Problem in understanding GW+BSE corrected optical response

Deals with issues related to computation of optical spectra, in RPA (-o c) or by solving the Bethe-Salpeter equation (-o b). Includes local field effects, excitons, etc.

Moderators: Davide Sangalli, Daniele Varsano, andrea.ferretti, andrea marini, Conor Hogan, myrta gruning

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Problem in understanding GW+BSE corrected optical response

Post by barnali » Wed Apr 11, 2018 7:47 am

Dear YAMBO user,
I want to calculate the optical properties of a 2D system using quantum espresso + YAMBO (for GW correction+ BSE). For this, I have done scf and nscf calculation in quantum espresso and used p2y from Yambo bin to make the database of YAMBO. I have checked the convergence in k-point, EXXRLvcs, NGsBlkXp, BndsRnXp, GbndRnge and finally found the GW corrected band gap is 1.386 eV. Then I calculated optical properties using yambo. In the output, "o.optic....." there are five column,

"E/ev[1] eps /Im[2] eps /Re[3] eps0/Im[4] eps0/Re[5]

I have found that the first peak (1.313 eV) of the imaginary part of dielectric function is slightly smaller than GW corrected electronic band gap (1.386 eV) for 2nd column (GW+BSE) and slightly higher than 1.386 eV(GW corrected electronic band gap) for 4th column (1.414 eV).

Now my question is
1) Why does the first peak of imaginary part of dielectric function not appear at exactly GW corrected electronic band gap as the system is direct band gap semiconductor?

Here I have pasted the output files (for GW and GW+BSE) for details information. I am waiting for a kind suggestion. Thanking you in advance.

0.GW.qp

"#
# ::: ::: ::: :::: :::: ::::::::: ::::::::
# :+: :+: :+: :+: +:+:+: :+:+:+ :+: :+: :+: :+:
# +:+ +:+ +:+ +:+ +:+ +:+:+ +:+ +:+ +:+ +:+ +:+
# +#++: +#++:++#++: +#+ +:+ +#+ +#++:++#+ +#+ +:+
# +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+
# #+# #+# #+# #+# #+# #+# #+# #+# #+#
# ### ### ### ### ### ######### ########
#
# GPL Version 3.4.2 Revision 93
# http://www.yambo-code.org
#
# GW [Newton Solver]
#
# PPA imaginary pt [ev]: 27.21138
# GW SC iterations :0
# dS/dw steps : 2
# dS/dw step [ev]: 0.10000
# X G`s [used]: 789
# X G`s [disk]: 789
# X bands : 1 44
# X poles [o/o]: 100.0000
# X e/h E range [ev]:-1.000000 -1.000000
# X xc-Kernel :none
# X BZ energy RIM : no
# X BZ RIM points :0
# Sc/G bands : 1 44
# Sc/G damping [ev]: 0.10000
# Sx RL components : 2623
# QP @ K 001 - 004 : b 001 - 044
#
# K-point Band Eo Eqp E-Eo Z
#
1.00000 1.00000 -18.09612 -17.89040 0.20572 0.23547
1.00000 2.00000 -15.77567 -15.47957 0.29610 0.38658
1.00000 3.00000 -15.77567 -15.45790 0.31778 0.38395
1.00000 4.00000 -14.72660 -14.22558 0.50102 0.17283
1.00000 5.00000 -14.72660 -14.21963 0.50697 0.17759
1.00000 6.00000 -14.02588 -14.05438 -0.02850 0.32499
1.00000 7.00000 -10.98395 -11.29189 -0.30794 0.78648
1.00000 8.00000 -10.98395 -11.29326 -0.30930 0.78350
1.00000 9.00000 -10.51175 -10.48247 0.02927 0.54506
1.00000 10.00000 -9.34818 -9.20134 0.14683 0.70058
1.00000 11.00000 -8.46295 -8.15761 0.30533 0.63320
1.00000 12.00000 -8.24038 -8.06049 0.17990 0.63169
1.00000 13.00000 -8.24038 -8.06085 0.17953 0.63212
1.00000 14.00000 -6.35144 -5.96036 0.39108 0.54478
1.00000 15.00000 -5.54145 -4.97975 0.56170 0.68340
1.00000 16.00000 -5.54145 -4.98067 0.56078 0.68339
1.00000 17.00000 -3.43869 -2.65588 0.78281 0.67068
1.00000 18.00000 -3.43869 -2.65704 0.78165 0.67064
1.00000 19.00000 -3.33658 -2.92054 0.41604 0.68771
1.00000 20.00000 -3.33658 -2.92049 0.41609 0.68773
1.00000 21.00000 -2.39828 -2.20102 0.19725 0.70824
1.00000 22.00000 -2.06586 -1.83485 0.23100 0.69378
1.00000 23.00000 -2.06586 -1.83489 0.23097 0.69366
1.00000 24.00000 -1.51538 -0.91927 0.59611 0.71426
1.00000 25.00000 2.54719 4.76927 2.22208 0.68454
1.00000 26.00000 3.74021 6.29496 2.55475 0.72466
1.00000 27.00000 3.74021 6.29517 2.55497 0.72471
1.00000 28.00000 4.04435 6.27739 2.23304 0.68214
1.00000 29.00000 4.04435 6.27851 2.23417 0.68233
1.00000 30.00000 4.31054 4.62320 0.31266 0.82084
1.000 31.00 5.146 5.151 0.5477E-2 0.8382
1.00000 32.00000 5.68353 5.22969 -0.45385 0.86645
1.00000 33.00000 6.41774 9.36914 2.95141 0.65414
1.00000 34.00000 6.53010 9.16998 2.63988 0.70521
1.00000 35.00000 6.53010 9.17096 2.64086 0.70549
1.00000 36.00000 7.16490 8.90515 1.74025 0.81058
1.00000 37.00000 7.38508 7.28413 -0.10096 0.85416
1.00000 38.00000 7.84716 8.96709 1.11993 0.83828
1.00000 39.00000 8.20753 8.40126 0.19373 0.84201
1.00000 40.00000 8.22256 9.76434 1.54178 0.83196
1.00000 41.00000 8.22256 9.76418 1.54162 0.83183
1.00000 42.00000 8.56146 9.42048 0.85902 0.82483
1.00000 43.00000 8.56146 9.42051 0.85905 0.82485
1.00000 44.00000 8.95624 9.39384 0.43760 0.78710
2.00000 1.00000 -18.02975 -18.20008 -0.17032 0.36504
2.00000 2.00000 -16.14646 -17.91191 -1.76546 -0.37084
2.00000 3.00000 -15.92885 -14.24180 1.68705 0.40884
2.00000 4.00000 -14.59638 -14.28380 0.31259 0.22531
2.00000 5.00000 -14.30142 -13.98598 0.31545 0.33780
2.00000 6.00000 -13.54153 -13.71980 -0.17827 0.38202
2.00000 7.00000 -12.01548 -12.07581 -0.06034 0.48471
2.00000 8.00000 -11.30015 -11.51378 -0.21363 0.59424
2.00000 9.00000 -9.89445 -9.81391 0.08054 0.64249
2.00000 10.00000 -9.73698 -9.76011 -0.02314 0.62020
2.00000 11.00000 -8.30031 -7.95304 0.34727 0.64510
2.00000 12.00000 -8.00842 -7.80120 0.20722 0.64566
2.00000 13.00000 -7.59161 -7.30058 0.29102 0.67546
2.00000 14.00000 -6.19988 -5.74154 0.45834 0.62024
2.00000 15.00000 -5.85906 -5.36669 0.49237 0.68624
2.00000 16.00000 -5.76114 -5.26862 0.49252 0.68776
2.00000 17.00000 -4.32769 -3.82861 0.49908 0.65006
2.00000 18.00000 -4.00445 -3.43819 0.56626 0.70157
2.00000 19.00000 -2.90914 -2.37881 0.53033 0.68108
2.00000 20.00000 -2.51073 -2.33532 0.17541 0.69927
2.00000 21.00000 -2.45241 -1.74925 0.70316 0.69293
2.00000 22.00000 -2.16696 -1.95571 0.21125 0.69392
2.00000 23.00000 -1.93620 -1.68123 0.25497 0.69680
2.000 24.00 -.8242 -.1528E-1 0.8089 0.7096
2.00000 25.00000 1.42028 3.46595 2.04567 0.71202
2.00000 26.00000 3.33100 5.50640 2.17540 0.70349
2.00000 27.00000 3.90515 6.52030 2.61516 0.72253
2.00000 28.00000 4.18107 6.80145 2.62037 0.71823
2.00000 29.00000 4.58322 4.92485 0.34163 0.82079
2.00000 30.00000 4.61448 7.13331 2.51883 0.72528
2.000 31.00 5.398 5.423 0.2521E-1 0.8382
2.00000 32.00000 5.72063 8.70857 2.98793 0.69407
