The possibility for a substance to form several distinct crystalline phases is a very broad phenomenon with tremendous implications for materials sciences. These crystals may display relatively comparable cohesive energies and thus even fine contributions to these energies must be captured for an accurate description of polymorphism. We recently showed that the van der Waals contribution to the energy is significant in glass-forming oxides such as SiO2 and B2O3 and that various DFT based approaches provide quite different physical pictures. In order to deal with the different challenges associated with polymorphism we will in this project develop a beyond-RPA electronic structure approach. This will allow us to determine the relative energies of several recently predicted crystal phases of boron oxide, for which the lack of experimental data renders the need of high-level calculations mandatory.