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FRINATEK-Fri mat.,naturv.,tek

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.

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. In the project reporting period, while waiting for newly hired project members to start in their positions, focus for the scientific work has been on improving the computational efficiency of the code for calculating relativistic energies and densities of solids. Multiple strategies have been used to achieve this goal. We have implemented the resolution-of-the-identity approach for Coulomb electron-repulsion integrals. Significant speedups by several orders of magnitude have been observed. Furthermore, the fast multipole method has been implemented for the Coulomb energies to speed up the infinite summations that appear in solid-state calculations. Taken together, these developments are essential in order to be able to enlarge the unit cells that can be handled by the program, a key step towards the ambition to apply the code developed to metal-organic frameworks (MOFs). These developments can be applied both for our relativistic and our non-relativistic codes. Another major development line has been a new formulation of the exact 2-component (X2C) formalism that allows the full 4-component relativistic wave function to be reduced to a 2-component wave functions, leading to significant computational savings. The work has so far been developed in the context of molecules. This reformulation has improved the accuracy of the approximation for multi-electron systems and have furthermore been formulated in a manner that makes it easily extendable to solids. This is expected to lead to a reduction of the computational time by a factor of 2-4 relative to full 4-component calculations, bringing the cost of these calculations down about twice the cost of a non-relativistic formulation. Articles describing these advances are expected to appear in the near future.

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.

Funding scheme:

FRINATEK-Fri mat.,naturv.,tek