5.5 Two dimensional (2D) crystals

2D-crystals, calculationType = -200/-201

For 2D-crystals, USPEX allows fixed and variable-composition calculations (-200/-201). Elemental and binary systems can be studied for now, ternary and more complex systems will be enabled later. Different from surface calculation (200/201), we need neither reference energies nor the substrate, but only the thickness confinement of initial 2D structures, for example:

3.0 : thicknessS

It means that we produce the initial 2D structures within a 3.0 Angstrom thick slab. The maximum final structures thickness is empirically confined as thicknessS + 3. Importantly, we also need to give a large enough vacuum size for 2D-crystals (default value is 10 Angstrom, sometimes this is enough). Different from surfaces (where symmetry is described by 17 plane groups), symmetry of 2D-crystals is described by 80 layer groups, which are listed in Appendix 9.5.

% symmetries
2-80
% endSymmetries

Please, do not forget to specify vaccumSize, which should be sufficently large to prevent interaction between periodic images of the slabs.

Fixed-composition structure prediction

We define the stoichiometric ratio by numSpecies keyblock, and then specify the minimum and maximum total numbers of atoms in the unit cell by minAt and maxAt. For example, here is what you would specify to perform 2D-crystal search for $B_2 O_3$ system with 4-20 atoms in the cell, that is, we are considering $B_2 O_3$ , $B_4 O_6$ , $B_6 O_9$ , $B_8 O_{12}$ within one USPEX calculation:

% numSpecies
2 3
% EndNumSpecies

% atomType
B O
% EndAtomType

4    : minAt
20   : maxAt

Variable-composition structure prediction

For a full variable-composition study of 2D-crystals, similar with 3D cases, we set up the matrix numSpecies:

% numSpecies
1 0
0 1
% EndNumSpecies

Note: Because we have confined the thickness for final 2D structures, we discard the structures with thickness after relaxation greater than thicknessS+3. For variable-composition calculations, we may need a relatively large value of initialPopSize (we suggest twice the populationSize), for example:

 90      : populationSize
180      : initialPopSize
100      : numGenerations

Summary of good structures

For -200, the information about good 2D structures can be found in goodStructures, which looks as shown below:

$\includegraphics[scale=0.5]{pic/fix2D.png}$

In the -201 regime, the convex hull graph is shown in the file extendedConvexHull.pdf, and information about all structures (starting from the stable ones) is output in the extended_convex_hull file, which looks like this:

$\includegraphics[scale=0.5]{pic/var2D.png}$

We provide an example (EX30) of a variable-composition prediction of stable 2D-crystals in the Sn-S system.