LPEAD effect on dielectric function

[hfarsakh]

Hello everyone,
I am trying to calculate the dielectric function using BSE. To reduce the memory demand required for dense k-meshes I am trying to follow the averaging over multiple shifted grids procedure explained in the manual. This requires setting ISYM=-1 in all input files and LPEAD=FALSE (to obtain WAVEDER) which uses density functional perturbation theory to calculate the derivatives of the wave functions and not the finite difference scheme used when LPEAD=True, as described.

I did two test calculations using e.g. a single 8x8x8 k-mesh, one with LPAED = true and the second is with it set to false (for Si, same as in the manual). The difference in the calculated real part of the dielectric function at zero energy (dielectric constant) is tangible (see attached figure). Attached are the input files, just toggle LPEAD). This also leads to a tangible difference in the real part obtained with the averaging procedure using 8x8x8 with 4x4x4 shifts and without it using a single 12x12x12 k-mesh.

My question is: Is such a difference expected? If no then where is the problem, and if yes then which dielectric constant is considered more accurate? and how to make the two calculations (with LPEAD=T or F) converge to the same result? Increasing the k-mesh significantly is not an option for me. Some tests show that the difference depends on the used k-mesh but not in a systematic way.
I am using version 6.4.2

Thank you for any feedback!
Hazem

Si_optical_single_8x8x8.tgz

[alexey.tal]

Hi Hazem,

The dielectric function calculated with LOPTICS=.TRUE. with LPEAD=.TRUE. should converge to the same result as LOPTICS=.TRUE. with LPEAD=.FALSE.. However, in the first case the dielectric function is converging from below and in the second case it is converging from above. In some calculations, for example in QPGW, the LPEAD=.TRUE. has to be used (see wiki).

[hfarsakh]

Hi,
Thank you for the reply.
I did some tests to check how to two calculations will convergence, attached.
The real part of the dielectric function at zero energy using LPEAD=.TRUE. increases with the k-mesh, while with LPEAD=.FALSE. decreases, but they don't seem to come to the same value, actually the difference between them seems to be increasing. Did I miss something?

Thanks again

[alexey.tal]

It is quite difficult to make such a comparison because you have several steps, i.e., DFT, GW, and only than BSE.
Furthermore, the grid of 12x12x12 k-points is probably too sparse to produce a converged dielectric function of Si.

If you would like to make sure that LPEAD converges to the same dielectric function you should be comparing the dielectric function in the independent particle approximation as calculated directly via LOPTICS.
Here is a quick test I've done for bulk Si

[hfarsakh]

Thanks again. This is consistent with what I observe with the IP approximation, even with 12x12x12 the agreement is good. However, still it seems that I will not be able to get the same results using the averaging over reduced shifted k-meshes procedure with BSE.

[alexey.tal]

However, still it seems that I will not be able to get the same results using the averaging over reduced shifted k-meshes procedure with BSE.

If you are using sufficiently dense k-point meshes the dielectric function should converge to the same result.

Also, you don't need to use LPEAD=T if you are performing a G0W0 calculation, i.e., don't change the wave functions.