Core level X-ray Photoelectron Spectroscopy (XPS) is one of the most widely used experimental techniques in surface science and surface analysis. However, the interpretation of recorded spectra is challenging. Often the amount of chemical insight that XPS can provide is compromised by problems with assigning detected “peaks” to specific chemical environments. Theoretical modelling can provide an alternative means for determining the spectroscopic signature associated with a given chemical environment, and could therefore be used to overcome the long-standing peak-assignment problem. In this project, the accuracy of existing theoretical methods for guiding the interpretation of XPS spectra will be tested, and new methods for predicting satellite peaks and simulating vibrational effects in core level XPS will be developed. In particular, the accuracy of the Δ-Self-Consistent-Field (ΔSCF) method will be tested for solids and surface species; the ΔSCF method will be combined with Time-Dependent Density Functional Theory (TDDFT) to predict satellite structures in core level photoemission spectra; and a fully quantum mechanical method based on the Density Functional Theory (DFT) and normal mode analysis will be developed for the simulation of vibrational effects in XPS. Through the testing and development of computationally affordable theoretical methods, this study will provide impetus and justification for users of XPS to take full advantage of theoretical modelling when interpreting their experimental results. Several dissemination and communication activities have been planned to ensure that the theoretical work will reach its inteneded audience and ultimately help XPS users from a wide range of fields to gain greater insight into the systems that they study.