2.00000 33.00000 5.95359 5.50813 -0.44546 0.86654
2.00000 34.00000 6.61930 7.29474 0.67544 0.81758
2.00000 35.00000 6.67050 9.05367 2.38317 0.66391
2.00000 36.00000 7.32931 10.08219 2.75288 0.69610
2.00000 37.00000 7.34337 7.91533 0.57196 0.82058
2.00000 38.00000 7.36359 9.33417 1.97058 0.81107
2.00000 39.00000 7.62940 7.54952 -0.07988 0.85417
2.00000 40.00000 7.63533 8.55937 0.92404 0.85334
2.00000 41.00000 7.95962 9.16028 1.20066 0.84044
2.00000 42.00000 8.06910 8.73419 0.66509 0.84333
2.00000 43.00000 8.09857 8.02257 -0.07601 0.86139
2.00000 44.00000 8.46665 9.67681 1.21017 0.82539
3.00000 1.00000 -17.95087 -17.36638 0.58450 0.37343
3.00000 2.00000 -16.42665 -23.59404 -7.16739 -0.10211
3.00000 3.00000 -16.03720 -13.77356 2.26364 -0.27091
3.00000 4.00000 -14.56280 -14.29915 0.26365 0.22256
3.00000 5.00000 -13.65131 -13.79212 -0.14081 0.40874
3.00000 6.00000 -12.90053 -12.70091 0.19962 0.53344
3.00000 7.00000 -12.75964 -13.18783 -0.42819 0.47212
3.000 8.000 -11.99 -11.99 0.3730E-4 0.6732
3.00000 9.00000 -10.15228 -10.10151 0.05077 0.59932
3.00000 10.00000 -9.42237 -9.39182 0.03055 0.60284
3.00000 11.00000 -8.11554 -7.69248 0.42306 0.67168
3.00000 12.00000 -7.61356 -7.33028 0.28329 0.69421
3.00000 13.00000 -7.12398 -6.74990 0.37408 0.68200
3.00000 14.00000 -6.28594 -5.90183 0.38411 0.65554
3.00000 15.00000 -6.03384 -5.66563 0.36821 0.64420
3.00000 16.00000 -5.97003 -5.46675 0.50328 0.59681
3.00000 17.00000 -4.87890 -4.45809 0.42081 0.66702
3.00000 18.00000 -4.21436 -3.72887 0.48549 0.63477
3.00000 19.00000 -2.83588 -2.33888 0.49700 0.66889
3.00000 20.00000 -2.65911 -2.51809 0.14103 0.69193
3.00000 21.00000 -2.22522 -2.02272 0.20250 0.69497
3.00000 22.00000 -1.81902 -1.54888 0.27014 0.69960
3.00000 23.00000 -1.75401 -0.98268 0.77133 0.70120
3.00000 24.00000 0.00000 1.00047 1.00047 0.72140
3.00000 25.00000 0.46366 2.38634 1.92268 0.72086
3.00000 26.00000 2.48511 4.54289 2.05779 0.71130
3.00000 27.00000 4.54848 7.27073 2.72225 0.71113
3.00000 28.00000 4.62530 7.44822 2.82292 0.70748
3.00000 29.00000 4.65997 7.32859 2.66863 0.70922
3.00000 30.00000 4.81890 7.21288 2.39398 0.68207
3.00000 31.00000 5.30782 5.71399 0.40617 0.81952
3.00000 32.00000 5.45519 5.87483 0.41964 0.81924
3.00000 33.00000 6.11715 6.29053 0.17338 0.83491
3.00000 34.00000 6.15800 6.25928 0.10129 0.83744
3.00000 35.00000 6.74533 6.32934 -0.41598 0.86495
3.00000 36.00000 6.76027 6.36466 -0.39561 0.86977
3.00000 37.00000 6.81909 9.23327 2.41418 0.66310
3.00000 38.00000 7.25194 9.56677 2.31484 0.78693
3.00000 39.00000 7.38957 8.20207 0.81250 0.82279
3.00000 40.00000 7.74035 9.59146 1.85111 0.83070
3.00000 41.00000 7.92112 8.53026 0.60914 0.85151
3.00000 42.00000 8.26981 8.74924 0.47943 0.85222
3.00000 43.00000 8.31965 8.40770 0.08805 0.86500
3.00000 44.00000 8.40337 8.46454 0.06117 0.87244
4.000 1.000 -17.95 -17.94 0.1407E-1 0.3942
4.00000 2.00000 -16.33791 -18.39029 -2.05238 0.06887
4.00000 3.00000 -16.17166 -18.41550 -2.24383 -0.54671
4.00000 4.00000 -14.20610 -14.03071 0.17539 0.21479
4.00000 5.00000 -14.03636 -13.92591 0.11045 0.37826
4.00000 6.00000 -13.14626 -13.37668 -0.23042 0.47970
4.00000 7.00000 -12.52111 -12.53742 -0.01631 0.52914
4.00000 8.00000 -11.63980 -11.87563 -0.23583 0.55223
4.00000 9.00000 -10.73516 -10.61206 0.12310 0.59596
4.00000 10.00000 -8.95091 -8.88560 0.06531 0.62550
4.00000 11.00000 -8.11846 -7.70528 0.41317 0.64403
4.00000 12.00000 -7.73559 -7.48378 0.25181 0.66369
4.00000 13.00000 -7.25499 -6.91440 0.34058 0.66617
4.00000 14.00000 -6.19341 -5.78930 0.40410 0.68367
4.00000 15.00000 -6.01450 -5.58723 0.42727 0.68338
4.00000 16.00000 -5.97911 -5.44534 0.53377 0.63668
4.00000 17.00000 -4.70157 -4.25514 0.44643 0.65970
4.00000 18.00000 -4.48241 -4.02812 0.45429 0.65724
4.00000 19.00000 -2.60196 -2.45610 0.14585 0.69815
4.00000 20.00000 -2.59853 -2.10632 0.49221 0.66953
4.00000 21.00000 -2.42979 -2.27474 0.15505 0.69102
4.00000 22.00000 -1.78326 -0.93086 0.85239 0.70023
4.00000 23.00000 -1.66524 -1.35882 0.30642 0.70230
4.00000 24.00000 -0.54851 0.46054 1.00905 0.71512
4.00000 25.00000 1.04917 2.94098 1.89181 0.71999
4.00000 26.00000 2.47259 4.52407 2.05148 0.70914
4.00000 27.00000 4.14266 6.82056 2.67789 0.71872
4.00000 28.00000 4.40542 6.69022 2.28480 0.68258
4.00000 29.00000 4.64211 7.42922 2.78711 0.71353
4.00000 30.00000 5.08460 7.86424 2.77964 0.69998
4.00000 31.00000 5.11180 5.49433 0.38253 0.82026
4.00000 32.00000 5.89793 5.97092 0.07299 0.83713
4.00000 33.00000 6.07273 6.58314 0.51040 0.81901
4.00000 34.00000 6.26349 6.72111 0.45762 0.82262
4.00000 35.00000 6.49084 6.09309 -0.39775 0.86602
4.00000 36.00000 6.81629 7.14211 0.32581 0.82846
4.00000 37.00000 6.92806 7.10301 0.17495 0.83929
4.00000 38.00000 7.38436 10.71700 3.33264 0.76955
4.00000 39.00000 7.53261 7.14175 -0.39086 0.87277
4.00000 40.00000 7.56563 7.25351 -0.31211 0.86643
4.00000 41.00000 7.83140 10.51533 2.68393 0.65378
4.00000 42.00000 7.96943 10.77088 2.80145 0.67439
4.00000 43.00000 8.11871 8.27820 0.15949 0.84635
4.00000 44.00000 8.78873 9.72469 0.93595 0.84129
#
# YAMBO@gra-login4 x 001 CPUs * 03/14/2018 07:48 [start]
# 03/14/2018 07:48 [end]
#
# Cpu Timing [Min/Max/Average]: 01s/01s/01s
#
# .-Input file : yambo.in
# | em1d # [R Xd] Dynamical Inverse Dielectric Matrix
# | ppa # [R Xp] Plasmon Pole Approximation
# | HF_and_locXC # [R XX] Hartree-Fock Self-energy and Vxc
# | gw0 # [R GW] GoWo Quasiparticle energy levels
# | FFTGvecs= 125589 RL # [FFT] Plane-waves
# | EXXRLvcs= 11 Ry # [XX] Exchange RL components
# | Chimod= "Hartree" # [X] IP/Hartree/ALDA/LRC/BSfxc
# | % BndsRnXp
# | 1 | 44 | # [Xp] Polarization function bands
# | %
# | NGsBlkXp= 5 Ry # [Xp] Response block size
# | % LongDrXp
# | 0.1000E-4 | 0.000 | 0.000 | # [Xp] [cc] Electric Field
# | %
# | PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
# | % GbndRnge
# | 1 | 44 | # [GW] G[W] bands range
# | %
# | GDamping= 0.10000 eV # [GW] G[W] damping
# | dScStep= 0.10000 eV # [GW] Energy step to evalute Z factors
# | DysSolver= "n" # [GW] Dyson Equation solver (`n`,`s`,`g`)
# | %QPkrange # [GW] QP generalized Kpoint/Band indices
# | 1| 1| 1| 49|
# | 2| 4| 1| 48|
# | 3| 3| 1| 49|
# | %
# | %QPerange # [GW] QP generalized Kpoint/Energy indices
# | 1| 16| 0.0|-1.0|
# | %
"
...........................................................................................................

