Dielectric tensor in metals

[maria_camarasa-gomez]

Dear Vasp developers,

I have three questions regarding how the inverse of the dielectric tensor for metals is obtained in Vasp. For GW calculations, it is specified in the "Practical guide to GW calculations" that LOPTICS should not be specified for metals, in general, and that WAVEDER file should be removed:

wiki/index.php/Practical_guide_to_GW_calculations

When I see the OUTCAR file of the resulting GW for metallic systems following those instructions, it can be seen that for the full frequency calculation, either INVERSE MACROSCOPIC DIELECTRIC TENSOR, the HEAD OF MICROSCOPIC TENSOR, or 1 + v P, with REDUCIBLE POLARIZABILTY provide the following output for all frequencies:

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

My questions are the following:

1.- Why is the value for the metal here always equal to 1.0?
2.- How does Vasp take into account the intraband and the interband transitions in a metal or is it LOPTICS giving only the interband contribution to the dielectric tensor?
3.- In particular, the intraband (Drude-like) contribution should diverge when w->0, what is happening in the code?

Thank you for your guidance,
Maria

[martin.schlipf]

Setting LOPTICS activates the computation of the dielectric function and produce the WAVEDER file. The wiki entry for this tag explains a bit more detail about what is computed and gives a reference if you want to know more details. If you set LOPTICS, you will indeed get a divergent contribution for ω -> 0 for metals. This is hard to converge with respect to the k-point mesh and there is another flag WPLASMAI that allows to approximate the Drude term instead.
I will ask for clarification on how to use GW for metals because the entries in the Wiki are a bit unclear at the moment.

[martin.schlipf]

Here is some clarification. The previous statement was correct in that the observed behavior is indeed due to the LOPTICS setting. However, the WPLASMAI flag is more of an expert feature. Its implementation is documented in the PhD thesis of Judith Harl (specifically section 2.8). For most practical GW calculations in metals it is not necessary.

Instead you should use the low-scaling GW approaches and set LFINITE_TEMPERATURE = TRUE. Remember that this setting is only compatible with Fermi-Dirac smearing (ISMEAR = -1). You also need to set the desired temperature with SIGMA. Please keep in mind that you need to increase the number of frequency point NOMEGA as you decrease the temperature. We do not recommend to decrease beyond 150 K (SIGMA = 0.013) as the required frequency mesh may be larger than possible (NOMEGA <= 24). Ideally, you start from a larger temperature like SIGMA = 0.2 and then decrease the smearing and increase the frequency mesh until you converge.

[maria_camarasa-gomez]

Thank you for your reply and for the clarification. I will proceed with the suggested procedure.

Best wishes,
María