Definitions and further details

    All the properties are computed at the DFT-PBE level. The only exceptions are binding energies, which were calculated using the DF2-C09 and the rVV10 van-der-Waals functionals. All 3D and 2D structures are treated as non-magnetic using spin-unpolarized DFT. The magnetic order has a negligible effect on the binding energies as discussed in Ref.[1] but caution is needed when looking at the electronic properties of materials with elements that might support a magnetic ground state. The magnetic properties of a subset of materials, easily exfoliable with at most 6 atoms per unit cell, have been computed in Ref.[1] and can be browsed at https://www.materialscloud.org/discover/mc2d/dashboard/ptable or downloaded https://doi.org/10.24435/materialscloud:2017.0008/v1.
 For consistency with the rest of the database, these materials are reported in this archive in their non-magnetic state.   
  
    Binding energies are calculated as total energy differences between relaxed 3D parents and as-exfoliated, unrelaxed 2D children. More details can be found in the Methods section of the main paper.

    Each 2D structure has at least one 3D parent structure. In those cases when the monolayers can be exfoliated from more than one parent, for each functional we choose as parent the one with the lowest binding energy, and then we select the functional giving the most favourable 2D classification, with a preference for DF2-C09 when an ambiguity persists. The list of all possible 3D parents of a given monolayer is reported in the dataset.


    In metals, the zero for energy bands is the Fermi energy, while for semiconductors the zero is set midway between the highest occupied state in the valence bands and the lowest unoccupied state in the conduction bands. For simplicity, we call this Fermi energy in the captions. Calculations have been performed with a finite smearing that might slightly influence its position

    Paths and special k-points follow the conventions for 2D systems from Ref. [2] as implemented in AiiDA [3,4].

References

[1] N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, N. Marzari, Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds, Nature Nanotech., (2018). DOI:10.1038/s41565-017-0035-5.

[2] R. Ramírez and M. C. Böhm, Simple geometric generation of special points in Brillouin-zone integrations. Two-dimensional Bravais lattices. Int. J. Quantum Chem. 30, 391–411 (1986).

[3] G. Pizzi,  A. Cepellotti, R. Sabatini, N. Marzari, and B. Kozinsky. AiiDA: automated interactive infrastructure and database for computational science. Computational Materials Science 111, 218 – 230 (2016).

[4] S.P. Huber, S. Zoupanos, M. Uhrin, L. Talirz, L. Kahle, R. Häuselmann, D. Gresch, T. Müller, A. V. Yakutovich, C. W. Andersen, F. F. Ramirez, C. S. Adorf, F. Gargiulo, S. Kumbhar, E. Passaro, C. Johnston, A. Merkys, A. Cepellotti, N. Mounet, N. Marzari, B. Kozinsky, and G. Pizzi. AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance. Scientific Data 7, 300 (2020).