o.optics.eps

#
# ::: ::: ::: :::: :::: ::::::::: ::::::::
# :+: :+: :+: :+: +:+:+: :+:+:+ :+: :+: :+: :+:
# +:+ +:+ +:+ +:+ +:+ +:+:+ +:+ +:+ +:+ +:+ +:+
# +#++: +#++:++#++: +#+ +:+ +#+ +#++:++#+ +#+ +:+
# +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+
# #+# #+# #+# #+# #+# #+# #+# #+# #+#
# ### ### ### ### ### ######### ########
#
# GPL Version 3.4.2 Revision 93
# http://www.yambo-code.org
#
# Absorption @ Q(1) [q->0 direction] :0.1000E-4 0.000 0.000
#
#
# - Energies are GoWo Plasmon Pole appox.
# - Wavefunctions are Perdew, Burke & Ernzerhof(X)+Perdew, Burke & Ernzerhof(C)
#
# - The Green`s function is causal -
# - Using Shifted Grids -
# - [r,Vnl] *is* included -
#
# BSK|Identifier :7665
# |Dimension :1024
# |Bands :21 - 40
# |Exchange [res]: yes
# |Correlation [res]: yes
# |Kernel`s coupling : yes
# |Exchange [cpl]: yes
# |W interaction is bare : no
# |Correlation [cpl]: no
# |ALDA kernel in R-space : no
# |RL vectors [exchange]:11
# |RL vectors [correlation]:1
# |E/h energy range [ev]:-1.000000 - -1.000000
# |Coupling range [o/o]: 100.0000 - 100.0000
# W |Interaction is diagonal : no
# |Matrix size :789
# |Bands :1 - 44
# |e/h energy range [ev]:-1.000000 - -1.000000
# |Poles [o/o]: 100.0000
# |Rl vectors in the sum :125589
# |[r,Vnl] included : yes
# |Field direction :0.1000E-4 0.000000 0.000000
# |Coulomb Cutoff :none
# |xc-Kernel :none
# RIM|RL components [col]:0
# |Random points [col]:0
#
# E/ev[1] eps /Im[2] eps /Re[3] eps0/Im[4] eps0/Re[5]
#
0.000 -.2879E-5 12.29 0.000 11.01
0.10101 0.12228 12.34889 0.09190 11.06017
0.20202 0.25327 12.53295 0.18955 11.19864
0.30303 0.40325 12.85400 0.29964 11.43887
0.40404 0.58635 13.33611 0.43102 11.79662
0.50505 0.82417 14.01927 0.59677 12.29766
0.60606 1.15304 14.96839 0.81779 12.98269
0.70707 1.63959 16.29032 1.13031 13.91671
0.80808 2.41842 18.16771 1.60253 15.20663
0.90909 3.79552 20.92772 2.37590 17.03621
1.01010 6.58257 25.17361 3.78274 19.73753
1.11111 13.41084 31.82373 6.74338 23.91802
1.21212 34.14644 38.14174 14.39528 30.32178
1.31313 65.77890 2.12857 37.86930 32.83426
1.41414 31.17385 -27.74190 53.64187 -9.83160
1.51515 12.55691 -20.64876 21.73792 -22.64296
1.61616 6.38883 -14.11608 9.28889 -15.69385
1.71717 3.87133 -9.84533 4.98859 -10.43385
1.818182 2.676478 -6.904477 3.164952 -6.949370
1.919192 2.094114 -4.689410 2.296234 -4.464452
2.020202 1.904474 -2.830228 1.906409 -2.503246
2.121212 2.158381 -1.044684 1.870113 -0.754791
2.222222 3.410958 0.871379 2.313742 1.048822
2.323232 7.625094 1.390938 3.960560 3.107412
2.424242 8.416333 -5.497201 9.238179 3.429155
2.52525 3.50046 -5.99351 10.00127 -5.15921
2.626262 1.750958 -4.451234 4.116020 -5.739527
2.727273 1.116125 -3.274140 2.066046 -3.932738
2.828283 0.848062 -2.383269 1.350396 -2.534356
2.929293 0.755118 -1.636348 1.088988 -1.433631
3.030303 0.817049 -0.927434 1.075476 -0.441456
3.131313 1.181885 -0.178606 1.348533 0.602805
3.232323 2.386234 0.220838 2.306847 1.803287
3.333333 2.948531 -1.097660 5.030854 1.952128
3.434343 2.694563 -1.802919 5.826069 -0.663054
3.535353 1.765350 -2.255274 6.022072 -2.894338
3.636364 0.972504 -1.949247 3.085907 -4.489169
3.737374 0.754832 -1.429104 1.417930 -3.512441
3.838384 0.846212 -1.330037 0.846581 -2.676048
3.939394 0.522154 -1.273978 0.578893 -2.115072
4.040404 0.382356 -1.012192 0.436978 -1.687832
4.141414 0.291681 -0.858102 0.335407 -1.367645
4.242424 0.204131 -0.669725 0.265744 -1.086834
4.343434 0.163151 -0.498073 0.223697 -0.848159
4.444444 0.140459 -0.349943 0.196460 -0.640879
4.545455 0.126755 -0.217987 0.179176 -0.454856
4.64646 0.11934 -0.09623 0.17031 -0.28189
4.74747 0.11845 0.02051 0.17076 -0.11420
4.84848 0.12814 0.13741 0.18517 0.05748
4.949495 0.159144 0.258873 0.228184 0.246386
5.050505 0.257289 0.373850 0.350640 0.467270
5.151515 0.364773 0.308099 0.722843 0.615200
5.252525 0.271878 0.355087 0.912094 0.157731
5.353535 0.358488 0.514194 0.637397 0.228721
5.454545 0.643518 0.394319 0.917200 0.393437
5.555555 0.406326 0.132586 1.039979 -0.221987
5.656566 0.223936 0.263733 0.478025 -0.268593
5.75758 0.20462 0.41054 0.27123 -0.03369
5.858586 0.261219 0.463732 0.211453 0.170518
5.959596 0.229377 0.518394 0.219485 0.358896
6.060606 0.330696 0.622241 0.319279 0.557297
6.161616 0.431166 0.437647 0.675420 0.667558
6.26263 0.23222 0.42207 0.85916 0.08531
6.364 0.1836 0.5272 0.3883 0.8817E-3
6.464646 0.172913 0.562661 0.219731 0.167887
6.565657 0.122646 0.626272 0.168117 0.300721
6.666667 0.101417 0.709847 0.142825 0.391351
6.76768 0.09980 0.79777 0.12703 0.48803
6.868686 0.113104 0.880386 0.141793 0.563405
6.969697 0.124073 0.969059 0.133827 0.632484
7.070707 0.160984 1.077854 0.165290 0.718443
7.171717 0.213279 1.169392 0.206053 0.733341
7.272727 0.261992 1.305084 0.168546 0.779863
7.373737 0.370956 1.494640 0.168771 0.885226
7.474747 0.636851 1.757109 0.217824 0.984944
7.575757 1.185032 1.968547 0.336290 1.060960
7.676767 2.500596 1.480352 0.344032 0.991372
7.777778 1.855609 -0.278391 0.282609 1.125217
7.87879 0.91611 -0.08362 0.33515 1.34336
7.979797 0.758555 0.259935 0.534676 1.622752
8.080808 0.806132 0.256563 1.141414 1.890926
8.181818 0.735879 0.239090 2.041155 1.126927
8.282828 0.579314 0.267768 1.344860 0.344493
8.383839 0.615178 0.326087 1.130687 0.697728
8.484849 0.484522 0.349545 1.551106 0.349240
8.58586 0.60314 0.53452 0.92572 0.02966
8.686869 0.780995 0.215704 0.756601 0.393800
8.787878 0.433292 0.168232 1.024040 0.385026
8.888888 0.365583 0.354419 0.904170 0.259399
8.989899 0.464310 0.442350 1.007745 0.230430
9.09091 0.56129 0.37400 0.90088 -0.02769
9.192 0.5667 0.2432 0.6972 -.2824E-2
9.29293 0.41526 0.08989 0.69772 -0.11713
9.393939 0.223743 0.145794 0.376951 -0.171687
9.495 0.1424 0.2597 0.2127 -.6227E-2
9.595960 0.127834 0.345536 0.165305 0.132360
9.696970 0.114363 0.400152 0.151455 0.212787
9.797979 0.103427 0.475636 0.120847 0.298397
9.898990 0.135323 0.566636 0.126103 0.400794
10.00000 0.26548 0.64615 0.19186 0.50462
#
# YAMBO@gra-login1 x 001 CPUs * 04/11/2018 01:46 [start]
# 04/11/2018 01:58 [end]
#
# Cpu Timing [Min/Max/Average]: 12m-02s/12m-02s/12m-02s
#
# .-Input file : yambo.in
# | optics # [R OPT] Optics
# | bse # [R BSE] Bethe Salpeter Equation.
# | bsk # [R BSK] Bethe Salpeter Equation kernel
# | bss # [R BSS] Bethe Salpeter Equation solver
# | em1d # [R Xd] Dynamical Inverse Dielectric Matrix
# | ppa # [R Xp] Plasmon Pole Approximation
# | FFTGvecs= 125589 RL # [FFT] Plane-waves
# | Chimod= "hartree" # [X] IP/Hartree/ALDA/LRC/BSfxc
# | BSEmod= "coupling" # [BSE] resonant/causal/coupling
# | BSKmod= "SEX" # [BSE] IP/Hartree/HF/ALDA/SEX
# | BSSmod= "d" # [BSS] (h)aydock/(d)iagonalization/(i)nversion/(t)ddft`
# | BSENGexx= 11 RL # [BSK] Exchange components
# | BSENGBlk= 1 RL # [BSK] Screened interaction block size
# | #WehCpl # [BSK] eh interaction included also in coupling
# | KfnQPdb= "E < RS/ndb.QP" # [EXTQP BSE] Database
# | % BEnRange
# | 0.00000 | 10.00000 | eV # [BSS] Energy range
# | %
# | % BDmRange
# | 0.10000 | 0.10000 | eV # [BSS] Damping range
# | %
# | BEnSteps= 100 # [BSS] Energy steps
# | % BLongDir
# | 0.1000E-4 | 0.000 | 0.000 | # [BSS] [cc] Electric Field
# | %
# | % BSEBands
# | 21 | 40 | # [BSK] Bands range
# | %
# | % BndsRnXp
# | 1 | 44 | # [Xp] Polarization function bands
# | %
# | NGsBlkXp= 5 Ry # [Xp] Response block size
# | % LongDrXp
# | 0.1000E-4 | 0.000 | 0.000 | # [Xp] [cc] Electric Field
# | %
# | PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
.......................................................................................................................................................




Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India

User avatar
Daniele Varsano
Posts: 2614
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

Re: Problem in understanding GW+BSE corrected optical respon

Post by Daniele Varsano » Wed Apr 11, 2018 8:33 am

Dear Barnali,
1) Why does the first peak of imaginary part of dielectric function not appear at exactly GW corrected electronic band gap as the system is direct band gap semiconductor?
This is just because of energy resolution, if you increase the number of energy steps

Code: Select all

 (BEnSteps)
or reduce your energy range

Code: Select all

BEnRange
in order to have more
points in the energy range of interest you should see that the Lorenzian is peaked exactly at the GW gap, as you can see withyou resolution your peak it is not symmetric.

Next, in the BSE calculation please pay attention to

Code: Select all

BSENGexx
and

Code: Select all

BSENGBlk
variables as you set a very low value which is surely out of convergence.

Code: Select all

BSENGBlk
should be set to the same value you calculated the screening (5 Ry) or may be lower but using 1RL you are strongly underestimating the eh interaction, and also

Code: Select all

BSENGexx
is very low.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Re: Problem in understanding GW+BSE corrected optical respon

Post by barnali » Mon Apr 23, 2018 12:30 pm

BSENGexx.TIF
BSENGBlk.TIF
Respected Daniele Varsano,
Thanks a lot for your kind response. As per your suggestion, I have checked the convergence of BSENGBlk, BSENGBlk and BSEBands (graphs are already attached). I have also increased the BEnSteps to 500 from 100 and decreased the BEnRange. But still, the first peak (1.130 eV) of the imaginary part of dielectric function for GW+BSE is smaller than GW corrected electronic band gap (1.386 eV). But for only GW (4th column) the first peak appears close to GW corrected electronic band gap (1.386 eV).
Now my question is
1) Why does the first peak of imaginary part of dielectric function for GW+BSE (2nd column) not appear at exactly GW corrected electronic band gap? Is there anything wrong in my calculation?
Please guide me.Here I have pasted the output files (for GW and GW+BSE) for details information. I am waiting for a kind suggestion. Thanking you in advance.
.........................
0.GW.qp

