling the mechanisms present in EPR and NMR and leading to the unique field of paramagnetic NMR.
All these spectroscopies are strongly affected by relativity. Indeed, some of the most valuable information in EPR spectroscopy would be completely absent without relativistic effects, and relativity may change the chemical shifts observed in NMR spectroscopy to such an extent that they shift outside the conventional window for the chemical shifts.
Great progress has been made in recent years in including relativistic effects in calculations of NMR and EPR parameters. However, the complexity arising from studying the NMR and EPR spectra crystals or crystalline materials is poorly developed and understood in general, and in particular for systems containing heavy-element. This project seeks to rectify this situation by developing the first code for relativistic calculations of NMR and EPR parameters of paramagnetic solids, extending the information that can be extracted from experimental NMR and EPR spectra.
During the reporting period, we have partly focused on increasing calculation efficiency, as well as started development towards calculations of molecular properties for solids.
To increase the calculation efficiency, we continued our work on approximation the electron density through a set of Gaussian functions. These Gaussian functions are then used in the most computationally intensive part of our code, namely the calculation of two-electron Coulomb integrals. Although the method is in common use for molecules, it presents some new challenges in solids. We have been able to show that the fitted Gaussian functions only need to be calculated for a single k-point (a single value of the electron momentum), which provides significant savings. The method has proven to be very effective, and gives a formal speed increase of almost a factor of 1000. This is critical for our method to be able to be used on large systems. We find no significant numerical consequences of using this approximate representation of the electron density.
Another development we are looking into is the possibility of being able to better vectorize a completely central routine for calculating the calculation-heavy Coulomb integrals. With vectorization, we will partly get a better use of memory, which will provide new performance improvements, but more importantly, this lays the foundation for putting calculation-intensive parts of the code out on GPUs. The work shows promising results.
For properties, we have worked along two different directions. In part, we have implemented the calculation of nuclear quadrupole coupling constants. These can be observed in solid-phase NMR spectra and are part of the reason why such spectra often are quite broad. More importantly, however, the combination of theoretical calculations and experimental observations is one of the most accurate methods for determining nuclear quadrupole moments. For one isotope, 209Bi, studies of atoms and molecules have given quite different results for the nuclear quadrupole moment, and the two results differ by almost 25%. In combination with old experimental data, we obtain results that support the molecular data. At about the same time, new atomic calculations were presented which now also give results in accordance with our and the molecular data.
Finally, we have begun to prepare studies of properties that depend more intricately on the electron density near the nucleus, and have implemented theoretical methods for studies of what is called transient X-ray spectroscopy. In such studies, one looks at the time development of the X-ray absorption signals, and can in this way study how the electron density changes over time when the molecule is exposed to X-ray radiation. This development is so far limited to studies on molecules, but will also be extended to solid substances.

Unpaired electrons play a key role in many chemical and physical processes, such as electron transport in lithium or sodium transition metal oxide-based battery materials or at catalytically active sites in metal-organic frameworks (MOFs). In order to optimise the performance of such materials, the relation between the structure and properties of materials must be established. Electron paramagnetic resonance (EPR) and paramagnetic nuclear magnetic resonance (pNMR) spectroscopy allow the structure of paramagnetic materials to be established, often aided and supported by computational studies that can help relate experimental spectra to details in the electronic structure of materials, and in this way facilitate the design of more efficient materials.
However, whereas the theoretical calculation of EPR and NMR spectra are well established for molecules in gas and liquid phases, and non-relativistic approaches for NMR spectra of closed-shell molecules exists for solids, there are currently no fully relativistic approach for the calculation of NMR spectra of paramagnetic solids, leaving a major gap in the ability of computational chemistry to contribute to rationalising structure-property relationships of such solid-state materials.
This project will fill this gap by developing an all-electron, fully relativistic, four-component density-functional theory formalism for the calculation of EPR and paramagnetic NMR spectra of solids. We will build on our recently developed four-component DFT code for solids and our recent advances in relativistic calculations of EPR and pNMR spectra of molecules to make a a major advance in the modeling of solid-state spectroscopy. This will allow us to advance the use of EPR and pNMR to the study of paramagnetic solids, and the inclusion of relativistic effects will allows us to reliably describe paramagnetic solids with heavy elements, such as lithium or sodium transition metal oxides, of relevance as battery materials.

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1.6BILL. NOKtotal funding in the programme period752PROJECTShave received funding in the programme period1SOURCEhas financed the programme