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

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 continued our work on increasing calculation efficiency, as well as continued to expansion of molecular properties at the relativistic level, both for molecules and for solids. In particular, we have introduced two simple, yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic(SC) and spin-orbit (SO) 2e picture-change effects (PCEs). The resulting X2C Hamiltonian models, dubbed amfX2C and e(xtended)amfX2C, allow to uniquely tailor PCE corrections to both Hartree-Fock or Kohn-Sham DFT. We are now working on the testing its performance for solids, but assessing the accuracy against our previous all-electron results relativistic band structures of the two-dimensional transition-metal dichalcogenides in various crystal structures. For properties, we have worked along three different directions. 1) Development and implementation of all-electron relativistic DFT approach for the calculation of EPR parameters are a key component of solid-state NMR spectra, and we have developed and implemented an all-electron relativistic DFT approach for their calculation of ground-state multiplets. In particular, we have addressed the challenge of gauge origin dependence of approximate calculations by a distributed-origin scheme based on the gauge-including atomic orbitals (GIAOs), combined with restricted magnetically balanced (RMB) basis in order to achieve robust convergence with regard to the basis set size. The approach furthermore utilises the non-collinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results together with spin-polarisation effects. Recently, we developed and implemented an (e)amfX2C variant of the RMB+GIAO approach to speed up calculations without loss of accuracy. 2) We have completed the development of an all-electron four-component relativistic implementation of electric field gradients (EFGs) at the nuclei using Gaussian-type orbitals and periodic boundary conditions. This enables to include relativistic effects variationally and to ensure an accurate treatment of both core and valence orbitals, as all these aspects are essential for reliable predictions of EFGs. Our calculations contribute to establishing a reliable estimate for the nuclear quadrupole moment of 209Bi, for which our best estimate is in excellent agreement with a recent re-evaluation of the nuclear quadrupole moment obtained from atomic data and ab initio calculations. Our results also suggest that there is a need to revisit the experimental data for the EFGs of several bismuth oxyhalides. 3) We have continued in the study of ultrafast attosecond spectroscopic phenomena. We discovered by means of first-principle pure electron dynamic simulations that it is possible to induce chirality in achiral oriented molecules using a chiral laser pulse, and this can be studied using a second laser pulse.

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.