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I would like to understand how to calculate the band structure of the Graphene monolayer system using DFT. I am using VASP for material simulation. My question is how to write the crystal structure information file (POSCAR) for a 2D system such as Graphene. I think I can write the POSCAR file for many 3D systems, but I would like to understand how to write the POSCAR file if I am dealing with a 2D material system.

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2 Answers 2

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You generally cannot calculate a 2D system per se with a plane-wave program, but rather you should do a vacuum slab calculation. As for graphene, you would essentially do a calculation on graphite, but with the interlayer distance set at a large value, say 20 Angstrom (and the lattice constant c enlarged accordingly), so that the different layers of graphene virtually do not interact with each other. Make sure to freeze the lattice constant c, and use only one k-point along the c direction, although you still need an appropriate number of k-points along the a and b directions.

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  • $\begingroup$ Thank you very much. But why is it not possible to calculate a 2D system from first principles? Is it a limitation of the current computer tools or is there some physical reason related to DFT theory? $\endgroup$
    – phdstudent
    Commented Jun 22, 2021 at 20:10
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    $\begingroup$ You can definitely carry out DFT calculations on 2D systems. It just requires a code that supports 2D periodic boundary conditions rather than the conventional 3D. For instance, the code Crystal can handle 2D systems without relying on artificial vacuum space. $\endgroup$ Commented Jun 23, 2021 at 0:05
  • $\begingroup$ You have to be aware that if the atomic coordinates are in fractional format, increasing c will do nothing. Also if you have a unit cell for graphite, v and increase c you will end not with only one layer of graphene, but with two, three... $\endgroup$
    – Camps
    Commented Jun 23, 2021 at 0:37
  • $\begingroup$ If the system is 2D need also 2D k-points, not just one. $\endgroup$
    – Camps
    Commented Jun 23, 2021 at 0:38
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    $\begingroup$ Thank you for all your comments - I edited my answer to reflect some of them. As @AndrewRosen said, some programs do support 2D calculations, but they must use atomic-centered basis functions instead of plane waves. As the OP is asking about VASP, I gave a conclusion that is valid for plane waves, but failed to point out that it is only valid for plane waves. $\endgroup$
    – wzkchem5
    Commented Jun 23, 2021 at 8:27
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The VASP package solving the KS-equation with periodic boundary conditions (PBC). For two-dimensional materials such as graphene, you only have two periodic directions along $\vec{a}$ and $\vec{b}$ but the VASP assumes you still have three directions. To avoid this, you need to add enough vacuum (in general large than 15 angstroms) along the $\vec{c}$ dirction.

Here is a POSCAR template:

C
1.0
    2.4600000381         0.0000000000         0.0000000000
   -1.2300000191         2.1304225263         0.0000000000
    0.0000000000         0.0000000000        15.0000000000  ! add vacuum along the assumed PBC direction.
C
2
Direct
    0.000000000         0.000000000         0.500000000
    0.333333359         0.666666706         0.500000000
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