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This thesis covers different problems that arise due to crystal and pseudospin anisotropy present in 3d and 5d transition metal oxides. We demonstrate that the methods of computational quantum chemistry can be fruitfully used for quantitative studies of such problems. In Chapter 2, Chapter 3, and Chapter 7 we show that it is possible to reliably calculate local multiplet splittings fully ab initio, and therefore help to assign peaks in experimental spectra to corresponding electronic states. In a situation of large number of peaks due to low local symmetry such assignment using semi-empirical methods can be very tedious and non-unique. Moreover, in Chapter 4 we present a computational scheme for calculating intensities as observed in the resonant inelastic X-ray scattering and X-ray absorption experiments. In our scheme highly-excited core-hole states are calculated explicitly taking into account corresponding orbital relaxation and electron polarization. Computed Cu L-edge spectra for the Li2CuO2 compound reproduce all features present in experiment. Unbiased ab initio calculations allow us to unravel a delicate interplay between the distortion of the local ligand cage around the transition metal ions and the anisotropic electrostatic interactions due to second and farther coordination shells. As shown in Chapter 5 and Chapter 6 this interplay can lead to the counter intuitive multiplet structure, single-ion anisotropy, and magnetic g factors. The effect is quite general and may occur in compounds with large difference between charges of metal ions that form anisotropic environment around the transition metal, like Ir 4+ in plane versus Sr 2+ out of plane in the case of Sr2IrO4. An important aspect of the presented study is the mapping of the quantum chemistry results onto simpler physical models, namely extended Heisenberg model, providing an ab initio parametrization. In Chapter 5 we employ the effective Hamiltonian technique for extracting parameters of the anisotropic Heisenberg model with single-ion anisotropy in the case of quenched orbital moment and second-order spin-orbit coupling. Calculated strong easy-axis anisotropy of the same order of magnitude as the symmetric exchange is consistent with experimentally-observer all-in/all-out magnetic order. In Chapter 6 we introduce new flavour of the mapping procedure applicable to systems with first-order spin-orbit coupling, such as 5d 5 iridates based on analysis of the wavefunction and interaction with magnetic field. In Chapter 6 and Chapter 7 we use this new procedure to obtain parameters of the pseudospin anisotropic Heisenberg model. We find large antisymmetric exchange leading to the canted antiferromagnetic state in Sr2IrO4 and nearly ideal one-dimensional Heisenberg behaviour of the CaIrO3, both agree very well with experimental findings.

This thesis covers different problems that arise due to crystal and pseudospin anisotropy present in 3d and 5d transition metal oxides. We demonstrate that the methods of computational quantum chemistry can be fruitfully used for quantitative studies of such problems. In Chapter 2, Chapter 3, and Chapter 7 we show that it is possible to reliably calculate local multiplet splittings fully ab initio, and therefore help to assign peaks in experimental spectra to corresponding electronic states. In a situation of large number of peaks due to low local symmetry such assignment using semi-empirical methods can be very tedious and non-unique. Moreover, in Chapter 4 we present a computational scheme for calculating intensities as observed in the resonant inelastic X-ray scattering and X-ray absorption experiments. In our scheme highly-excited core-hole states are calculated explicitly taking into account corresponding orbital relaxation and electron polarization. Computed Cu L-edge spectra for the Li2CuO2 compound reproduce all features present in experiment. Unbiased ab initio calculations allow us to unravel a delicate interplay between the distortion of the local ligand cage around the transition metal ions and the anisotropic electrostatic interactions due to second and farther coordination shells. As shown in Chapter 5 and Chapter 6 this interplay can lead to the counter intuitive multiplet structure, single-ion anisotropy, and magnetic g factors. The effect is quite general and may occur in compounds with large difference between charges of metal ions that form anisotropic environment around the transition metal, like Ir 4+ in plane versus Sr 2+ out of plane in the case of Sr2IrO4. An important aspect of the presented study is the mapping of the quantum chemistry results onto simpler physical models, namely extended Heisenberg model, providing an ab initio parametrization. In Chapter 5 we employ the effective Hamiltonian technique for extracting parameters of the anisotropic Heisenberg model with single-ion anisotropy in the case of quenched orbital moment and second-order spin-orbit coupling. Calculated strong easy-axis anisotropy of the same order of magnitude as the symmetric exchange is consistent with experimentally-observer all-in/all-out magnetic order. In Chapter 6 we introduce new flavour of the mapping procedure applicable to systems with first-order spin-orbit coupling, such as 5d 5 iridates based on analysis of the wavefunction and interaction with magnetic field. In Chapter 6 and Chapter 7 we use this new procedure to obtain parameters of the pseudospin anisotropic Heisenberg model. We find large antisymmetric exchange leading to the canted antiferromagnetic state in Sr2IrO4 and nearly ideal one-dimensional Heisenberg behaviour of the CaIrO3, both agree very well with experimental findings.