cRPA calculations with q=0 k-p theory corrections (WAVEDER yes / no)

[the-hampel]

Dear Vasp team,

First I would like to thank for the new detailed cRPA documentation https://www.vasp.at/wiki/index.php/Cons ... _formalism . This gives a nice overview over the options implemented in Vasp. However I would like to ask / comment / correct on statement on the bottom of the page under caveats:

The cRPA method is usually applied to systems with a zero-band gap (metallic system) and, thus, suffers from slow k-point convergence. Most reliably, the usage of k-p perturbation theory should be avoided. That is, LOPTICS=.FALSE. should be set in the preceding DFT step and/or the WAVEDER should be deleted before the cRPA step.

This indicates that one should avoid using derivatives of the wavefunctions to correct the q=0 polarizability. However, in the cRPA example for SrVO3 https://www.vasp.at/wiki/index.php/CRPA_of_SrVO3 this is done. And I would even argue it is crucial to perform these corrections to achieve accurate results for smaller k-meshes. However, maybe you have a good reason why one should avoid doing this and read in the WAVEDER to perform the corrections. If I understand correctly Vasp will just set eps(q=0)=1 if the WAVEDER is not read, correct? At least this is what is printed under

Code: Select all

NQ=   1    0.0000    0.0000    0.0000, 
       CHI:  cpu time     86.9279: real time     23.9377
   SCATTER:  cpu time      0.0412: real time      0.0231
    LFIELD:  cpu time      0.0000: real time      0.0000

 HEAD OF MICROSCOPIC DIELECTRIC TENSOR (INDEPENDENT PARTICLE)
 -------------------------------------
 w=     0.000     0.000
         1.0000    0.0000      0.0000    0.0000      0.0000    0.0000
         0.0000    0.0000      1.0000    0.0000      0.0000    0.0000
         0.0000    0.0000      0.0000    0.0000      1.0000    0.0000

        0.000         1.000     0.000 dielectric  constant

without reading the WAVEDER.

I did some convergence test for SrVO3 and found this for kpoint convergence:

crpa_k_conv.png

I plotted results as NK^(-1/3) which should be roughly the kpoint convergence for GW / polarizability, I think. From this it becomes clear that at the highest kmesh I calculated (11x11x11) the screened U is still 20% off, and will only convergence to the k-p corrected value at around 200x200x200 kpoints, which is clearly unfeasible to calculate.

I think, most other codes use these corrections to correctly capture the q=0 contributions without going to large k-meshes (Abinit / RESPACK). However, maybe you have specific reasons in the implementation why you do not recommend using k-p theory for q=0 corrections? Otherwise I thought it might be nice to change the sentences in wiki accordingly. Either the one in the cRPA tutorial for SrVO3 or the cRPA overview.

Best,
Alexander Hampel (CCQ, Flatiron Institute)

[merzuk.kaltak]

Dear Alexander,

SrVO3 is a special case, where the correlated subspace (the t2g states of V) coincides with (partially occupied) Bloch bands around the Fermi energy.
Ultimately, the effective cRPA screening in SrVO3 behaves like a semiconductor, because the three partially occupied Bloch bands are neglected in the calculation of the cRPA polarizability.
That is all transition energies in the cRPA polarizability are larger than zero and no metallic contributions are present.
In such cases one can use k-p perturbation theory (i.e. the WAVEDER file) to improve k-point convergence of the cRPA matrix elements.

In contrast, systems where the correlated subspace cannot be separated exactly in k-space, there are still some residual metallic contributions in the cRPA polarizability left.
For such systems k-p perturbation theory breaks down, because zero transition energies are present in the cRPA polarizability.

Following rule of thumb for the WAVEDER method is suggested:
If NCRPA_BANDS is set and includes all partially occupied bands,
one can use WAVEDER in cRPA calculations to accelerate k-point convergence.

[the-hampel]

Hi Merzuk,

thank you for the detailed answer. That makes perfect sense. I checked a bit the literature and it is clear now why this fails for metals. For me this is solved. However, I think it would be nice to make a small addition to the explanation on the cRPA compendium page in the direction you mentioned. Often the states at the Fermi level are part of the target space in cRPA and if the user guarantees that there is not entanglement one can definitely use kp theory.
Best,
Alex