Gamma point energy comparison

[SKM]

hi

i am preparing slabs and bulks of different facets of same material and wish to compare energy of systems designed. Obviously the models have different lattice parameters based on facets concerned. Is it prudent enough to compare the surface or system energies of all models at KPOINTS = [1 1 1] only energy optimization calculations, keeping ENCUT also same for all?

Regards

[marie-therese.huebsch]

Hi SKM,

The answer depends on the system you are investigating, but probably it is not sufficient to compare the Gamma point only.

It might be best to perform a convergence study of the energy difference between bulk and slab with respect to the number of k points to determine the precision of your calculation. The energy of the individual calculation, i.e., bulk and each slab, should not change significantly when increasing the number of k points compared to the energy difference between systems you are comparing.

Also, consider the following: To create a slab, you had to take multiples of the bulk primitive unit cell and pad it with a vacuum (or any other material). Any additional k point describes the interaction with neighboring unit cells. Thus along this extended direction, any additional k point describes the interaction with neighboring slabs, so that you probably want to consider only one k point perpendicular to the surface. But another aspect of taking multiples of the bulk unit cell is that you take into account long-range interactions that you would neglect in the bulk calculation if you only consider the Gamma point and the primitive unit cell in the bulk calculation.

Best regards,
Marie-Therese

[SKM]

Hi Marie
Thanks for the detailed reply.
Having the topic intact, to understand further, i have few questions:

1. "In what situations the Gamma point-only calculations will be useful?"
2. "does this mean [as per your reply] the energy at the Gamma point in the two cases are not the same? The two cases being
(i) a Gamma point only run at KPOINTS [1 1 1], and
(ii) the energy at the Gamma point of a run at different KPOINTS like [5 5 5], for a same model/system?

Regards
SKM

[marie-therese.huebsch]

Hi SKM,

Ad 1, from the top of my head, I can think of
(i) isolated systems, where you have an atom or molecule in one unit cell surrounded by a lot of vacuum,
(ii) large supercell calculations, e.g., to simulate doping and impurities, or phonons,
(iii) large systems, e.g., ab-initio molecular dynamics of liquids,
and there are probably many more. As a side remark, in the Gamma-only version of VASP (vasp_gam), some arrays can be assumed to be real at the time of compilation, which renders it computationally more efficient than the standard version of VASP (vasp_std) in case of performing Gamma-only calculations.

Ad 2, let us make one distinction first: You could compare the system's total energy or the band energies at the Gamma point. The total energy is sensitive to the k mesh, and thus the converged charge density depends on the k mesh. The Kohn-Sham Hamiltonian, its eigenvectors, and eigenenergies are determined at each k point based on the charge density. So if a Gamma-only calculation leads to a different ground state, i.e., charge density, then the band energies at the Gamma point can also be different. So in all likelihood, neither the band energies nor the total energy will be the same, assuming long-range interactions are neglected although important in that system.

That said, please run tests on the system you are investigating to get a quantitative understanding. For instance, run VASP for NxNxN, with N=1,2,..,5 using a Gamma-centered k mesh. Then, plot the total energy over N. You can also plot the band energies at the Gamma-point over N. There is nothing wrong with aiming for the lowest possible precision that can still accurately answer your research question. But this is system-dependent and cannot be answered here.

Please consider sharing the results of your convergence study so that the next user might learn from it.

Best regards,
Marie-Therese

[SKM]

Thank you Marie for the explanation.

1. Yes. will do some tests and post the results. However, as per my original query, i am working on bulk and slab system. Because of some unexpected results of previous run, i have increased the bulk system layers and now computation time increased.
But, will do some test as you suggested to confirm.
Just confirm if i do as follows, should be fine to check.
1. i will reduce the bulk system to 3 layers.
2. will do different runs, say [1 1 1], [2 2 2], ....[5 5 5]
3. and plot the energies as suggested.

Regards
SKM

[marie-therese.huebsch]

Hi SKM,

Sorry, I am confused by point 1. What layers are there in your bulk system? For the bulk calculation, I assumed you have a primitive unit cell defined in the POSCAR file.

For point 2, take care not to mix Gamma-centered and non-Gamma-centered k grids in your convergence study. Otherwise, you will see systematic oscillations due to the change in the k grid and not the convergence with respect to the number of k points.

Best regards,
Marie-Therese