The potential energy surfaces of oxirene and diazirinyl anion are characterised by means of density functional theory. A number of stationary points on the Kohn-Sham/BLYP surfaces is located and characterised by analytic second derivatives of the energy. An interconversion path for ketene, which is thought to be part of a prototype Wolff rearrangement, is estimated from this information and compared with recent, high-level ab initio computations. The deprotonation energy of diazirine is calculated and possible structures of the resulting anion are characterised and compared with ab initio methods. Oxirene (C-2v) and diazirinyl anion (C-s) are predicted to be transition states, which is at variance with the best ab initio calculations.