Fission is one of the most challenging processes to describe in nuclear physics. Contrary to most of the nuclear properties, which can be explained in terms of a smaller set of valence nucleons, in fission all the particles are involved. To link the properties of the nascent fragments with the structure of the initial compound nucleus, it seems adequate to consider a two-centre basis to build the many-body wave functions. In the present work, symmetry-unrestricted two-centre harmonic oscillator states are used – within the density functional solver HFODD – to solve the Hartree-Fock equations. Moreover, the separation between fragments as well as their deformation is explored, comparing the results with the classical one-centre calculations. As it will be shown (spoiler alert), not only the fission channel but also fusion or alpha decay reactions can be modelled with this newly developed technique.