The goal of solid state physics and chemistry is to gain deeper understanding of the basic principles of condensed matter. This ongoing process is achieved by the combination of experimental methods and theoretical models. One theoretical approach are the so-called first-principles calculations, which are based on the concept of density functional theory (DFT). In order to test the reliability of a band structure calculation, its results have to be compared with experiments. Since the electron density, the main constituent of DFT codes, cannot be directly determined experimentally with sufficient accuracy (e.g., by X-ray diffraction), other experimentally available properties are needed for the comparison with the calculation. A quantity that can be measured with high accuracy and that provides indirect information about the electron density is the electric field gradient (EFG). The EFG reflects local structural symmetry properties of the charge distribution surrounding a nucleus: the EFG is nonzero if the density deviates from cubic symmetry and therefore generates an inhomogeneous electric field at the nucleus. Since the EFG is highly sensitive to structural parameters and to disorder, it is a valuable tool to extract structural information. Furthermore, the evaluation of the EFG can provide valuable insight into the chemical bonding. Whereas the experimental determination of the quadrupole frequency and the closely related EFG has been possible for more than 70 years, reliable values for calculated EFGs could not be obtained before 1985, when an EFG module was implemented in the full-potential, linearised-augmented-plane-wave code WIEN. Since the full-potential local-orbital minimum-basis scheme FPLO is numerically very efficient and its local-orbital scheme allows an easy analysis of the different contributions to the EFG, one goal of this work was the implementation of an EFG module within the FPLO code. The newly implemented EFG module was applied to different systems: starting from simple metals, then approaching more complex systems and finally tackling strongly correlated oxides. Simultaneously, the EFGs for the studied compounds were determined experimentally by NMR spectroscopists. This close collaboration enables the comparison of the calculated EFGs with the experimental observations, which makes it possible to extract more physical and chemical information from the measured values regarding structural relaxation, distortion, the chemical bond or the relevance of electron correlation. In the last part of this work, the importance of corrections that go beyond the EFG are discussed. Such corrections arise for any multipole order of the hyperfine interactions, and are due to electron penetration into the nucleus. A correction similar to the isomer shift, coined here the "quadrupole shift" is examined in detail.

The goal of solid state physics and chemistry is to gain deeper understanding of the basic principles of condensed matter. This ongoing process is achieved by the combination of experimental methods and theoretical models. One theoretical approach are the so-called first-principles calculations, which are based on the concept of density functional theory (DFT). In order to test the reliability of a band structure calculation, its results have to be compared with experiments. Since the electron density, the main constituent of DFT codes, cannot be directly determined experimentally with sufficient accuracy (e.g., by X-ray diffraction), other experimentally available properties are needed for the comparison with the calculation. A quantity that can be measured with high accuracy and that provides indirect information about the electron density is the electric field gradient (EFG). The EFG reflects local structural symmetry properties of the charge distribution surrounding a nucleus: the EFG is nonzero if the density deviates from cubic symmetry and therefore generates an inhomogeneous electric field at the nucleus. Since the EFG is highly sensitive to structural parameters and to disorder, it is a valuable tool to extract structural information. Furthermore, the evaluation of the EFG can provide valuable insight into the chemical bonding. Whereas the experimental determination of the quadrupole frequency and the closely related EFG has been possible for more than 70 years, reliable values for calculated EFGs could not be obtained before 1985, when an EFG module was implemented in the full-potential, linearised-augmented-plane-wave code WIEN. Since the full-potential local-orbital minimum-basis scheme FPLO is numerically very efficient and its local-orbital scheme allows an easy analysis of the different contributions to the EFG, one goal of this work was the implementation of an EFG module within the FPLO code. The newly implemented EFG module was applied to different systems: starting from simple metals, then approaching more complex systems and finally tackling strongly correlated oxides. Simultaneously, the EFGs for the studied compounds were determined experimentally by NMR spectroscopists. This close collaboration enables the comparison of the calculated EFGs with the experimental observations, which makes it possible to extract more physical and chemical information from the measured values regarding structural relaxation, distortion, the chemical bond or the relevance of electron correlation. In the last part of this work, the importance of corrections that go beyond the EFG are discussed. Such corrections arise for any multipole order of the hyperfine interactions, and are due to electron penetration into the nucleus. A correction similar to the isomer shift, coined here the "quadrupole shift" is examined in detail.