Abstract The rare-earth elements (REEs) and bismuth, being classified as the ‘most critical raw materials’ (European Raw Materials Initiatives, 2017), have a high economic importance to the EU combined with a high relative supply risk. REEs are highly important for the evolving technologies such as clean-energy applications, high-technology components, rechargeable batteries, permanent magnets, electric and hybrid vehicles, and phosphors monitors. This scientific research work aims at building a fundamental knowledge base concerning the electronic/molecular structure and properties of rare-earth element (REE) and bismuth complexes with dithiocarbamate (DTC) and 1,10-phenanthroline (PHEN) by employing state-of-the-art experimental techniques such as nuclear magnetic resonance (NMR) spectroscopy and X-ray diffraction (XRD) techniques together with ab initio quantum mechanical computational methods. This combination of methods has played a vital role in analysing the direct and significant effect of the heavy metal ions on the structural and magnetic resonance properties of the complexes, thereby, providing a framework of structure elucidation. This is of special importance for REEs, which are known to exhibit similar chemical and physical properties. The objectives of the work involve i) a systematic investigation of series of REE(III) as well as bismuth(III) complexes to get a profound understanding of the structure-properties relationship and ii) to find an appropriate theoretical modelling and NMR calculation methods, especially, for heavy metal systems in molecular and/or solid-state. This information can later be used in surface interaction studies of REE/bismuth minerals with DTC as well as in design and development of novel ligands for extraction/separation of metal ions. The REE(III) and bismuth(III) complexes with DTC and PHEN ligands have all provided a unique NMR fingerprint of the metal centre both in liquid and solid phase. The solid-state ¹³C and ¹⁵N NMR spectra of the diamagnetic REE(III) and bismuth(III) complexes were in accord with their structural data obtained by single crystal XRD. The density functional theory (DFT) methods were used to get complementary and refined structural and NMR parameters information for all diamagnetic complexes in the solid-state. The relativistic contributions due to scalar and spin-orbit correlations for the calculated ¹H/¹³C/¹⁵N chemical shifts of REE complexes were analysed using two-component zeroth-order regular approximation (ZORA)/DFT while the ‘crystal-lattice’ effects on the NMR parameters were calculated by combining DFT calculations on molecular and periodic solid-state models. The paramagnetic REE complexes display huge differences in their ¹H and ¹³C NMR spectral patterns. The experimental paramagnetic NMR (pNMR) chemical shifts, as well as the sizable difference of the ¹H and ¹³C NMR shifts for these isoelectronic complexes, are well reproduced by the advanced calculations using ab initio/DFT approach. The accuracy of this approach is very promising for further applications to demanding pNMR problems involving paramagnetic f-block elements. The results presented in this thesis demonstrate that a multidisciplinary approach of combined experimental NMR and XRD techniques along with computational modelling and property calculations is highly efficient in studying molecular complexes and solids containing heavy metal systems, such as rare-earths and bismuth.

Abstract This thesis reports simulations of direct observables in electron and nuclear spin relaxation experiments in an example paramagnetic system, as well as polarization transfer occurring in a spin-exchange optical pumping (SEOP) experiment. Studies of paramagnetic relaxation are important, e.g., in the development of agents used for enhanced contrast in magnetic resonance imaging. SEOP is used to produce hyperpolarized noble gases, which are then used to, e.g., enhance sensitivity in structural studies of matter with nuclear magnetic resonance. Presently the theory, available software and hardware for such computational modeling have reached a state in which quantitative reproduction of the experimentally observed magnetization decay is possible from first principles. The present multiscale computations are carried out from first principles combining molecular dynamics simulations of atomistic motion and quantum-chemical electronic structure calculations of the spin interaction parameters that enter the effective spin Hamiltonian. A time series of the spin Hamiltonian is then explicitly used to propagate spin dynamics in the system, and dynamical time constants of the magnetization are obtained through ensemble averaging. The complete decay of electron spin magnetization could be followed directly within the duration of the simulation, whereas the nuclear spin relaxation rates were extracted using Kubo’s theory regarding generalized cumulant expansion and stochastic processes. The extracted electron and nuclear spin relaxation rates for the chosen prototypic system, the aqueous solution of Ni²⁺, are in quantitative and semi-quantitative agreement, respectively, with the available experimental results. The simulations of polarization transfer corroborate the empirical observations on the importance of van der Waals complexes and binary collisions in the spin-exchange process. Long van der Waals complexes represent the overwhelmingly most significant kind of individual events, but the short binary collisions can also give a relatively important contribution due to their vast abundance. This thesis represents a first study in which first principles-calculated trajectories of individual events could be followed. The simulations reported in this thesis were run without any empirical parametrization and thus represent a significant step in first-principles computational modeling of magnetization dynamics.

