PPA plasmon pole imaginary frequency

[brsahu]

Hi,

How do one set 'PPAPntXp', the PPA imaginary energy, for computing the screening function, for different elements such as Si, diamond, Ge etc. Is there any additional calculation need to be done before doing G_0W_0 in order to set this parameter.

Moreover, for convergence of the quasiparticle gap obtained by G_0W_0, in addition to the parameter FFTGvec, are the following also convergence parameters?

BndsRnXp=ploarization function bands
NGsBlkXp = Response block size

Bhagawan Sahu, Researcher
Microelectronics Research Center
University of Texas, Austin, TX 78758

[myrta gruning]

Dear Sahu,

How do one set 'PPAPntXp', the PPA imaginary energy, for computing the screening function, for different elements such as Si, diamond, Ge etc. Is there any additional calculation need to be done before doing G_0W_0 in order to set this parameter.

Usually the PPA is quite independent from the actual value, and you can use the default. In fact a strong dependence of the results on this value, means that the PPA is not a good approximation for the given system. If you wish you can put the plasma frequency corresponding to the average electronic density n of your system (\omega_p = \sqrt{4\pi n e^2/m_e}). You get n simply by dividing the number of electron per unit cell by the unit cell volume, all information available from the output.

Moreover, for convergence of the quasiparticle gap obtained by G_0W_0, in addition to the parameter FFTGvec, are the following also convergence parameters?

BndsRnXp=ploarization function bands
NGsBlkXp = Response block size

Yes, you need to converge these two parameters, basically to converge the screening in the screened interaction W (see eq. 6-9 in the yambo paper).

Cheers,

m

[brsahu]

Hi,

In the calculation of QP corrections to the bulk Si eigenvalues (using yambo -g n -p p), does the Imaginary and real part of the dielectric function is written out in the output explicitly. The input used is:
___________________________
gw0 # [R GW] GoWo Quasiparticle energy levels
ppa # [R Xp] Plasmon Pole Approximation
xxvxc # [R XX] Hartree-Fock Self-energy and Vxc
em1d # [R Xd] Dynamical Inverse Dielectric Matrix
EXXRLvcs= 7391 RL # [XX] Exchange RL components
% QpntsRXp
1 | 29 | # [Xp] Transferred momenta
%
% BndsRnXp
1 | 60 | # [Xp] Polarization function bands
%
NGsBlkXp= 169 RL # [Xp] Response block size
% LongDrXp
1.000000 | 0.000000 | 0.000000 | # [Xp] [cc] Electric Field
%
PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
% GbndRnge
1 | 200 | # [GW] G[W] bands range
%
GDamping= 0.10000 eV # [GW] G[W] damping
QPreport= "kpbne0ees0" # [GW] QP info. Keys: kp/bn/xx/xc/s0/sq/e0/eq/ee/zf/ds/lm/lf
%QPkrange # [GW] QP generalized Kpoint/Band indices
1| 1| 1| 10|
21| 21| 1| 10|
_______________

If yes, which output file, form the fun yambo -g n -p p) contain these data?

If No, how to extract the real and imaginary part of the dielectric function as a function of the frequency from the Yambo run? Are these obtained using a different run-level?

Bhagawan Sahu, Researcher
Microelectronics Research Center
University of Texas, Austin TX 78758

[myrta gruning]

In the calculation of QP corrections to the bulk Si eigenvalues (using yambo -g n -p p), does the Imaginary and real part of the dielectric function is written out in the output explicitly.

Dear Sahu,

First note that for calculating the screening in QP calculation you are using the plasmon pole model (see Eq. 9 of the yambo paper).

If No, how to extract the real and imaginary part of the dielectric function as a function of the frequency from the Yambo run? Are these obtained using a different run-level?

If you are interested in optical properties you need indeed to run a different calculation. rpa is invoked by yambo -o c, you can follow the the quick guided tour part 3. More examples can be found in the TDDFT tutorials.

cheers,
m

[brsahu]

Dear Myrta,

Thanks.

1) Does it mean in Yambo, G_0W_0 is done only with plasmon pole approximation? If full frequency approach is used, can the full dielectric functions will be written out in the output? Or PPA is only way to do G_0W_0?

