New first principles approaches for the structural and electronic properties of two dimensional materials In this thesis new first principles approaches for the structural and electronic properties of materials interfaces and two dimensional materials are developed. First we investigate an extension of the hybrid functional formalism by local emulation of the dielectric function. This is done via a local sampling of a density based estimator which can be computed efficiently using fast Fourier transform algorithms and allows the correct description of the local electronic properties of inhomogeneous systems. The resulting formalism is applied to different model interfaces showing comparable accuracy to more advanced methods at a more modest cost. Second we develop a large scale dataset for the electronic band gap of semiconductors. This dataset is built in the spirit of high throughput calculations allowing reproducible results due to relying on mature crystal structure databases. Several approximations to the exchange correlation functional (from every rung of Jacobs ladder) are then tested and analysed with mBJ HSE06 and HLE16 providing the best overall results. Third an efficient and unbiased method for the prediction of two dimensional structures is devised based on the minima hopping method. This technique is applied to successfully draw the phase diagram of two dimensional carbon silicon tin. Additionally the thermodynamic stability of two dimensional silicon carbide is studied. For all compositions new low energy phases were found many of which would probably be missed due to not having the traditional hexagonal symmetries of their monolayer prototypes. Fourth the effect of the approximation to the exchange correlation functional on different aspects of the mechanical stability of two dimensional materials is explored. In addition the thermal stability of group IV honeycomb monolayers is also studied.