Abstract In this thesis, the classic Kurland-McGarvey theory for the nuclear magnetic resonance (NMR) chemical shift is presented in a modern framework for paramagnetic systems containing one or more unpaired electrons. First-principles computations are carried out for the NMR shielding tensors in paramagnetic transition-metal complexes. A combined ab initio/density-functional theory (DFT) approach is applied to obtain the necessary electron paramagnetic resonance (EPR) property tensors, i.e., the g-tensor, zero-field splitting tensor (D) and hyperfine coupling tensors (A). In DFT, both the generalised-gradient approximation and hybrid DFT are applied to calculate A. The complete active space self-consistent field theory (CASSCF) and N-electron valence-state perturbation theory (NEVPT2) are applied to calculate the g- and D-tensors. Scalar relativistic effects are included at the second-order Douglas-Kroll-Hess level for the g- and D-tensors and, for A, at the fully relativistic four-component matrix-Dirac-Kohn-Sham level. This methodology is applied to study ¹³C and ¹H chemical shifts and shielding anisotropies in a series of Co(II) pyrazolylborate complexes, a Cr(III) quinolyl-functionalised cyclopentadienyl complex, Ni(II) acetylacetonate complexes and various metallocenes. The results obtained from these calculations are generally in a good agreement with the experimental data, in some cases, for Ni(II) complexes, allowing to correct the experimental spectral signal assignment. CASSCF/NEVPT2 computations (especially for the D-tensor) are more accurate than DFT, which is useful for the purpose of obtaining the NMR chemical shifts. The computational results obtained are dependent on the choice of molecular geometry (experimental X-ray or computationally optimised), wavefunction used for g and D (CASSCF or NEVPT2), DFT functional for A, and the quality of the basis sets. The locally dense basis method used for the CASSCF/NEVPT2 computations is less expensive and gives equally good results for g and D as fully balanced basis sets. The scalar relativistic influences are usually small for g and D, but are large for A. Due to that, scalar relativistic effects are important for the chemical shift and shielding anisotropy, especially for carbon nuclei. These first-principles computations based on combined ab initio/DFT methodology are promising for the treatment of important electron correlation and scalar relativistic effects in the calculation of pNMR chemical shifts and shielding anisotropies. This work provides a straightforward platform for further development of pNMR shielding theory in terms of first-principles wavefunctions, as well as for applications in current problems in bio- and materials sciences, including low-temperature experiments. / Original papers The original papers are not included in the electronic version of the dissertation. Vaara, J., Rouf, S. A., & Mareš, J. (2015). Magnetic Couplings in the Chemical Shift of Paramagnetic NMR. Journal of Chemical Theory and Computation, 11(10), 4840–4849. https://doi.org/10.1021/acs.jctc.5b00656 Rouf, S. A., Mareš, J., & Vaara, J. (2015). ¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study. Journal of Chemical Theory and Computation, 11(4), 1683–1691. https://doi.org/10.1021/acs.jctc.5b00193 Rouf, S. A., Jakobsen, V. B., Mareš, J., Jensen, N. D., McKenzie, C. J., Vaara, J., & Nielsen, U. G. (2017). Assignment of solid-state ¹³C and ¹H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations. Solid State Nuclear Magnetic Resonance, 87, 29–37. https://doi.org/10.1016/j.ssnmr.2017.07.003 Rouf, S. A., Mareš, J., & Vaara, J. (2017). Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems. Journal of Chemical Theory and Computation, 13(8), 3731–3745. https://doi.org/10.1021/acs.jctc.7b00168 http://jultika.oulu.fi/Record/nbnfi-fe201801031039