2) I used "yambo -o c" with the following input:


-------------------------------------------------------------------------
optics # [R OPT] Optics
chi # [R CHI] Dyson equation for Chi.
% QpntsRXd
1 | 29 | # [Xd] Transferred momenta
%
% BndsRnXd
1 | 200 | # [Xd] Polarization function bands
%
NGsBlkXd= 1 RL # [Xd] Response block size
% EnRngeXd
0.00000 | 10.00000 | eV # [Xd] Energy range
%
% DmRngeXd
0.10000 | 0.10000 | eV # [Xd] Damping range
%
ETStpsXd= 200 # [Xd] Total Energy steps
% LongDrXd
1.000000 | 0.000000 | 0.000000 | # [Xd] [cc] Electric Field
-------------------------------------------

The output contains one file each for the momenta (there are 29 or them). The first column is energy and second/third are imaginary and real part of the dielectric function? what does the third and fourth column mean?

I E/ev[1] EEL/Im[2] EEL/Re[3] EELo/Im[4] EELo/Re[5]
#
0.0000 0.0015 -0.0575 0.0015 -0.0575
0.0503 0.0015 -0.0575 0.0015 -0.0575
0.1005 0.0015 -0.0575 0.0015 -0.0575
0.1508 0.0015 -0.0574 0.0015 -0.0574
-----

3) Is it true that the absorption spectra in experiments are always q --> 0 and to compare with experiments, only the Gamma point file from Yambo i. e. o.eel_q001-rpa need to be plotted?

4) Is the local field effect included at the RPA level ie invoking yambo -o -c?

Sahu

[brsahu]

Hi Mryta,

A small correction to my previous mail.

1) It seems 'yambo -o c' does solve Dyson equation for 'chi' for the full frequency response of the dielectric function. Does equation (6) is used to calculate inverse of the epsilon (q,w) matrix? how are the real and imaginary parts are separated from the calculated epsilon(q,w)?

2) Is the full frequency approach to calculate the inverse of epsilon(q,w) implemented in Yambo? It seems there is a computational reason for not doing it from the Yambo papar (the discussion following equation (8)).

Sahu

[myrta gruning]

Hallo Sahu,

Does it mean in Yambo, G_0W_0 is done only with plasmon pole approximation? If full frequency approach is used, can the full dielectric functions will be written out in the output? Or PPA is only way to do G_0W_0?

Is the full frequency approach to calculate the inverse of epsilon(q,w) implemented in Yambo? It seems there is a computational reason for not doing it from the Yambo papar (the discussion following equation (8)).

Yes, in the GPL version only the PPA approach is available. This approximation greatly simplifies/speeds the calculations since you get an analytic expression for eq. 5. See as well here. For most of the systems this approximation is fine. In any case even performing numerically the integration on \omega' in eq. 5, \epsilon^{-1} (em1) is computed only a for a limited number of frequencies.

The output contains one file each for the momenta (there are 29 or them). The first column is energy and second/third are imaginary and real part of the dielectric function? what does the third and fourth column mean?
3) Is it true that the absorption spectra in experiments are always q --> 0 and to compare with experiments, only the Gamma point file from Yambo i. e. o.eel_q001-rpa need to be plotted?

4) Is the local field effect included at the RPA level ie invoking yambo -o -c

Starting from the 4th: yes you can include LF by changing the size of NGsBlkXd, the response block size. By default this is 1 RL, so no LF.
About 3: be careful!!! You have two sets of output: o.eps* and o.eel*.

The 2rd column of o.eps_q001-rpa corresponds to the optical absorption spectrum. o.eel_q001-rpa to the zero momentum electron energy loss. The 3rd column contains the real part of the respective quantities.(See e.g. II.B of Rev. Mod. Phys. 74, 601).

The 4/5 column refers to the independent particle approx. So by comparing e.g. the 2nd and 4th you may see the effect of LF on the spectrum.

It seems 'yambo -o c' does solve Dyson equation for 'chi' for the full frequency response of the dielectric function. Does equation (6) is used to calculate inverse of the epsilon (q,w) matrix? how are the real and imaginary parts are separated from the calculated epsilon(q,w)?

Sorry, I am not sure I understand this question. You mean how do we get the (real/imaginary part of) the macroscopic dielectric function (eM)? We get em1 by solving 6-8 and then eM from (14). Does this answer your question? The RPA is explained in the first part of 2.2 of the yambo paper. Also you can look @ the online documentation/understanding yambo.

cheers
m

[brsahu]

Dear Myrta,

Thanks

Let me put the questions in a different way. May be I was not clear. Let's refer to the Yambo paper.

1) To calculate frequency-dependent dielectric function, you said we solve eq. 6-8 and then use eq. 14 to get the macroscopic dielectric constant. In using equation 6-8 to get inverse of the microscopic dielectric function, it seems the integration is done in the reciprocal space and the in the frequency space that means we do not adopt PPA to get inverse of microscopic dielectric constant meaning the discussions after eq. 8 is not applicable to calculate macroscopic dielectric constant. pl. comment.