"#
# ::: ::: ::: :::: :::: ::::::::: ::::::::
# :+: :+: :+: :+: +:+:+: :+:+:+ :+: :+: :+: :+:
# +:+ +:+ +:+ +:+ +:+ +:+:+ +:+ +:+ +:+ +:+ +:+
# +#++: +#++:++#++: +#+ +:+ +#+ +#++:++#+ +#+ +:+
# +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+ +#+
# #+# #+# #+# #+# #+# #+# #+# #+# #+#
# ### ### ### ### ### ######### ########
#
# GPL Version 3.4.2 Revision 93
# http://www.yambo-code.org
#
# GW [Newton Solver]
#
# PPA imaginary pt [ev]: 27.21138
# GW SC iterations :0
# dS/dw steps : 2
# dS/dw step [ev]: 0.10000
# X G`s [used]: 789
# X G`s [disk]: 789
# X bands : 1 44
# X poles [o/o]: 100.0000
# X e/h E range [ev]:-1.000000 -1.000000
# X xc-Kernel :none
# X BZ energy RIM : no
# X BZ RIM points :0
# Sc/G bands : 1 44
# Sc/G damping [ev]: 0.10000
# Sx RL components : 2623
# QP @ K 001 - 004 : b 001 - 044
#
# K-point Band Eo Eqp E-Eo Z
#
1.00000 1.00000 -18.09612 -17.89040 0.20572 0.23547
1.00000 2.00000 -15.77567 -15.47957 0.29610 0.38658
1.00000 3.00000 -15.77567 -15.45790 0.31778 0.38395
1.00000 4.00000 -14.72660 -14.22558 0.50102 0.17283
1.00000 5.00000 -14.72660 -14.21963 0.50697 0.17759
1.00000 6.00000 -14.02588 -14.05438 -0.02850 0.32499
1.00000 7.00000 -10.98395 -11.29189 -0.30794 0.78648
1.00000 8.00000 -10.98395 -11.29326 -0.30930 0.78350
1.00000 9.00000 -10.51175 -10.48247 0.02927 0.54506
1.00000 10.00000 -9.34818 -9.20134 0.14683 0.70058
1.00000 11.00000 -8.46295 -8.15761 0.30533 0.63320
1.00000 12.00000 -8.24038 -8.06049 0.17990 0.63169
1.00000 13.00000 -8.24038 -8.06085 0.17953 0.63212
1.00000 14.00000 -6.35144 -5.96036 0.39108 0.54478
1.00000 15.00000 -5.54145 -4.97975 0.56170 0.68340
1.00000 16.00000 -5.54145 -4.98067 0.56078 0.68339
1.00000 17.00000 -3.43869 -2.65588 0.78281 0.67068
1.00000 18.00000 -3.43869 -2.65704 0.78165 0.67064
1.00000 19.00000 -3.33658 -2.92054 0.41604 0.68771
1.00000 20.00000 -3.33658 -2.92049 0.41609 0.68773
1.00000 21.00000 -2.39828 -2.20102 0.19725 0.70824
1.00000 22.00000 -2.06586 -1.83485 0.23100 0.69378
1.00000 23.00000 -2.06586 -1.83489 0.23097 0.69366
1.00000 24.00000 -1.51538 -0.91927 0.59611 0.71426
1.00000 25.00000 2.54719 4.76927 2.22208 0.68454
1.00000 26.00000 3.74021 6.29496 2.55475 0.72466
1.00000 27.00000 3.74021 6.29517 2.55497 0.72471
1.00000 28.00000 4.04435 6.27739 2.23304 0.68214
1.00000 29.00000 4.04435 6.27851 2.23417 0.68233
1.00000 30.00000 4.31054 4.62320 0.31266 0.82084
1.000 31.00 5.146 5.151 0.5477E-2 0.8382
1.00000 32.00000 5.68353 5.22969 -0.45385 0.86645
1.00000 33.00000 6.41774 9.36914 2.95141 0.65414
1.00000 34.00000 6.53010 9.16998 2.63988 0.70521
1.00000 35.00000 6.53010 9.17096 2.64086 0.70549
1.00000 36.00000 7.16490 8.90515 1.74025 0.81058
1.00000 37.00000 7.38508 7.28413 -0.10096 0.85416
1.00000 38.00000 7.84716 8.96709 1.11993 0.83828
1.00000 39.00000 8.20753 8.40126 0.19373 0.84201
1.00000 40.00000 8.22256 9.76434 1.54178 0.83196
1.00000 41.00000 8.22256 9.76418 1.54162 0.83183
1.00000 42.00000 8.56146 9.42048 0.85902 0.82483
1.00000 43.00000 8.56146 9.42051 0.85905 0.82485
1.00000 44.00000 8.95624 9.39384 0.43760 0.78710
2.00000 1.00000 -18.02975 -18.20008 -0.17032 0.36504
2.00000 2.00000 -16.14646 -17.91191 -1.76546 -0.37084
2.00000 3.00000 -15.92885 -14.24180 1.68705 0.40884
2.00000 4.00000 -14.59638 -14.28380 0.31259 0.22531
2.00000 5.00000 -14.30142 -13.98598 0.31545 0.33780
2.00000 6.00000 -13.54153 -13.71980 -0.17827 0.38202
2.00000 7.00000 -12.01548 -12.07581 -0.06034 0.48471
2.00000 8.00000 -11.30015 -11.51378 -0.21363 0.59424
2.00000 9.00000 -9.89445 -9.81391 0.08054 0.64249
2.00000 10.00000 -9.73698 -9.76011 -0.02314 0.62020
2.00000 11.00000 -8.30031 -7.95304 0.34727 0.64510
2.00000 12.00000 -8.00842 -7.80120 0.20722 0.64566
2.00000 13.00000 -7.59161 -7.30058 0.29102 0.67546
2.00000 14.00000 -6.19988 -5.74154 0.45834 0.62024
2.00000 15.00000 -5.85906 -5.36669 0.49237 0.68624
2.00000 16.00000 -5.76114 -5.26862 0.49252 0.68776
2.00000 17.00000 -4.32769 -3.82861 0.49908 0.65006
2.00000 18.00000 -4.00445 -3.43819 0.56626 0.70157
2.00000 19.00000 -2.90914 -2.37881 0.53033 0.68108
2.00000 20.00000 -2.51073 -2.33532 0.17541 0.69927
2.00000 21.00000 -2.45241 -1.74925 0.70316 0.69293
2.00000 22.00000 -2.16696 -1.95571 0.21125 0.69392
2.00000 23.00000 -1.93620 -1.68123 0.25497 0.69680
2.000 24.00 -.8242 -.1528E-1 0.8089 0.7096
2.00000 25.00000 1.42028 3.46595 2.04567 0.71202
2.00000 26.00000 3.33100 5.50640 2.17540 0.70349
2.00000 27.00000 3.90515 6.52030 2.61516 0.72253
2.00000 28.00000 4.18107 6.80145 2.62037 0.71823
2.00000 29.00000 4.58322 4.92485 0.34163 0.82079
2.00000 30.00000 4.61448 7.13331 2.51883 0.72528
2.000 31.00 5.398 5.423 0.2521E-1 0.8382
2.00000 32.00000 5.72063 8.70857 2.98793 0.69407
2.00000 33.00000 5.95359 5.50813 -0.44546 0.86654
2.00000 34.00000 6.61930 7.29474 0.67544 0.81758
2.00000 35.00000 6.67050 9.05367 2.38317 0.66391
2.00000 36.00000 7.32931 10.08219 2.75288 0.69610
2.00000 37.00000 7.34337 7.91533 0.57196 0.82058
2.00000 38.00000 7.36359 9.33417 1.97058 0.81107
2.00000 39.00000 7.62940 7.54952 -0.07988 0.85417
2.00000 40.00000 7.63533 8.55937 0.92404 0.85334
2.00000 41.00000 7.95962 9.16028 1.20066 0.84044
2.00000 42.00000 8.06910 8.73419 0.66509 0.84333
2.00000 43.00000 8.09857 8.02257 -0.07601 0.86139
2.00000 44.00000 8.46665 9.67681 1.21017 0.82539
3.00000 1.00000 -17.95087 -17.36638 0.58450 0.37343
3.00000 2.00000 -16.42665 -23.59404 -7.16739 -0.10211
3.00000 3.00000 -16.03720 -13.77356 2.26364 -0.27091
3.00000 4.00000 -14.56280 -14.29915 0.26365 0.22256
3.00000 5.00000 -13.65131 -13.79212 -0.14081 0.40874
3.00000 6.00000 -12.90053 -12.70091 0.19962 0.53344
3.00000 7.00000 -12.75964 -13.18783 -0.42819 0.47212
3.000 8.000 -11.99 -11.99 0.3730E-4 0.6732
3.00000 9.00000 -10.15228 -10.10151 0.05077 0.59932
3.00000 10.00000 -9.42237 -9.39182 0.03055 0.60284
3.00000 11.00000 -8.11554 -7.69248 0.42306 0.67168
3.00000 12.00000 -7.61356 -7.33028 0.28329 0.69421
3.00000 13.00000 -7.12398 -6.74990 0.37408 0.68200
3.00000 14.00000 -6.28594 -5.90183 0.38411 0.65554
3.00000 15.00000 -6.03384 -5.66563 0.36821 0.64420
3.00000 16.00000 -5.97003 -5.46675 0.50328 0.59681
3.00000 17.00000 -4.87890 -4.45809 0.42081 0.66702
3.00000 18.00000 -4.21436 -3.72887 0.48549 0.63477
3.00000 19.00000 -2.83588 -2.33888 0.49700 0.66889
3.00000 20.00000 -2.65911 -2.51809 0.14103 0.69193
3.00000 21.00000 -2.22522 -2.02272 0.20250 0.69497
3.00000 22.00000 -1.81902 -1.54888 0.27014 0.69960
3.00000 23.00000 -1.75401 -0.98268 0.77133 0.70120
3.00000 24.00000 0.00000 1.00047 1.00047 0.72140
3.00000 25.00000 0.46366 2.38634 1.92268 0.72086
3.00000 26.00000 2.48511 4.54289 2.05779 0.71130
3.00000 27.00000 4.54848 7.27073 2.72225 0.71113
3.00000 28.00000 4.62530 7.44822 2.82292 0.70748
3.00000 29.00000 4.65997 7.32859 2.66863 0.70922
3.00000 30.00000 4.81890 7.21288 2.39398 0.68207
3.00000 31.00000 5.30782 5.71399 0.40617 0.81952
3.00000 32.00000 5.45519 5.87483 0.41964 0.81924
3.00000 33.00000 6.11715 6.29053 0.17338 0.83491
3.00000 34.00000 6.15800 6.25928 0.10129 0.83744
3.00000 35.00000 6.74533 6.32934 -0.41598 0.86495
3.00000 36.00000 6.76027 6.36466 -0.39561 0.86977
3.00000 37.00000 6.81909 9.23327 2.41418 0.66310
3.00000 38.00000 7.25194 9.56677 2.31484 0.78693
3.00000 39.00000 7.38957 8.20207 0.81250 0.82279
3.00000 40.00000 7.74035 9.59146 1.85111 0.83070
3.00000 41.00000 7.92112 8.53026 0.60914 0.85151
3.00000 42.00000 8.26981 8.74924 0.47943 0.85222
3.00000 43.00000 8.31965 8.40770 0.08805 0.86500
3.00000 44.00000 8.40337 8.46454 0.06117 0.87244
4.000 1.000 -17.95 -17.94 0.1407E-1 0.3942
4.00000 2.00000 -16.33791 -18.39029 -2.05238 0.06887
4.00000 3.00000 -16.17166 -18.41550 -2.24383 -0.54671
4.00000 4.00000 -14.20610 -14.03071 0.17539 0.21479
4.00000 5.00000 -14.03636 -13.92591 0.11045 0.37826
4.00000 6.00000 -13.14626 -13.37668 -0.23042 0.47970
4.00000 7.00000 -12.52111 -12.53742 -0.01631 0.52914
4.00000 8.00000 -11.63980 -11.87563 -0.23583 0.55223
4.00000 9.00000 -10.73516 -10.61206 0.12310 0.59596
4.00000 10.00000 -8.95091 -8.88560 0.06531 0.62550
4.00000 11.00000 -8.11846 -7.70528 0.41317 0.64403
4.00000 12.00000 -7.73559 -7.48378 0.25181 0.66369
4.00000 13.00000 -7.25499 -6.91440 0.34058 0.66617
4.00000 14.00000 -6.19341 -5.78930 0.40410 0.68367
4.00000 15.00000 -6.01450 -5.58723 0.42727 0.68338
4.00000 16.00000 -5.97911 -5.44534 0.53377 0.63668
4.00000 17.00000 -4.70157 -4.25514 0.44643 0.65970
4.00000 18.00000 -4.48241 -4.02812 0.45429 0.65724
4.00000 19.00000 -2.60196 -2.45610 0.14585 0.69815
4.00000 20.00000 -2.59853 -2.10632 0.49221 0.66953
4.00000 21.00000 -2.42979 -2.27474 0.15505 0.69102
4.00000 22.00000 -1.78326 -0.93086 0.85239 0.70023
4.00000 23.00000 -1.66524 -1.35882 0.30642 0.70230
4.00000 24.00000 -0.54851 0.46054 1.00905 0.71512
4.00000 25.00000 1.04917 2.94098 1.89181 0.71999
4.00000 26.00000 2.47259 4.52407 2.05148 0.70914
4.00000 27.00000 4.14266 6.82056 2.67789 0.71872
4.00000 28.00000 4.40542 6.69022 2.28480 0.68258
4.00000 29.00000 4.64211 7.42922 2.78711 0.71353
4.00000 30.00000 5.08460 7.86424 2.77964 0.69998
4.00000 31.00000 5.11180 5.49433 0.38253 0.82026
4.00000 32.00000 5.89793 5.97092 0.07299 0.83713
4.00000 33.00000 6.07273 6.58314 0.51040 0.81901
4.00000 34.00000 6.26349 6.72111 0.45762 0.82262
4.00000 35.00000 6.49084 6.09309 -0.39775 0.86602
4.00000 36.00000 6.81629 7.14211 0.32581 0.82846
4.00000 37.00000 6.92806 7.10301 0.17495 0.83929
4.00000 38.00000 7.38436 10.71700 3.33264 0.76955
4.00000 39.00000 7.53261 7.14175 -0.39086 0.87277
4.00000 40.00000 7.56563 7.25351 -0.31211 0.86643
4.00000 41.00000 7.83140 10.51533 2.68393 0.65378
4.00000 42.00000 7.96943 10.77088 2.80145 0.67439
4.00000 43.00000 8.11871 8.27820 0.15949 0.84635
4.00000 44.00000 8.78873 9.72469 0.93595 0.84129
#
# YAMBO@gra-login4 x 001 CPUs * 03/14/2018 07:48 [start]
# 03/14/2018 07:48 [end]
#
# Cpu Timing [Min/Max/Average]: 01s/01s/01s
#
# .-Input file : yambo.in
# | em1d # [R Xd] Dynamical Inverse Dielectric Matrix
# | ppa # [R Xp] Plasmon Pole Approximation
# | HF_and_locXC # [R XX] Hartree-Fock Self-energy and Vxc
# | gw0 # [R GW] GoWo Quasiparticle energy levels
# | FFTGvecs= 125589 RL # [FFT] Plane-waves
# | EXXRLvcs= 11 Ry # [XX] Exchange RL components
# | Chimod= "Hartree" # [X] IP/Hartree/ALDA/LRC/BSfxc
# | % BndsRnXp
# | 1 | 44 | # [Xp] Polarization function bands
# | %
# | NGsBlkXp= 5 Ry # [Xp] Response block size
# | % LongDrXp
# | 0.1000E-4 | 0.000 | 0.000 | # [Xp] [cc] Electric Field
# | %
# | PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
# | % GbndRnge
# | 1 | 44 | # [GW] G[W] bands range
# | %
# | GDamping= 0.10000 eV # [GW] G[W] damping
# | dScStep= 0.10000 eV # [GW] Energy step to evalute Z factors
# | DysSolver= "n" # [GW] Dyson Equation solver (`n`,`s`,`g`)
# | %QPkrange # [GW] QP generalized Kpoint/Band indices
# | 1| 1| 1| 49|
# | 2| 4| 1| 48|
# | 3| 3| 1| 49|
# | %
# | %QPerange # [GW] QP generalized Kpoint/Energy indices
# | 1| 16| 0.0|-1.0|
# | %
"
...........................................................................................................

