Coulomb cutoff and RPA calculation

[tolsen]

Hi

I am looking at a two-dimensional slab and seem to get some weird results when I use the coulomb cutoff. More specifically, I get negative real part of the RPA dielectric matrix at q=0 and w=0. Can this be right??? When I do not use the coulomb cutoff, the result resembles the eps0 result and seem to be more sensisible. For q not equal to zero, the results seems to be better, but the RPA eps differ a quite a bit from eps0, which I do not find without the coulomb cutoff (but I guess this could be right). I attach some output below:

By the way, I have also performed GW and BSE calculations for the same system with the coulomb cutoff and there the results seem to be sensible. But the RPA dielectric matrix should also enter in these calculations, so I am a bit puzzled about this. I am pretty sure the cutoff is chosen well (the density extends about ~10 A in the z direction and the cell is 23 A in the z direction)

RPA with coulomb cutoff:

# Absorption @ Q(1) [q->0 direction] : 1.0000000 0.0000000 0.0000000
#
#
# - Energies are Perdew & Wang (xc)
# - Wavefunctions are Perdew & Wang (xc)
#
# - The Green`s function is T-ordered -
# - Using the Length Gauge -
# - [r,Vnl] *is* included -
#
# E/ev[1] eps /Im[2] eps /Re[3] eps0/Im[4] eps0/Re[5]
#
0.000000 0.010891 -0.312466 0.119165 5.384171
1.000000 0.012648 -0.275398 0.179644 5.841753
2.000000 0.081160 -0.151626 3.122047 7.326695
3.0000000 0.1033793 -0.1218150 4.2699428 6.6096296
4.000000 0.213050 0.088330 4.095881 0.926817
5.0000000 0.2659587 0.1172918 3.6819868 0.8471405
6.0000000 0.3001478 0.1697883 2.7925606 0.2881704
7.0000000 0.1874874 0.2429490 1.8897014 -0.5650077
8.0000000 0.2687885 0.4063132 1.1138854 0.2998447
9.0000000 0.3458680 0.4672604 1.0422524 0.7438841
10.000000 0.589867 0.427168 1.296835 1.402509
# .-Input file : yambo.in
# | optics # [R OPT] Optics
# | chi # [R CHI] Dyson equation for Chi.
# | rim_cut # [R RIM CUT] Coulomb interaction
# | RandQpts= 1000000 # [RIM] Number of random q-points in the BZ
# | RandGvec= 1 RL # [RIM] Coulomb interaction RS components
# | CUTGeo= "box z" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere
# | % CUTBox
# | 0.00000 | 0.00000 | 43.46370 | # [CUT] [au] Box sides
# | %
# | CUTRadius= 0.000000 # [CUT] [au] Sphere/Cylinder radius
# | CUTCylLen= 0.000000 # [CUT] [au] Cylinder length
# | % QpntsRXd
# | 1 | 1 | # [Xd] Transferred momenta
# | %
# | % BndsRnXd
# | 1 | 190 | # [Xd] Polarization function bands
# | %
# | NGsBlkXd= 197 RL # [Xd] Response block size
# | % EnRngeXd
# | 0.00000 | 50.00000 | eV # [Xd] Energy range
# | %
# | % DmRngeXd
# | 0.10000 | 0.10000 | eV # [Xd] Damping range
# | %
# | ETStpsXd= 51 # [Xd] Total Energy steps
# | % LongDrXd
# | 0.1000E-4 | 0.000 | 0.000 | # [Xd] [cc] Electric Field
# | %

and without coulomb cutoff:

# Absorption @ Q(1) [q->0 direction] : 1.0000000 0.0000000 0.0000000
#
#
# - Energies are Perdew & Wang (xc)
# - Wavefunctions are Perdew & Wang (xc)
#
# - The Green`s function is T-ordered -
# - Using the Length Gauge -
# - [r,Vnl] *is* included -
#
# E/ev[1] eps /Im[2] eps /Re[3] eps0/Im[4] eps0/Re[5]
#
0.0000000 0.1114145 5.1963749 0.1191615 5.3840613
1.0000000 0.1663984 5.6233716 0.1796355 5.8416471
2.0000000 2.7439096 7.1263142 3.1219890 7.3266234
3.0000000 4.0498567 6.7720366 4.2698679 6.6095142
4.0000000 4.0052090 0.3393865 4.0958276 0.9268147
5.0000000 3.1476829 0.6117864 3.6819119 0.8471421
6.0000000 2.5239587 0.5722061 2.7925055 0.2881684
7.0000000 1.9907686 -0.5797463 1.8896458 -0.5650163
8.0000000 1.1324837 0.2880351 1.1138529 0.2998427
9.0000000 1.0233759 0.6173966 1.0422207 0.7438838
# .-Input file : yambo.in
# | optics # [R OPT] Optics
# | chi # [R CHI] Dyson equation for Chi.
# | % QpntsRXd
# | 1 | 1 | # [Xd] Transferred momenta
# | %
# | % BndsRnXd
# | 1 | 190 | # [Xd] Polarization function bands
# | %
# | NGsBlkXd= 197 RL # [Xd] Response block size
# | % EnRngeXd
# | 0.00000 | 50.00000 | eV # [Xd] Energy range
# | %
# | % DmRngeXd
# | 0.10000 | 0.10000 | eV # [Xd] Damping range
# | %
# | ETStpsXd= 51 # [Xd] Total Energy steps
# | % LongDrXd
# | 0.1000E-4 | 0.000 | 0.000 | # [Xd] [cc] Electric Field
# | %

BR
Thomas Olsen
Post Doc
Technical University of Denmark

[Daniele Varsano]

Dear Thomas,

yes, I agree with you there's something weird. The coulomb cutoff fourier components can have
negative values, but the eps(0) should be positive. Moreover I would not expect strong effects
in the rpa spectrum, while it looks you have big shifts in the Imaginary parts. I do not know what's
happening. I can just suggest you a test:
If you do a Bethe-Salpeter calculations activating the coupling part putting just the exchange
in the resonant and coupling part, this is an RPA calculation (you are just changing the basis) and
you should obtain the same results (of course put the same number of bands, and the same Gvec in
the exchange you used in the Gblk for the RPA). May be from this test we can see if there is some bug.
Please check also the eels output. Unfortunately, I do not have time in these days to work at it.

Cheers,

Daniele

[andrea marini]

Thomas, could you attach all necessary files to reproduce the negative absorption ? If it is a bug or something wrong in the code we can spot the problem only by running the code.

Cheers

Andrea