Scanning tunneling microscopy (STM) images and scanning tunneling spectroscopy (STS) spectra of galena (PbS) and hematite (a-Fe203) were calculated using ab-initio methods in order to interpret experimental images and spectra that were taken in previous studies. These calculations have helped to understand which states of the mineral surfaces were imaged depending on the bias voltage and tip-sample separation. The computational results also gave insight in electron transfer processes that take place during surface adsorption/oxidation/reduction processes. In this context, different oxidation (using O₂ and ferric iron as oxidants) and gold adsorption/reduction mechanisms on galena were evaluated at an atomic level. On hematite, the main emphasis was determining the differences in the local electronic structure of specific sites above the surface and the electronic structure of the bulk. Hereby, step sites turned out to have an increased local density of states at certain electron binding energies that are absent on flat surfaces. states can explain the highly increased reactivity of step sites as compared to terraces. X-ray photoelectron spectra (XPS) were calculated to compare the photoelectron peaks of the calculated specific surface structures (that do not have a bulk equivalent) with experimentally obtained XPS spectra. Most of the calculated peak chemical shifts coincided with those that were found in experiments and that were previously interpreted in terms of known bulk structures. Therefore, it can be inferred that the conventional way of interpreting XPS spectra might be incomplete if specific surface structures are neglected. In order to understand step velocities on a gypsum (010) surface, step energies of different step directions were calculated using an ab-initio approach. An approximately linear relationship was found between the calculated step energies and the experimentally determined step velocities. / Ph. D.