OPTICS.eps.
......................................
#
# Y88b / e e e 888~~\ ,88~-_
# Y88b / d8b d8b d8b 888 | d888 \
# Y88b/ /Y88b d888bdY88b 888 _/ 88888 |
# Y8Y / Y88b / Y88Y Y888b 888 \ 88888 |
# Y /____Y88b / YY Y888b 888 | Y888 /
# / / Y88b / Y888b 888__/ `88_-~
#
# GPL Version 3.4.2 Revision 93
# http://www.yambo-code.org
#
# Absorption @ Q(1) [q->0 direction] :0.1000E-4 0.000 0.000
#
#
# - Energies are GoWo Plasmon Pole appox.
# - Wavefunctions are Perdew, Burke & Ernzerhof(X)+Perdew, Burke & Ernzerhof(C)
#
# - The Green`s function is causal -
# - Using Shifted Grids -
# - [r,Vnl] *is* included -
#
# BSK|Identifier :6886
# |Dimension :320
# |Bands :21 - 29
# |Exchange [res]: yes
# |Correlation [res]: yes
# |Kernel`s coupling : yes
# |Exchange [cpl]: yes
# |W interaction is bare : no
# |Correlation [cpl]: no
# |ALDA kernel in R-space : no
# |RL vectors [exchange]:11703
# |RL vectors [correlation]:789
# |E/h energy range [ev]:-1.000000 - -1.000000
# |Coupling range [o/o]: 100.0000 - 100.0000
# W |Interaction is diagonal : no
# |Matrix size :789
# |Bands :1 - 44
# |e/h energy range [ev]:-1.000000 - -1.000000
# |Poles [o/o]: 100.0000
# |Rl vectors in the sum :125589
# |[r,Vnl] included : yes
# |Field direction :0.1000E-4 0.000000 0.000000
# |Coulomb Cutoff :none
# |xc-Kernel :none
# RIM|RL components [col]:0
# |Random points [col]:0
#
# E/ev[1] eps /Im[2] eps /Re[3] eps0/Im[4] eps0/Re[5]
#
0.000 -.4522E-5 12.17 0.000 10.98
0.1202E-1 0.1867E-1 12.17 0.1083E-1 10.98
0.02405 0.03736 12.17381 0.02167 10.97789
0.03607 0.05611 12.17926 0.03253 10.98109
0.04810 0.07493 12.18690 0.04341 10.98556
0.06012 0.09384 12.19674 0.05434 10.99133
0.07214 0.11288 12.20879 0.06531 10.99837
0.08417 0.13206 12.22306 0.07633 11.00671
0.09619 0.15141 12.23958 0.08743 11.01636
0.10822 0.17097 12.25836 0.09860 11.02732
0.12024 0.19075 12.27943 0.10985 11.03959
0.13226 0.21078 12.30281 0.12121 11.05319
0.14429 0.23109 12.32854 0.13267 11.06813
0.15631 0.25172 12.35664 0.14425 11.08444
0.16834 0.27269 12.38716 0.15595 11.10211
0.18036 0.29403 12.42012 0.16780 11.12116
0.19238 0.31578 12.45559 0.17980 11.14161
0.20441 0.33797 12.49359 0.19196 11.16349
0.21643 0.36064 12.53419 0.20430 11.18680
0.22846 0.38382 12.57743 0.21683 11.21157
0.24048 0.40756 12.62337 0.22956 11.23781
0.25251 0.43190 12.67208 0.24251 11.26557
0.26453 0.45688 12.72363 0.25569 11.29485
0.27655 0.48254 12.77809 0.26911 11.32569
0.28858 0.50895 12.83554 0.28279 11.35812
0.30060 0.53614 12.89604 0.29675 11.39215
0.31263 0.56418 12.95971 0.31101 11.42784
0.32465 0.59313 13.02662 0.32557 11.46520
0.33667 0.62305 13.09689 0.34047 11.50429
0.34870 0.65400 13.17062 0.35571 11.54513
0.36072 0.68607 13.24791 0.37132 11.58777
0.37275 0.71932 13.32891 0.38733 11.63224
0.38477 0.75384 13.41373 0.40375 11.67860
0.39679 0.78972 13.50251 0.42060 11.72691
0.40882 0.82705 13.59542 0.43792 11.77717
0.42084 0.86595 13.69258 0.45573 11.82947
0.43287 0.90652 13.79420 0.47405 11.88387
0.44489 0.94888 13.90043 0.49293 11.94043
0.45691 0.99317 14.01148 0.51237 11.99918
0.46894 1.03952 14.12754 0.53243 12.06021
0.48096 1.08810 14.24885 0.55314 12.12360
0.49299 1.13906 14.37562 0.57453 12.18941
0.50501 1.19260 14.50812 0.59664 12.25771
0.51703 1.24891 14.64661 0.61953 12.32859
0.52906 1.30822 14.79139 0.64322 12.40214
0.54108 1.37076 14.94275 0.66777 12.47845
0.55311 1.43679 15.10103 0.69323 12.55760
0.56513 1.50661 15.26657 0.71967 12.63973
0.57715 1.58054 15.43977 0.74713 12.72491
0.58918 1.65892 15.62105 0.77567 12.81327
0.60120 1.74214 15.81082 0.80538 12.90492
0.61323 1.83064 16.00956 0.83632 13.00001
0.62525 1.92488 16.21778 0.86857 13.09866
0.63727 2.02542 16.43602 0.90221 13.20102
0.64930 2.13282 16.66488 0.93734 13.30723
0.66132 2.24777 16.90499 0.97406 13.41748
0.67335 2.37099 17.15705 1.01247 13.53192
0.68537 2.50332 17.42178 1.05268 13.65073
0.69739 2.64569 17.69997 1.09483 13.77413
0.70942 2.79916 17.99249 1.13905 13.90230
0.72144 2.96493 18.30025 1.18548 14.03549
0.73347 3.14434 18.62427 1.23429 14.17390
0.74549 3.33894 18.96562 1.28566 14.31779
0.75752 3.55049 19.32541 1.33976 14.46746
0.76954 3.78098 19.70490 1.39683 14.62316
0.78156 4.03273 20.10543 1.45707 14.78523
0.79359 4.30839 20.52837 1.52074 14.95395
0.80561 4.61102 20.97521 1.58812 15.12971
0.81764 4.94417 21.44751 1.65951 15.31288
0.82966 5.31197 21.94687 1.73525 15.50386
0.84168 5.71922 22.47495 1.81570 15.70306
0.85371 6.17154 23.03336 1.90128 15.91098
0.86573 6.67553 23.62368 1.99242 16.12811
0.87776 7.23897 24.24730 2.08965 16.35495
0.88978 7.87100 24.90533 2.19351 16.59214
0.90180 8.58247 25.59841 2.30463 16.84024
0.91383 9.38620 26.32637 2.42371 17.09996
0.92585 10.29743 27.08793 2.55153 17.37199
0.93788 11.33420 27.88001 2.68897 17.65712
0.94990 12.51781 28.69703 2.83702 17.95621
0.96192 13.87337 29.52966 2.99679 18.27013
0.97395 15.43010 30.36327 3.16955 18.59984
0.98597 17.22157 31.17561 3.35672 18.94643
0.99800 19.28534 31.93382 3.55995 19.31099
1.01002 21.66163 32.59040 3.78108 19.69479
1.02204 24.39034 33.07800 4.02227 20.09902
1.03407 27.50506 33.30373 4.28595 20.52513
1.04609 31.02268 33.14357 4.57493 20.97456
1.05812 34.92685 32.43947 4.89249 21.44886
1.07014 39.14467 31.00398 5.24240 21.94967
1.08216 43.51863 28.63925 5.62904 22.47864
1.09419 47.78327 25.17805 6.05754 23.03749
1.10621 51.56425 20.54854 6.53390 23.62786
1.11824 54.42293 14.84744 7.06516 24.25137
1.13026 55.95494 8.38437 7.65960 24.90940
1.14228 55.91652 1.65333 8.32703 25.60301
1.15431 54.31461 -4.78044 9.07904 26.33270
1.16633 51.40406 -10.43032 9.92933 27.09809
1.17836 47.59412 -14.99774 10.89418 27.89754
1.19038 43.32213 -18.39622 11.99289 28.72738
1.20240 38.95735 -20.70444 13.24820 29.58117
1.21443 34.75938 -22.09258 14.68688 30.44824
1.22645 30.88065 -22.75875 16.34004 31.31211
1.23848 27.39058 -22.88915 18.24322 32.14767
1.25050 24.30325 -22.64011 20.43585 32.91830
1.26253 21.60054 -22.13391 22.95971 33.57106
1.27455 19.24833 -21.46201 25.85512 34.03133
1.28657 17.20664 -20.69052 29.15410 34.19698
1.29860 15.43531 -19.86611 32.86839 33.93263
1.31062 13.89698 -19.02098 36.97079 33.06808
1.32265 12.55831 -18.17690 41.36986 31.40549
1.33467 11.39030 -17.34817 45.88078 28.74323
1.34669 10.36807 -16.54386 50.20457 24.92386
1.35872 9.47049 -15.76941 53.93536 19.90457
1.37074 8.67970 -15.02775 56.61818 13.83061
1.38277 7.98063 -14.32010 57.86113 7.06779
1.39479 7.36054 -13.64652 57.46349 0.15342
1.40681 6.80873 -13.00637 55.49146 -6.33454
1.41884 6.31611 -12.39847 52.25260 -11.92952
1.43086 5.87500 -11.82141 48.18568 -16.37191
1.44289 5.47888 -11.27358 43.73286 -19.61504
1.45491 5.12218 -10.75334 39.25213 -21.76686
1.46693 4.80014 -10.25900 34.98594 -23.01374
1.47896 4.50871 -9.78894 31.07045 -23.55985
1.49098 4.24436 -9.34158 27.56258 -23.59142
1.50301 4.00409 -8.91540 24.46798 -23.26201
1.51503 3.78529 -8.50898 21.76319 -22.69040
1.52705 3.58569 -8.12096 19.41108 -21.96469
1.53908 3.40332 -7.75009 17.36996 -21.14824
1.55110 3.23646 -7.39515 15.59893 -20.28550
1.56313 3.08362 -7.05507 14.06031 -19.40707
1.57515 2.94349 -6.72877 12.72066 -18.53346
1.58717 2.81491 -6.41531 11.55106 -17.67811
1.59920 2.69688 -6.11376 10.52674 -16.84941
1.61122 2.58851 -5.82328 9.62666 -16.05232
1.62325 2.48902 -5.54308 8.83309 -15.28948
1.63527 2.39773 -5.27240 8.13105 -14.56175
1.64729 2.31403 -5.01055 7.50790 -13.86910
1.65932 2.23741 -4.75685 6.95296 -13.21064
1.67134 2.16739 -4.51070 6.45724 -12.58517
1.68337 2.10358 -4.27147 6.01309 -11.99111
1.69539 2.04564 -4.03863 5.61400 -11.42684
1.70741 1.99327 -3.81162 5.25442 -10.89061
1.71944 1.94623 -3.58994 4.92964 -10.38073
1.731463 1.904325 -3.373090 4.635576 -9.895507
1.743487 1.867386 -3.160587 4.368738 -9.433326
1.755511 1.835302 -2.951971 4.126106 -8.992668
1.767535 1.807998 -2.746792 3.905080 -8.572031
1.779559 1.785439 -2.544602 3.703389 -8.170085
1.791583 1.767635 -2.344969 3.519061 -7.785505
1.803607 1.754637 -2.147463 3.350381 -7.417119
1.815631 1.746549 -1.951657 3.195844 -7.063766
1.827655 1.743519 -1.757123 3.054141 -6.724406
1.839679 1.745756 -1.563431 2.924109 -6.398044
1.851703 1.753530 -1.370159 2.804742 -6.083761
1.863727 1.767178 -1.176865 2.695144 -5.780686
1.875751 1.787119 -0.983127 2.594537 -5.488020
1.887776 1.813866 -0.788495 2.502225 -5.204984
1.899799 1.848034 -0.592541 2.417609 -4.930885
1.911824 1.890367 -0.394824 2.340153 -4.665027
1.923848 1.941750 -0.194920 2.269392 -4.406793
1.9359 2.0032 0.0076 2.2049 -4.1556
1.947896 2.076125 0.213032 2.146405 -3.910770
