# Different energies for two different geometries where only the monolayer c lattice constant is different?

I carried out a simple single-point PBE calculation on two different graphene monolayers (only c is different) using VASP with 12x12x1 k-grid.

Geometry 1:

graphene
1.0
1.22800000 -2.12695839  0.00000000
1.22800000  2.12695839  0.00000000
0.00000000  0.00000000  25
2
direct
0.00000000  0.00000000  0.25000000
0.33333333  0.66666667  0.25000000


Geometry 2:

graphene
1.0
1.22800000 -2.12695839  0.00000000
1.22800000  2.12695839  0.00000000
0.00000000  0.00000000  100
2
direct
0.00000000  0.00000000  0.25000000
0.33333333  0.66666667  0.25000000


I get two different energy results and a different number of maximum number of plane waves from the output. Why? Since they don't have periodicity on the z-direction how this effects?

Is there a protocol to follow for 2D materials calculations in VASP? I don't know what I am doing wrong.

• A VASP calculation will always have periodicity in all three spatial directions. The reason you are building a large vacuum in the z-direction is to minimize the interaction between periodic images so that you approach the true non-periodic limit. The vacuum space in the z-direction becomes a convergence parameter against which you need to test your results. – ProfM Sep 17 '20 at 16:45
• +1. But please do look at the edits I made as it is important to make your best possible effort at writing a clean and understandable, grammatically correct question. – Nike Dattani Sep 17 '20 at 16:52
• Yeah but isn't both 25A and 100A enough to eliminate these interactions? Also, I don't understand how number of maximum plane waves for 100A one is 3,4 times bigger than 25A one? Since when I use this number for NBANDS keyword for GW calculations, it ridiculously requires more memory. – Alfred Sep 17 '20 at 17:00
• As your coordinates are in fractional format, changing the cell parameters automatically change the atom positions, so, there are two different cell with atoms in different positions. This imply in different system energy. – Camps Sep 17 '20 at 17:26
• This material is planar though so that fractional format won't matter for these calculations (it will as soon as you have atoms out of that plane though). @Alfred can you clarify what energy differences you are seeing? – Tristan Maxson Sep 17 '20 at 19:48

I guess what your calculation is not done correctly.

I have run the self-consistent calculation with VASP. For the first structure, I obtain the energy is $$\boxed{-18.438584 (\text{eV})}$$

For the second structure, I obtain the energy is: $$\boxed{-18.438713 (\text{eV})}$$

The energy difference between the two structures is negligible. So the first vacuum space in the $$z$$-direction is good to obtain the converged results.

Is there a protocol to follow for 2D materials calculations in VASP?

• Yeah, probably my calculation was not correct. Thanks for the calculation! I have another question; due to the plane waves, when you use larger vacuum space it produces a larger number of maximum plane waves which is equal to NBANDS input for further GW, MP2 calculations and it causes. How can I justify using a lower number of NBANDS with larger vacuum geometry? – Alfred Sep 18 '20 at 9:13
• For example, for 25A vacuum spaced geometry it finds around 3400 maximum plane waves but for 100 A one it finds about 13600 (4times). Can I use 3400 maximum plane waves for 100A geometry since these geometries are equivalent in principle? – Alfred Sep 18 '20 at 9:17
• Why you don't use the 25 $A$ geometry with 3400 maximum plane waves? If you just want more plane waves and more NBANDS in your calculation, you should increase cutoff energy rather than the vacuum space. – Jack Sep 18 '20 at 10:57
• Yeah I could use but, I already have geometries with vacuum space of 100A, so I have to make calculations with them... – Alfred Sep 18 '20 at 11:10
• @Alfred From my experience, 100 $A$ is too much. – Jack Sep 18 '20 at 11:13