2) But to get the response function for the Dyson equation to get the quasi-particle corrections, inverse of epsilon is calculated only at the plasmon frequency although in principle the response function and inverse of epsilon can be used as calculated in step (1) to get the self-energy in the Dyson equation. Pl. suggest.

3) In eq. 14, q-->0 limit is taken for epsilon_M. Does this mean one need to plot only the file o.eps_q001-rpa, which is for q= (0,0,0)for the imaginary part in order to compare with the experimental absorption spectrum?

4) It is not clear to me after solving eq. 14, how to separate the imaginary and real part of the epsilon_M which are printed in the file say o.eps_q001-rpa?

5) If the local field effects are taken into account by increasing the reciprocal space grid G and G' i.e. the response function block, then in eq. 14 which uses the response function 'chi' in evaluating inverse of epsilon, how to interpret using inverse of epsilon at G=0, G'=0.

Hope I am clear now.

Sahu

[myrta gruning]

Dear Sahu,

1) To calculate frequency-dependent dielectric function, you said we solve eq. 6-8 and then use eq. 14 to get the macroscopic dielectric constant. In using equation 6-8 to get inverse of the microscopic dielectric function, it seems the integration is done in the reciprocal space and the in the frequency space that means we do not adopt PPA to get inverse of microscopic dielectric constant meaning the discussions after eq. 8 is not applicable to calculate macroscopic dielectric constant. pl. comment.

Yes, the PPA is used only for the QP corrections.

2) But to get the response function for the Dyson equation to get the quasi-particle corrections, inverse of epsilon is calculated only at the plasmon frequency although in principle the response function and inverse of epsilon can be used as calculated in step (1) to get the self-energy in the Dyson equation. Pl. suggest.

Yes, in principle there is no need for the PPA, the reason numerical. Note that for getting the macroscopic dielectric constant you need just one element of eqs.6,7 (G=0, G'=0), while in eq. (5) you will need many elements G,G', so this is computationally heavier.

3) In eq. 14, q-->0 limit is taken for epsilon_M. Does this mean one need to plot only the file o.eps_q001-rpa, which is for q= (0,0,0)for the imaginary part in order to compare with the experimental absorption spectrum?

Yes, you get the absorption spectrum within RPA plotting the second against the first column of o.eps_q001-rpa.

4) It is not clear to me after solving eq. 14, how to separate the imaginary and real part of the epsilon_M which are printed in the file say o.eps_q001-rpa?

Do you mean which columns in the o.eps_q001-rpa corresponds to Im/Re part?
In this case if look into the file you see it contains 5 columns which are specified by a head line.

Code: Select all

#  E/ev[1]    e/Im[2]    e/Re[3]    eo/Im[4]   eo/Re[5]
#
   0.00000    0.04842    3.04842    0.04842    3.04842

the first is the energy in Ev (E/ev[1]), the second (e/Im[2]) is the imaginary part of epsilon_M (so you should print this out to print the imaginary spectrum), the third (e/Re[3]) the real part, the 4th/5th the imaginary/real part of the non-interacting spectrum ( eo/Im[4],eo/Re[5])

5) If the local field effects are taken into account by increasing the reciprocal space grid G and G' i.e. the response function block, then in eq. 14 which uses the response function 'chi' in evaluating inverse of epsilon, how to interpret using inverse of epsilon at G=0, G'=0.

The _response function_ block regards how many elements you calculate in 8, and thus in the sum over G" in 7. If you consider eq. 8 just for G=G' (response block = 1 RL) you will find that (eq 14) simplifies and becomes the just the spatial macroscopic average of the dielectric function [1-v(q)\chi_0(q,G=0,G'=0)].

I hope this answers your questions,

cheers

m

[brsahu]

Dear Myrta,

Thanks

About (3): For each transferred momenta i.e q' s in yambo.in, yambo -o c write one file including q= (0,0,0) point, if this point is in the q-list. My question was to compare with experimental absorption spectra, do one use only the file for q=(0,0,0) and plot second versus the first column in o.eps_q001-rpa? Also only q=(0,0,0) is considered because the contribution to absorption spectra is the dominant one compared to other q's in the list?

About (4): I was asking how one separates explicitly the real and imaginary part of the macroscopic dielectric constant after solving equation (14), I mean how the code does it. It is clear from your previous mails which columns in the file corresponds to the re/im part of it.

About (5): I mean if G=G'=0 is the limit taken while calculating equation (14), then are we including the local field effects in the spatial average of the macroscopic dielectric constant because only G=G'=0 is only one component.

Sahu