  The exfoliation energy - quantifying the energy required to extract a
two-dimensional (2D) sheet from the surface of a bulk material - is a key
parameter determining the synthesizability of 2D compounds. Here, using ab
initio calculations, we present a new group of non-van der Waals 2D materials
derived from non-layered crystals which exhibit ultra low exfoliation energies.
In particular for sulfides, surface relaxations are essential to correctly
describe the associated energy gain needed to obtain reliable results. Taking
into account long-range dispersive interactions has only a minor effect on the
energetics and ultimately proves that the exfoliation energies are close to the
ones of traditional van der Waals bound 2D compounds. The candidates with the
lowest energies, 2D SbTlO$_3$ and MnNaCl$_3$, exhibit appealing electronic,
potential topological, and magnetic features as evident from the calculated
band structures making these systems an attractive platform for fundamental and
applied nanoscience.
