How to check the convergence of ADMM

[ma455...@gmail.com]

Hi,

I am a rookie in using cp2k. In my project I need to use HSE06 for a large system (1000 atoms) calculation. I have a few questions about using HSE06. Could somebody provide me some suggestions?

(1) In pure DFT calculations (such PBE), I can use MONKHORST-PACK kpoints scheme (e.g. 8 8 8) and run CELL_OPT calculations to get the optimized lattice parameters and then compare these parameters with literatures to confirm that the BASIS_SET and other settings used in the cp2k calculation are good enough to reproduce this sytem. However, in HFX calculations, it looks we can only use GAMMA kpoints scheme. The CELL_OPT with single kpoint can not get the correct lattice parameters. Then how can we confirm the BASIS_SET and setting in the cp2k calculations are accurate enough?

(2) HFX calculations are highly expensive so using ADMM approach is necessary. In the tutorial, it says "Always check the convergence of the primary and ADMM basis sets". I'm wondering what does this mean and how exactly should we do the check the convergence of the ADMM basis set? Or in another word, how do we usually choose which ADMM we use for our calculations?

(3) My material is Si, a semiconductor. I'm wondering is it possible that I can read the band-gap value directly from the output file after the SCF calcualtion?

I really appreciate it if somebody could provide some help.

Thanks&Regards,

Hongyang

[Nicholas Winner]

Hi Hongyang,

(1) Currently, you are right, HFX needs to use only gamma point. Therefore, instead of k-points you have to rely on supercell approach in order to converge the properties. One can get good properties using supercells of sufficient size. For example, a Si primitive cell with 2 atoms and 8x8x8 k-points would be roughly equivalent to a 1024 atom cell at gamma point only. Alternatively, you can run smalleer cell and still get good results. I would guess that ~250 atoms will give good lattice constants for Si. If you *must* perform cell optimization using hybrid, then this is what I would suggest; however, even using ADMM that would be a costly calculation. Bulk properties like lattice constants are often correctly predicted by GGA, and so you might consider simply optimizing the lattice constants at the GGA level and then passing the calculation to HSE06 after. This will depend on your system, but give it some thought. 

(2) This is a little opaque yes. In general, I believe that you don't have to worry about the convergence of the ADMM basis set for 3 reasons: (1) the ADMM has been demonstrated to perform well in many papers in the literature, and so the use of ADMM will not be questioned by many these days. (2) checking ADMM against the primary basis is absurdly expensive, to the point where it is often impossible to check. You can check the convergence of just the auxiliary bases by comparing the energies different auxiliary basis sets to one another in a series of static calculations if you want to be thorough. (3) You have already committed to sacrificing a tiny bit of accuracy by using the ADMM instead of the primary basis. It's the compromise you make in order to run large calculations, and so you shouldn't expect it to perfectly reproduce the primary basis, but it will do a decent job.

(3) The band gap can be read off by setting the SCF solver to OT and then turning on FORCE_EVAL%DFT%PRINT%MO_CUBES. A minimal working example of what I mean:

&FORCE_EVAL

    &DFT

        &SCF

            &OT

            &END

        &END

        &PRINT

            &MO_CUBES

                NHOMO -1

                NLUMO -1 

            &END

    &END

&END

Hope this helps.

-Nick

[ma455...@gmail.com]

Hi Nick,

Thank you very much! This helps a lot!

Regarding the first question, I compared the lattice parameters abtained from VASP and cp2k both using PBE functional and the results are basically same (maybe ~0.0001 A difference which I think is negligible). So do you think using the lattice parameters getting from VASP HSE06 calculation with multiple k-points as the lattice parameters for cp2k HSE06 would work too?

And another question if I may ask is that for PBE calculations, I tested different methods (e.g., DIAGONALIZATION and OT with different MIXING and MINIMIZER) and found that DIAGONALIZATION with Pulay Mixing is the most efficient. But clearly this won't work for HSE06 for the large system. So based on your expertise, do you think I'd better use totally same methods (i.e. OT) for both PBE and HSE calculations rather than using different methods for PBE and HSE (i.e., DIAGONALIZATION for PBE and OT for HSE, respectively)?

Thanks&Regards,

Hongyang

[Nicholas Winner]

The lattice parameter obtained by VASP HSE06 with kpoints and a hypothetical cp2k HSE06 calculation with kpoints should be very similar because at that point (assuming converged basis sets) the only difference is the pseudopotential and both vasp and cp2k have quality pseudopotentials. So I would say they should be fairly commensurate. There will be a small discrepancy beyond pseudopotentials because your supercell for ADMM will be equivalent to coarser k-point mesh, but since the pressure-volume energy is quite small, it shouldn't affect your results too much.

Using different methods shouldn't matter very much as long as they are both converged. They are just they way to solve the SCF. They should converge almost identical energies so long as the system has a band gap to ensure OT is appropriate.

[ma455...@gmail.com]

Hi Nick,

Thank you very much for your suggestions! I will run some tests.

Thanks&Regards,

Hongyang