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Dear all,
I have done a PBE+BSE calculation for treating a 2D system with a 0.16 eV gap. However, the excitonic peak has even a negative intensity as shown in the attachment.
Could anybody please give me some suggestions? Thank you very much!
Here is my input file


em1s # [R Xs] Static Inverse Dielectric Matrix
optics # [R OPT] Optics
bss # [R BSS] Bethe Salpeter Equation solver
rim_cut # [R RIM CUT] Coulomb potential
bse # [R BSE] Bethe Salpeter Equation.
bsk # [R BSK] Bethe Salpeter Equation kernel
NLogCPUs=0 # [PARALLEL] Live-timing CPU`s (0 for all)
PAR_def_mode= "memory" # [PARALLEL] Default distribution mode ("balanced"/"memory"/"workload")
X_all_q_CPU= "1 1 24 2" # [PARALLEL] CPUs for each role
X_all_q_ROLEs= "q k c v" # [PARALLEL] CPUs roles (q,g,k,c,v)
X_all_q_nCPU_LinAlg_INV= 4 # [PARALLEL] CPUs for Linear Algebra
#BS_CPU= "" # [PARALLEL] CPUs for each role
#BS_ROLEs= "" # [PARALLEL] CPUs roles (k,eh,t)
BS_nCPU_LinAlg_INV= 4 # [PARALLEL] CPUs for Linear Algebra
BS_nCPU_LinAlg_DIAGO= 4 # [PARALLEL] CPUs for Linear Algebra
RandQpts=2000000 # [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/ws X/Y/Z/XY..
% CUTBox
0.00 | 0.00 | 36.00 | # [CUT] [au] Box sides
%
CUTRadius= 0.000000 # [CUT] [au] Sphere/Cylinder radius
CUTCylLen= 0.000000 # [CUT] [au] Cylinder length
CUTwsGvec= 0.700000 # [CUT] WS cutoff: number of G to be modified
Chimod= "HARTREE" # [X] IP/Hartree/ALDA/LRC/PF/BSfxc
BSEmod= "retarded" # [BSE] resonant/retarded/coupling
BSKmod= "SEX" # [BSE] IP/Hartree/HF/ALDA/SEX
BSSmod= "d" # [BSS] (h)aydock/(d)iagonalization/(i)nversion/(t)ddft`
BSENGexx= 50 Ry # [BSK] Exchange components
BSENGBlk= 12 Ry # [BSK] Screened interaction block size
#WehCpl # [BSK] eh interaction included also in coupling
WRbsWF
% BEnRange
0.00000 | 5.00000 | eV # [BSS] Energy range
%
% BDmRange
0.10000 | 0.10000 | eV # [BSS] Damping range
%
BEnSteps= 600 # [BSS] Energy steps
% BLongDir
1.000000 | 0.000000 | 0.000000 | # [BSS] [cc] Electric Field
%
% BSEBands
36 | 39 | # [BSK] Bands range
%
% BndsRnXs
1 | 125 | # [Xs] Polarization function bands
%
NGsBlkXs= 12 Ry # [Xs] Response block size
% DmRngeXs
0.10000 | 0.10000 | eV # [Xs] Damping range
%
% LongDrXs
1.000000 | 0.000000 | 0.000000 | # [Xs] [cc] Electric Field
%

Dear Shan Dong,
this happens because you have a positive peak at negative energies (you can check it by extending your range at negative energy).
The problem here is that solving BSE on top of a KS electronic structure without considering quasiparticle corrections it is not consistent (KS gap is not meaningful). You may take qp corrections into account either performing a GW calculation first and then reading QP energies (using KfnQPdb), or assigning a scissor operator by using the KfnQP_E variable (e.g. taking insight from experiments or models) to open the gap.

Best,
Daniele

Dear Daniele ,

Thanks for your reply.I have checked it by extending its range at negative energy.I wonder why there were positive peaks at negative energies and negative peaks at positive energy. Is this related to the sign of transition energy? How does the program handle positive and negative transition energy?
Waiting for your replay. Thank you.

Dear Shan Dong,
this is because of the time-ordering of the response function, here should be "causal".
This enforces the spectrum to be odd with respect the origin.
Anyway, your problem here is that you did not take into account the QP correction, so the BSE it is not fully consistent, and you have binding energy larger than the gap.

Best,
Daniele