Problems with cell optimization of graphene

[Riccardo Pezzetta]

Dear CP2K community,

I am trying to optimize the lattice constant of a graphene cell with RPA at the Gamma point. I performed energy calculations with different lattice constants, but I get a very strange behavior close to the minimum. As shown in the image attached to this mail, the RPA energy shows an unphysical drop close to the minimum. With PBE the curve is regular, while the HF@PBE energy (i.e., RPA without the correlation term) shows the same irregular profile as RPA, so the issue seems to originate from the Hartree-Fock exchange term. In my input, that you find attached to the mail, the only parameter I set in the HF section is the cutoff of the truncated Coulomb operator, I set it equal to 4 Angstrom so that it does not exceed half the cell size for all values of the lattice constant considered. Have you ever encountered a similar problem? What can be the cause of this unphysical behavior? Thank you in advance for your answer.
Kind regards,

Riccardo Pezzetta

[Augustin Bussy]

Dear Riccardo,

your HFX input is not ideal, because a 4 Angstrom cutoff is probably too short. There are 2 things to consider when selecting a value for the cutoff:

1) is should not exceed half the cell size (OK in your case)

2) it should be long enough. In most cases, a value of ~6 Ang is deemed sufficient, but technically, the ideal cutoff depends on the system band gap (for smaller gap systems, a longer cutoff might be required)

I suggest you take a supercell, and extend the cutoff.

Note that the value of EPS_PGF_ORB you use is way too small (1.0E-16), and it will dramatically impact performance. Please read section 2.2 of https://pubs.acs.org/jpcbfk/article/130/4/1237/5088250/The-CP2K-Program-Package-Made-Simple for an explanation.

If using a supercell makes the RPA part of your calculation too expensive (RPA scales as N^4 with system size), consider using the low-scaling implementation; it is particularly efficient for 2D systems.

Best,
Augustin

[Riccardo Pezzetta]

Thank you very much for the answer.

Kind regards,

Riccardo Pezzetta 

[Frederick Stein]

Dear Riccardo,

You are using smearing. Can you turn it off? Are all orbitals fully occupied? How does the band-gap change with cell volume? Beware that our RPA-implementation does NOT consider partial occupation. Even worse, partially occupied orbitals are considered as fully occupied by our implementation such that the energies may even differ with the available orbitals.

In addition, I am not entirely sure how well the 2D-periodicity is covered in your executable of CP2K and I would rather use PERIODIC XYZ instead.

Best,

Frederick