A complication of the parameter estimation is that the bilevel structure of Problem (PE) introduces discontinuities into the total merit function . One possible explanation for this is the fact that the crystal intermolecular energy surface is innately non-convex and can contain many minima with distinct crystal energy/geometry. As the outer optimisation alters the parameter values, the inner optimisations may converge to different minima as the contours of the energy surface (and the minima present on the surface) change. If the optimised crystal energy and/or geometry change dramatically because of this, it will manifest as discontinuities in the T M F solution surface.