## Optical matrix elements

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.
Daniele Varsano
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Joined: Tue Mar 17, 2009 2:23 pm
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### Re: Optical matrix elements

Dear Shudong,
it is not clear to me what do you mean by "transition dipoles including e-h pairs?
What are you interested in exactly?

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/

sdwang
Posts: 224
Joined: Fri Apr 09, 2010 12:30 pm

### Re: Optical matrix elements

Dear Daneile,
I want to know the BSE exciton transition dipole of the system.

Thanks!

SD
S. D. Wang
IMU,HOHHOT,CHINA
E-mail: sdwang@imu.edu.cn

Daniele Varsano
Posts: 2660
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Shudong,
sorry, but I don't get it. Transition dipoles are calculated on the basis of KS wave function.
What you want are the dipole moments for a given excitation weighted by the BSE eigenstate?
i.e.
for a given excitation lambda:
|\sum_cv Acv_lambda*<c|r|v>|^2

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/

sdwang
Posts: 224
Joined: Fri Apr 09, 2010 12:30 pm

### Re: Optical matrix elements

Dear Daniele,
I think you are right. Waht I need is the the dipole moments for a given excitation. For example, I want to know the dipole of the first exction in the BSE absorption. Where I can get it?

Thanks!

SD
S. D. Wang
IMU,HOHHOT,CHINA
E-mail: sdwang@imu.edu.cn

Daniele Varsano
Posts: 2660
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Shudong,

ok, correct if I've not well understood, you want to look at the intensity (oscillator strength of the excitation), so the expression I reported above, which is built as a linear combination of dipole moments weighted by the BSE eigenvector right?

This is calculated by ypp when sorting excitation and reported as intensity (o.exc_I_sorted).
In the output file, the values are normalized to the max value of the intensity, in the recent versions of yambo the max value is reported in the output as:

Code: Select all

 Maximum Residual Value=
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/

sdwang
Posts: 224
Joined: Fri Apr 09, 2010 12:30 pm

### Re: Optical matrix elements

Daniele Varsano wrote:
Tue Aug 27, 2019 12:19 pm

*Short explanation:
Read the dipole variable i<v|r|c> and <v|P|c>.
The dipole variable has 4 indexes that are:
1: Valence index from 1 to Nv (python index start from 0)
2: Conduction index from 0 to Nc (0 is the first conduction band up to the last calculated)
3: Direction 0,1,2 --> x,y,z
4. 0/1. real and imaginary part
Dear Daniele,
Just a question for sure. In the script you mentiond, 1 means the VBM, and 2 is VBM-1, 3 is CBM and 4 is CBM+1? Right?

Thanks!

Best
Shudong
S. D. Wang
IMU,HOHHOT,CHINA
E-mail: sdwang@imu.edu.cn

Daniele Varsano
Posts: 2660
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Shudong,
actually I do not know of what script you are talking about, anyway if the script it is meant to read dipoles databases,
is sound strange to me that it could be:
1 means the VBM, and 2 is VBM-1
as valence bands are ordered from the first band computed to the VBM, while for conduction the index runs from CBM to the last band computed.
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/

sdwang
Posts: 224
Joined: Fri Apr 09, 2010 12:30 pm

### Re: Optical matrix elements

Dear Daniele,
Thank you for the quick reply. Yes I mean the read dipole script.
I extend the script to include more valence and conduction bands (in current scriot is 2v+2c).
My sytem has 16 valence bands, so if I want to konw the dipole between VBM and CBM, I shoud giveit as:
print ("<16|p|17>=",DIP_P[15,0,0],DIP_P[15,0,1],DIP_P[15,0,2],sqrt(abs(DIP_P[15,0,0])**2+abs(DIP_P[15,0,1])**2+abs(DIP_P[15,0,2])**2))

Am I right?

Thanks!

Shudong
S. D. Wang
IMU,HOHHOT,CHINA
E-mail: sdwang@imu.edu.cn

Daniele Varsano
Posts: 2660
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Shudong,
yes, it seems correct.

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/

sdwang
Posts: 224
Joined: Fri Apr 09, 2010 12:30 pm

### Re: Optical matrix elements

Dear Daniele,
I got the dipole moments of 2 layer MoS2 and it is as:
Dipole P
('<52|p|53>=', (4.8576367e-05+0.00028422844j), (-0.00020457263+3.4868885e-05j), (-8.9401248e-05+1.5234437e-05j), 0.0003666550846841008)
In which the modules is 0.0003666550846841008. And I used it to compare with the μS^2(I used as 0.0003666550846841008X27.2114^2 eV to transfer it into the unit of eV,right?), which is the square modulus of the BSE exciton transition
dipole using Yambo in paper "Exciton Radiative Lifetimes in Two-Dimensional Transition Metal Dichalcogenides, Nano Lett. 2015, 15, 2794−2800". and it seems
my results here is several orders of magnitude less than the published paper. But my absoption and quasiparticle quantites are almost the same as that in the paper.
What's the problem?

Thanks!

Best wishes,

Shudong
S. D. Wang
IMU,HOHHOT,CHINA
E-mail: sdwang@imu.edu.cn