## Calculating probability exciton is in a specific region

Anything regarding the post-processing utility (e.g. excitonic wavefunction analysis) is dealt with in this forum.

Moderators: Davide Sangalli, andrea marini, Daniele Varsano

arb83@cam.ac.uk
Posts: 98
Joined: Thu Jul 02, 2020 3:56 pm

### Calculating probability exciton is in a specific region

Dear Yambo Community Forum

Is it possible to calculate the probability the exciton is in a specific region of the unit cell? i.e. \int_{region}\Xsi(r_{elec},r_{hole})^{2}dr_{elec}dr_{hole}/ \int_{full unit cell}\Xsi(r_{elec},r_{hole})^{2}dr_{elec}dr_{hole}?

With best wishes,

Alan
Alan Bowman
University of Cambridge

Daniele Varsano
Posts: 2997
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Calculating probability exciton is in a specific region

Dear Alan,
this quantity is not implemented, but you can do by yourself with an external code by reading the excitonic wave functions e.g. asking them in cube format.

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/

arb83@cam.ac.uk
Posts: 98
Joined: Thu Jul 02, 2020 3:56 pm

### Re: Calculating probability exciton is in a specific region

Dear Daniele

This may be very obvious, but how do I output the full excitonic wavefunction in a cube format? I'm currently only aware of how to output part of the wavefunction with the electron or hole in a fixed position.

With best wishes,

Alan
Alan Bowman
University of Cambridge

Daniele Varsano
Posts: 2997
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Calculating probability exciton is in a specific region

Dear Alan,

Code: Select all

Format= "c"                  # Output format [(c)ube/(g)nuplot/(x)crysden]
Direction= "123"              # [rlu] [1/2/3] for 1d or [12/13/23] for 2d [123] for 3D
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/

arb83@cam.ac.uk
Posts: 98
Joined: Thu Jul 02, 2020 3:56 pm

### Re: Calculating probability exciton is in a specific region

Dear Daniele

Within the ypp file I still need to set the hole position. Therefore, am I not outputting the electron wavefunction given that the hole is in a specific position? i.e. I would still need to know the probability of the hole at each position to reproduce the value I am interested in?

All the best,

Alan
Alan Bowman
University of Cambridge

Daniele Varsano
Posts: 2997
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Calculating probability exciton is in a specific region

Sorry,
I did not get it.
So, no it is not implemented.
What has been recently implemented is the average Psi_exc over the position of the hole (or electron)
\rho_e (r_e) = \int | \psi (r_e, r_h) |^2 d r_h

but this is not in the GPL release (it will be in the next release).
What you aim to do is to collect a 6 variable function and integrate over space, it could be done but it is quite cubersome.
Note that the integral the whole space you indicated should be 1 by normalization condition.

Anyway, maybe you can consider the freehole option which is now implemented defined as:
\Psi_exc(re,rh=re)
essentially it is a transition density.

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/

arb83@cam.ac.uk
Posts: 98
Joined: Thu Jul 02, 2020 3:56 pm

### Re: Calculating probability exciton is in a specific region

Dear Daniele

That makes sense, thanks for the clarification. When will the next GPL release be coming out?

In the meantime I realised that I could plot the exciton distribution in 1D as I am only interested in where it is likely to be in the z direction. When I do this with the hole fixed in one position, could you confirm that the output is normalised please? Is there any way to change this (i.e. so I can get something resembling actual probability values)?

All the best,

Alan
Alan Bowman
University of Cambridge

Daniele Varsano
Posts: 2997
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Calculating probability exciton is in a specific region

Dear Alan,
yes, it should be normalized to the maximum value, i.e. max(wf)=1.
If you do not want this normalization, for the 1D plot, you can change the value of the flag in this subroutine:
/ypp/plotting/plot_gnuplot.F
assigning the l_norm_to_one

Code: Select all

l_norm_to_one=.false.

before this line:

Code: Select all

102      if (l_norm_to_one) v2plot2D=v2plot2D/v_max
About the new release, I cannot tell you a precise date, but it should happen before the end of the year.
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/

arb83@cam.ac.uk
Posts: 98
Joined: Thu Jul 02, 2020 3:56 pm

### Re: Calculating probability exciton is in a specific region

Dear Daniele

Thank you! One final question - when I remove the normalisation, what are the output values. Is this the sqrt of the probability density, the probability density, or the probability density divided by the probability the hole is in that fixed position?

All the best,

Alan
Alan Bowman
University of Cambridge

Daniele Varsano
Posts: 2997
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Calculating probability exciton is in a specific region

Dear Alan,
it is a conditional probability: the probability to find an electron given the hole fixed in the position you placed it.

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/