1.959920 2.161897 0.421768 2.093530 -3.671854
1.971944 2.262367 0.634014 2.046047 -3.438309
1.983968 2.379685 0.849856 2.003751 -3.209614
1.995992 2.516423 1.069186 1.966474 -2.985277
2.008016 2.675631 1.291584 1.934096 -2.764848
2.020040 2.860933 1.516205 1.906524 -2.547839
2.032064 3.076604 1.741551 1.883718 -2.333815
2.044088 3.327641 1.965226 1.865674 -2.122322
2.056112 3.619788 2.183528 1.852426 -1.912919
2.068136 3.959488 2.390933 1.844059 -1.705179
2.080160 4.353681 2.579421 1.840699 -1.498654
2.092184 4.809258 2.737571 1.842524 -1.292903
2.104208 5.332113 2.849587 1.849773 -1.087488
2.116232 5.925319 2.894298 1.862744 -0.881968
2.128257 6.586397 2.844651 1.881807 -0.675878
2.140280 7.303226 2.668408 1.907414 -0.468767
2.152305 8.049295 2.331286 1.940111 -0.260151
2.16433 8.77948 1.80390 1.98055 -0.04958
2.176353 9.429698 1.072763 2.029513 0.163437
2.188377 9.924090 0.153083 2.087929 0.379366
2.20040 10.19179 -0.90314 2.15690 0.59867
2.21242 10.18880 -2.01142 2.23776 0.82177
2.224449 9.914124 -3.073711 2.332047 1.049083
2.236473 9.410188 -4.004501 2.441644 1.280924
2.248497 8.747149 -4.750222 2.568759 1.517496
2.260521 8.001001 -5.294262 2.716039 1.758845
2.272545 7.236547 -5.649136 2.886620 2.004735
2.284569 6.499671 -5.843843 3.084244 2.254568
2.296593 5.817606 -5.912630 3.313327 2.507169
2.308617 5.202910 -5.887934 3.579084 2.760564
2.320641 4.658385 -5.797079 3.887572 3.011620
2.332665 4.181079 -5.661501 4.245726 3.255544
2.344689 3.765149 -5.497237 4.661280 3.485275
2.356713 3.403689 -5.315896 5.142406 3.690563
2.368737 3.089715 -5.125669 5.697064 3.856964
2.380761 2.816727 -4.932204 6.331600 3.964590
2.392786 2.578909 -4.739305 7.048491 3.987076
2.404809 2.371202 -4.549479 7.842669 3.891178
2.416834 2.189258 -4.364289 8.696600 3.638100
2.428858 2.029394 -4.184674 9.574519 3.188123
2.44088 1.88849 -4.01112 10.41829 2.50980
2.45291 1.76391 -3.84382 11.14849 1.59383
2.46493 1.65345 -3.68275 11.67555 0.46753
2.47695 1.55523 -3.52777 11.92148 -0.79836
2.48898 1.46769 -3.37865 11.84523 -2.09869
2.50100 1.38948 -3.23511 11.45815 -3.31941
2.51303 1.31949 -3.09682 10.81955 -4.36749
2.52505 1.25674 -2.96347 10.01540 -5.19040
2.537074 1.200437 -2.834721 9.133104 -5.777688
2.549098 1.149877 -2.710251 8.243790 -6.149850
2.561122 1.104472 -2.589749 7.395936 -6.343265
2.573146 1.063716 -2.472902 6.616930 -6.398114
2.585171 1.027184 -2.359417 5.918384 -6.351210
2.597194 0.994508 -2.249012 5.301655 -6.232966
2.609219 0.965380 -2.141414 4.762237 -6.066941
2.621243 0.939538 -2.036367 4.292883 -5.870621
2.633267 0.916765 -1.933619 3.885386 -5.656569
2.645291 0.896883 -1.832935 3.531685 -5.433613
2.657315 0.879746 -1.734079 3.224325 -5.207798
2.669339 0.865244 -1.636833 2.956713 -4.983187
2.681363 0.853293 -1.540973 2.723120 -4.762414
2.693387 0.843843 -1.446292 2.518652 -4.547126
2.705411 0.836867 -1.352579 2.339154 -4.338272
2.717435 0.832371 -1.259635 2.181122 -4.136332
2.729459 0.830388 -1.167250 2.041602 -3.941463
2.741483 0.830983 -1.075227 1.918101 -3.753598
2.753507 0.834250 -0.983365 1.808528 -3.572540
2.765531 0.840323 -0.891462 1.711105 -3.397990
2.777555 0.849375 -0.799322 1.624343 -3.229606
2.789579 0.861622 -0.706741 1.546972 -3.067008
2.801603 0.877332 -0.613528 1.477921 -2.909810
2.813627 0.896834 -0.519488 1.416277 -2.757618
2.825651 0.920525 -0.424442 1.361266 -2.610049
2.837675 0.948883 -0.328220 1.312229 -2.466727
2.849699 0.982483 -0.230672 1.268605 -2.327285
2.861723 1.022013 -0.131695 1.229920 -2.191375
2.87375 1.06829 -0.03123 1.19577 -2.05865
2.88577 1.12231 0.07070 1.16582 -1.92880
2.897796 1.185216 0.173937 1.139792 -1.801502
2.909820 1.258395 0.278163 1.117446 -1.676457
2.921844 1.343463 0.382799 1.098601 -1.553368
2.933868 1.442284 0.486899 1.083111 -1.431957
2.945892 1.556982 0.589005 1.070869 -1.311944
2.957916 1.689878 0.686943 1.061808 -1.193057
2.969940 1.843376 0.777564 1.055892 -1.075032
2.981964 2.019711 0.856448 1.053123 -0.957600
2.993988 2.220462 0.917572 1.053538 -0.840503
3.006012 2.445813 0.953113 1.057212 -0.723472
3.018036 2.693394 0.953518 1.064258 -0.606249
3.030060 2.956873 0.908240 1.074833 -0.488564
3.042084 3.224559 0.807541 1.089139 -0.370153
3.054108 3.478934 0.645568 1.107433 -0.250743
3.066132 3.698211 0.424244 1.130028 -0.130065
3.0782 3.8609 0.1562 1.1573 -0.0078
3.090180 3.952165 -0.135272 1.189740 0.116191
3.102204 3.969995 -0.421677 1.227870 0.242300
3.114228 3.926166 -0.676834 1.272366 0.370738
3.126252 3.842545 -0.884106 1.324018 0.501729
3.138277 3.744230 -1.039246 1.383769 0.635467
3.150301 3.653381 -1.148978 1.452739 0.772076
3.162325 3.585584 -1.227431 1.532264 0.911594
3.174349 3.548596 -1.292399 1.623926 1.053913
3.186373 3.542331 -1.362340 1.729598 1.198724
3.198397 3.559340 -1.453820 1.851475 1.345409
3.210421 3.585707 -1.578972 1.992127 1.492925
3.222445 3.602980 -1.742848 2.154486 1.639602
3.234469 3.591633 -1.941486 2.341832 1.782905
3.246493 3.535701 -2.162005 2.557676 1.919109
3.258517 3.426929 -2.385406 2.805496 2.042884
3.270541 3.266684 -2.591431 3.088248 2.146862
3.282565 3.064785 -2.763395 3.407470 2.221231
3.294589 2.836054 -2.891358 3.761982 2.253615
3.306613 2.596280 -2.972690 4.146006 2.229630
3.318637 2.358997 -3.010650 4.547174 2.134635
3.330661 2.133918 -3.011994 4.945085 1.957255
3.342685 1.926772 -2.984705 5.312111 1.694401
3.354710 1.740057 -2.936453 5.617805 1.356328
3.366734 1.574033 -2.873768 5.837124 0.968505
3.378757 1.427606 -2.801825 5.959500 0.567370
3.390782 1.299021 -2.724512 5.993624 0.190467
3.402806 1.186270 -2.644624 5.964815 -0.134683
3.414830 1.087364 -2.564134 5.906329 -0.397170
3.426854 1.000457 -2.484374 5.849565 -0.602747
3.438878 0.923891 -2.406215 5.817209 -0.769112
3.450902 0.856225 -2.330215 5.820533 -0.919616
3.462926 0.796220 -2.256693 5.859862 -1.077907
3.474950 0.742816 -2.185816 5.926842 -1.264371
3.486974 0.695114 -2.117644 6.006852 -1.494448
3.498998 0.652348 -2.052161 6.080613 -1.778014
3.511022 0.613872 -1.989311 6.124929 -2.118156
3.523046 0.579137 -1.929004 6.114186 -2.508625
3.535070 0.547675 -1.871138 6.024751 -2.931212
3.547094 0.519085 -1.815596 5.842000 -3.356463
3.559118 0.493029 -1.762263 5.566481 -3.749683
3.571142 0.469212 -1.711023 5.214742 -4.080338
3.583166 0.447383 -1.661766 4.813935 -4.329722
3.595190 0.427323 -1.614380 4.393481 -4.493219
3.607214 0.408842 -1.568765 3.978425 -4.577516
3.619239 0.391770 -1.524828 3.586231 -4.595677
3.631263 0.375960 -1.482477 3.226803 -4.562665
3.643286 0.361278 -1.441625 2.904151 -4.492504
3.655311 0.347603 -1.402188 2.618314 -4.396886
3.667335 0.334830 -1.364081 2.367110 -4.284957
3.679359 0.322867 -1.327223 2.147268 -4.163504
3.691383 0.311638 -1.291530 1.955187 -4.037396
3.703407 0.301080 -1.256933 1.787326 -3.910024
3.715431 0.291144 -1.223367 1.640452 -3.783710
3.727455 0.281785 -1.190769 1.511696 -3.659970
3.739479 0.272964 -1.159096 1.398570 -3.539783
3.751503 0.264644 -1.128303 1.298949 -3.423753
3.763527 0.256791 -1.098347 1.211015 -3.312212
3.775551 0.249370 -1.069195 1.133239 -3.205347
3.787575 0.242351 -1.040810 1.064297 -3.103261
3.799599 0.235706 -1.013162 1.003043 -3.005983
3.811623 0.229407 -0.986217 0.948441 -2.913515
3.823647 0.223429 -0.959949 0.899525 -2.825834
3.835671 0.217747 -0.934329 0.855362 -2.742849
3.847696 0.212339 -0.909332 0.815043 -2.664364
3.859719 0.207182 -0.884930 0.777727 -2.590024
3.871743 0.202256 -0.861098 0.742719 -2.519327
3.883768 0.197541 -0.837808 0.709548 -2.451651
3.895792 0.193023 -0.815032 0.678007 -2.386401
3.907815 0.188690 -0.792747 0.648103 -2.323101
3.919840 0.184533 -0.770925 0.619950 -2.261448
3.931864 0.180544 -0.749548 0.593684 -2.201316
3.943888 0.176718 -0.728599 0.569390 -2.142704
3.955912 0.173047 -0.708061 0.547088 -2.085676
3.967936 0.169526 -0.687918 0.526731 -2.030333
3.979960 0.166148 -0.668161 0.508223 -1.976777
3.991984 0.162905 -0.648772 0.491420 -1.925122
4.004008 0.159790 -0.629740 0.476131 -1.875460
4.016032 0.156798 -0.611053 0.462111 -1.827883
4.028056 0.153922 -0.592699 0.449053 -1.782421
4.040080 0.151156 -0.574666 0.436609 -1.739014
4.052104 0.148495 -0.556943 0.424428 -1.697494
4.064128 0.145933 -0.539521 0.412230 -1.657563
4.076152 0.143467 -0.522387 0.399870 -1.618834
4.088176 0.141092 -0.505532 0.387365 -1.580943
4.100201 0.138804 -0.488946 0.374862 -1.543598
4.112225 0.136600 -0.472619 0.362567 -1.506636
4.124249 0.134475 -0.456544 0.350674 -1.470024
4.136272 0.132428 -0.440711 0.339325 -1.433782
4.148297 0.130454 -0.425112 0.328599 -1.397980
4.160321 0.128552 -0.409738 0.318526 -1.362692
4.172345 0.126719 -0.394583 0.309096 -1.327981
4.184369 0.124952 -0.379637 0.300278 -1.293886
4.196393 0.123250 -0.364895 0.292032 -1.260434
4.208417 0.121611 -0.350348 0.284311 -1.227635
4.220441 0.120033 -0.335990 0.277071 -1.195490
4.232465 0.118515 -0.321815 0.270269 -1.163994
4.244489 0.117054 -0.307814 0.263869 -1.133127
4.256513 0.115651 -0.293982 0.257837 -1.102875
4.268537 0.114303 -0.280313 0.252141 -1.073217
4.280561 0.113010 -0.266801 0.246756 -1.044134
4.292585 0.111772 -0.253439 0.241657 -1.015601
4.304609 0.110586 -0.240220 0.236824 -0.987597
4.316633 0.109454 -0.227141 0.232239 -0.960103
4.328657 0.108374 -0.214192 0.227886 -0.933099
4.340681 0.107347 -0.201372 0.223750 -0.906558
4.352705 0.106372 -0.188672 0.219818 -0.880465
4.364729 0.105450 -0.176087 0.216078 -0.854800
4.376754 0.104581 -0.163611 0.212522 -0.829543
4.388777 0.103766 -0.151238 0.209139 -0.804678
4.400802 0.103005 -0.138964 0.205921 -0.780187
4.412826 0.102300 -0.126780 0.202861 -0.756053
4.424850 0.101651 -0.114682 0.199952 -0.732260
4.436873 0.101061 -0.102664 0.197189 -0.708790
4.44890 0.10053 -0.09072 0.19457 -0.68563
4.46092 0.10006 -0.07884 0.19208 -0.66276
4.47295 0.09966 -0.06703 0.18973 -0.64018
4.48497 0.09932 -0.05526 0.18750 -0.61786
4.49699 0.09906 -0.04355 0.18540 -0.59579
4.50902 0.09887 -0.03187 0.18342 -0.57396
4.52104 0.09876 -0.02023 0.18156 -0.55236
4.5331 0.0987 -0.0086 0.1798 -0.5310
4.545 0.9880E-1 0.2982E-2 0.1782 -.5098
4.55711 0.09896 0.01457 0.17669 -0.48876
4.56914 0.09923 0.02616 0.17530 -0.46793
4.58116 0.09962 0.03775 0.17403 -0.44726
4.59319 0.10013 0.04936 0.17287 -0.42674
4.60521 0.10078 0.06100 0.17183 -0.40635
4.61723 0.10158 0.07268 0.17091 -0.38608
4.62926 0.10255 0.08440 0.17011 -0.36593
4.64128 0.10370 0.09618 0.16943 -0.34587
4.653306 0.105070 0.108029 0.168878 -0.325894
4.665330 0.106673 0.119957 0.168457 -0.305990
4.677355 0.108543 0.131974 0.168169 -0.286142
4.689379 0.110716 0.144090 0.168020 -0.266337
4.701403 0.113234 0.156313 0.168016 -0.246560
4.713427 0.116149 0.168650 0.168164 -0.226796
4.725451 0.119520 0.181102 0.168470 -0.207027
4.737475 0.123417 0.193667 0.168945 -0.187244
4.749499 0.127923 0.206334 0.169597 -0.167423
4.761523 0.133136 0.219076 0.170439 -0.147552
4.773547 0.139171 0.231855 0.171484 -0.127607
4.785571 0.146162 0.244604 0.172746 -0.107574
4.79760 0.15426 0.25722 0.17424 -0.08743
4.80962 0.16363 0.26954 0.17599 -0.06716
4.82164 0.17444 0.28136 0.17802 -0.04673
4.83367 0.18687 0.29236 0.18034 -0.02612
4.8457 0.2010 0.3021 0.1830 -0.0053
4.85772 0.21694 0.31004 0.18602 0.01571
4.86974 0.23447 0.31545 0.18944 0.03700
4.88176 0.25318 0.31757 0.19331 0.05857
4.89379 0.27225 0.31560 0.19767 0.08046
4.905812 0.290402 0.309026 0.202582 0.102686
4.917836 0.305960 0.297841 0.208120 0.125291
4.929860 0.317156 0.282845 0.214362 0.148305
4.941884 0.322605 0.265701 0.221402 0.171761
4.953908 0.321786 0.248653 0.229348 0.195688
4.965932 0.315263 0.233954 0.238330 0.220111
4.977956 0.304481 0.223288 0.248501 0.245055
4.989980 0.291288 0.217481 0.260042 0.270532
5.002004 0.277454 0.216546 0.273163 0.296540
5.014028 0.264372 0.219951 0.288119 0.323054
5.026052 0.252993 0.226911 0.305206 0.350021
5.038076 0.243882 0.236601 0.324777 0.377339
5.050100 0.237341 0.248275 0.347239 0.404837
5.062124 0.233512 0.261297 0.373063 0.432250
5.074148 0.232464 0.275128 0.402782 0.459172
5.086172 0.234251 0.289303 0.436975 0.485015
5.098197 0.238932 0.303379 0.476231 0.508925
5.110220 0.246586 0.316888 0.521080 0.529716
5.122244 0.257297 0.329291 0.571863 0.545779
5.134268 0.271113 0.339931 0.628535 0.555033
5.146293 0.287979 0.347992 0.690338 0.554954
5.158317 0.307629 0.352494 0.755440 0.542776
5.170341 0.329452 0.352333 0.820556 0.515983
5.182364 0.352343 0.346425 0.880829 0.473150
5.194389 0.374619 0.333966 0.930275 0.414970
5.206413 0.394101 0.314784 0.962976 0.345055
5.218437 0.408441 0.289655 0.974846 0.269839
5.230461 0.415660 0.260387 0.965118 0.197259
5.242485 0.414677 0.229526 0.936691 0.134665
5.25451 0.40556 0.19981 0.89507 0.08705
5.26653 0.38941 0.17357 0.84665 0.05639
5.27856 0.36799 0.15243 0.79713 0.04208
5.29058 0.34329 0.13715 0.75082 0.04196
5.30261 0.31721 0.12775 0.71049 0.05324
5.31463 0.29132 0.12369 0.67768 0.07315
5.32665 0.26672 0.12409 0.65313 0.09928
5.338677 0.244059 0.127982 0.637094 0.129584
5.350701 0.223600 0.134433 0.629609 0.162411
5.362725 0.205352 0.142680 0.630660 0.196334
5.374750 0.189175 0.152138 0.640248 0.230050
5.386774 0.174866 0.162387 0.658409 0.262244
5.398798 0.162216 0.173138 0.685178 0.291484
5.410821 0.151038 0.184185 0.720505 0.316127
5.422846 0.141169 0.195377 0.764132 0.334260
5.434870 0.132462 0.206602 0.815444 0.343670
5.446894 0.124785 0.217769 0.873265 0.341866
5.458918 0.118018 0.228816 0.935602 0.326155
5.470942 0.112050 0.239698 0.999274 0.293886
5.482966 0.106783 0.250386 1.059577 0.243024
5.494990 0.102131 0.260865 1.110256 0.173148
5.50701 0.09802 0.27113 1.14426 0.08660
5.51904 0.09438 0.28118 1.15538 -0.01087
5.53106 0.09116 0.29102 1.14031 -0.11071
5.54309 0.08831 0.30066 1.09998 -0.20358
5.55511 0.08580 0.31011 1.03929 -0.28182
5.56713 0.08358 0.31939 0.96533 -0.34107
5.57916 0.08164 0.32851 0.88540 -0.38047
5.59118 0.07995 0.33748 0.80544 -0.40174
5.60321 0.07849 0.34632 0.72949 -0.40797
5.61523 0.07724 0.35504 0.65985 -0.40255
5.62725 0.07620 0.36365 0.59747 -0.38862
5.63928 0.07536 0.37218 0.54241 -0.36875
5.65130 0.07470 0.38062 0.49428 -0.34493
5.66333 0.07424 0.38900 0.45243 -0.31866
5.67535 0.07397 0.39732 0.41612 -0.29098
5.68738 0.07390 0.40561 0.38466 -0.26263
5.69940 0.07402 0.41386 0.35740 -0.23413
5.71142 0.07436 0.42211 0.33375 -0.20580
5.72345 0.07491 0.43035 0.31322 -0.17784
5.73547 0.07571 0.43859 0.29539 -0.15039
5.74750 0.07678 0.44686 0.27989 -0.12352
5.75952 0.07813 0.45515 0.26642 -0.09723
5.77154 0.07982 0.46348 0.25474 -0.07154
5.78357 0.08186 0.47184 0.24462 -0.04643
5.79559 0.08433 0.48024 0.23591 -0.02185
5.808 0.8727E-1 0.4887 0.2285 0.2239E-2
5.81964 0.09076 0.49710 0.22214 0.02587
5.83166 0.09489 0.50552 0.21687 0.04911
5.84369 0.09975 0.51387 0.21257 0.07200
5.85571 0.10545 0.52208 0.20919 0.09460
5.867735 0.112133 0.530025 0.206686 0.116952
5.879759 0.119925 0.537546 0.205028 0.139116
5.891784 0.128961 0.544403 0.204209 0.161146
5.903808 0.139346 0.550268 0.204230 0.183092
5.915832 0.151123 0.554708 0.205108 0.205006
5.927855 0.164209 0.557174 0.206873 0.226936
5.939880 0.178318 0.557022 0.209574 0.248933
5.951904 0.192861 0.553594 0.213273 0.271045
5.963928 0.206878 0.546367 0.218055 0.293315
5.975952 0.219052 0.535180 0.224025 0.315781
5.987976 0.227898 0.520480 0.231314 0.338480
6.000000 0.232114 0.503434 0.240083 0.361431
#
# YAMBO@gra-login4 x 001 CPUs * 04/21/2018 05:24 [start]
# 04/21/2018 05:41 [end]
#
# Cpu Timing [Min/Max/Average]: 16m-28s/16m-28s/16m-28s
#
# .-Input file : yambo.in
# | optics # [R OPT] Optics
# | bse # [R BSE] Bethe Salpeter Equation.
# | bsk # [R BSK] Bethe Salpeter Equation kernel
# | bss # [R BSS] Bethe Salpeter Equation solver
# | em1s # [R Xs] Static Inverse Dielectric Matrix
# | em1d # [R Xd] Dynamical Inverse Dielectric Matrix
# | ppa # [R Xp] Plasmon Pole Approximation
# | FFTGvecs= 125589 RL # [FFT] Plane-waves
# | Chimod= "hartree" # [X] IP/Hartree/ALDA/LRC/BSfxc
# | BSEmod= "coupling" # [BSE] resonant/causal/coupling
# | BSKmod= "SEX" # [BSE] IP/Hartree/HF/ALDA/SEX
# | BSSmod= "d" # [BSS] (h)aydock/(d)iagonalization/(i)nversion/(t)ddft`
# | BSENGexx= 30 Ry # [BSK] Exchange components
# | BSENGBlk= 5 Ry # [BSK] Screened interaction block size
# | #WehCpl # [BSK] eh interaction included also in coupling
# | KfnQPdb= "E < RS/ndb.QP" # [EXTQP BSE] Database
# | % BEnRange
# | 0.000000 | 6.000000 | eV # [BSS] Energy range
# | %
# | % BDmRange
# | 0.10000 | 0.10000 | eV # [BSS] Damping range
# | %
# | BEnSteps= 500 # [BSS] Energy steps
# | % BLongDir
# | 0.1000E-4 | 0.000 | 0.000 | # [BSS] [cc] Electric Field
# | %
# | % BSEBands
# | 21 | 29 | # [BSK] Bands range
# | %
# | % BndsRnXs
# | 1 | 44 | # [Xs] Polarization function bands
# | %
# | NGsBlkXs= 5 Ry # [Xs] Response block size
# | % LongDrXs
# | 0.1000E-4 | 0.000 | 0.000 | # [Xs] [cc] Electric Field
# | %
# | % BndsRnXp
# | 1 | 44 | # [Xp] Polarization function bands
# | %
# | NGsBlkXp= 5 Ry # [Xp] Response block size
# | % LongDrXp
# | 0.1000E-4 | 0.000 | 0.000 | # [Xp] [cc] Electric Field
# | %
# | PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
.......................................



Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India
You do not have the required permissions to view the files attached to this post.

User avatar
Daniele Varsano
Posts: 2614
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

Re: Problem in understanding GW+BSE corrected optical respon

Post by Daniele Varsano » Mon Apr 23, 2018 1:15 pm

Dear Barnali,
next time please upload your file instead of copy/paste as in this manner they are easier to scroll. In order to upload them, you need to rename wit a .txt suffix.

The 4th column is the independent quasi-particle gap, which means the transition occurring between a free electron and free hole and it happens correctly at the energy of the GW gap. The 2th column is the solution of the BSE equation, so you are adding the interaction (attraction) between the energy and the hole. It is found at a lower energy than the GW gap as the excitation (exciton) is bound. You have a binding energy of 0.256eV which is the energy you need to separate the electron and the hole in free particles.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Re: Problem in understanding GW+BSE corrected optical respon

Post by barnali » Mon Apr 23, 2018 1:45 pm

Respected Daniele Varsano,
Thanks a lot for your suggestion. Next time I will upload the output.
Still I have some doubt

I have run two calculation for optical response

In one case, I have commented WehCpl (#WehCpl # [BSK] eh interaction included also in coupling)
and in another case uncommented the line (WehCpl # [BSK] eh interaction included also in coupling)

but surprisingly two outputs are same, that means the first peak of imaginary part of dielectric function appears at same energy.

please explain Why ???

My other queries are

GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap for a direct band gap semiconductor. Is it feasible or indicate something wrong with my calculation?
What happens in case of indirect band gap semiconductor? I guess the, in this case, GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap.

I am waiting for your suggestion. thanking you.

Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Re: Problem in understanding GW+BSE corrected optical respon

Post by barnali » Mon Apr 23, 2018 1:52 pm

Respected Daniele Varsano,
Thanks a lot for your suggestion. Next time I will upload the output.
Still I have some doubt

I have run two calculation for optical response

In one case, I have commented WehCpl (#WehCpl # [BSK] eh interaction included also in coupling)
and in another case uncommented the line (WehCpl # [BSK] eh interaction included also in coupling)

but surprisingly two outputs are same, that means the first peak of imaginary part of dielectric function appears at same energy.

please explain Why ???

My other queries are

GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap for a direct band gap semiconductor. Is it feasible or indicate something wrong with my calculation?
What happens in case of indirect band gap semiconductor? I guess the, in this case, GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap.

I am waiting for your suggestion. thanking you.

Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India

User avatar
Daniele Varsano
Posts: 2614
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

Re: Problem in understanding GW+BSE corrected optical respon

Post by Daniele Varsano » Mon Apr 23, 2018 2:47 pm

Dear Barnali,
In one case, I have commented WehCpl (#WehCpl # [BSK] eh interaction included also in coupling)
and in another case uncommented the line (WehCpl # [BSK] eh interaction included also in coupling)
but surprisingly two outputs are same, that means the first peak of imaginary part of dielectric function appears at same energy.
This is not surprising, it just means that the Tamm-Dancoff approximation works well in your system, as is usually the case and this is the reason why WehCpl it is not activated by default. There is a lot of literature on that.
GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap for a direct band gap semiconductor.
They should be the same and it seems to me that it is the case in your calculation:

Code: Select all

                                Eks      Eqp.     deltaE
3.00000 24.00000 0.00000 1.00047 1.00047 0.72140
3.00000 25.00000 0.46366 2.38634 1.92268 0.72086
The QP direct gap is 1.38 as your IP peak.
What happens in case of indirect band gap semiconductor? I guess the, in this case, GW corrected (independent quasi-particle gap) optical band gap appears at larger energy than electronic GW band -gap.
If you mean indirect gap yes, the direct transition will be higher by construction.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Re: Problem in understanding GW+BSE corrected optical respon

Post by barnali » Mon Apr 23, 2018 3:09 pm

Respected Daniele Varsano,

Thanks a lot for your help.

Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India

barnali
Posts: 25
Joined: Sat Nov 08, 2014 5:53 am

Re: Problem in understanding GW+BSE corrected optical respon

Post by barnali » Tue Apr 24, 2018 3:41 pm

o-GW.txt
opticsstep-10000.txt
r-GW.txt
Respected Daniele Varsano,
I am facing another problem in calculating GW corrected optical band gap of a 2D indirect band gap semiconductor (Al-N-doped). the DFT band gap of this system is -
Indirect Gaps [ev]: 3.233862 3.537505
Direct Gaps [ev]: 3.321744 3.800647

I have checked the convergence in k-point, EXXRLvcs, NGsBlkXp, BndsRnXp, GbndRnge and finally found the GW corrected band gap as
Direct Gaps= 6.048064 eV
Indirect Gaps= 5.970016 eV

For GW+BSE calculation, the first peak of imaginary part of dielectric function (for only GW ) appears at 6.20382 eV which is even greater than GW-corrected direct band gap.
I have increased the 'BEnSteps' to 10000 keeping the 'BEnRange' fixed, but the problem remains same.

Please help me to fix this problem.
I am waiting for your kind response.
Thanking you.

Sincerely
Barnali
Ph.D student (CSIR SRF)
Department of physics,
Assam University, India
You do not have the required permissions to view the files attached to this post.

User avatar
Daniele Varsano
Posts: 2614
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

Re: Problem in understanding GW+BSE corrected optical respon

Post by Daniele Varsano » Tue Apr 24, 2018 4:28 pm

Dear Barnali,
take into account that in the spectra you have a Lorenztian function around each pole having a fixed width: the default value is 0.1 eV:
You can reduce the width by reducing it e.g. setting
% BDmRange
# | 0.010000 | 0.010000 | eV # [BSS] Damping range
# | %

Moreover, it is also possible that the direct gap transition it is not optically active and the main peak is due to other transitions at higher energies.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Post Reply