Calculating probability exciton is in a specific region
Moderators: Davide Sangalli, andrea marini, Daniele Varsano

 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
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
University of Cambridge
 Daniele Varsano
 Posts: 2719
 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
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
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 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
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
University of Cambridge
 Daniele Varsano
 Posts: 2719
 Joined: Tue Mar 17, 2009 2:23 pm
 Contact:
Re: Calculating probability exciton is in a specific region
Dear Alan,
in your ypp.in file set:
Best,
Daniele
in your ypp.in file set:
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
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 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
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
University of Cambridge
 Daniele Varsano
 Posts: 2719
 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
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
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 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
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
University of Cambridge
 Daniele Varsano
 Posts: 2719
 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_onebefore this line:
About the new release, I cannot tell you a precise date, but it should happen before the end of the year.
Best,
Daniele
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.
Code: Select all
102 if (l_norm_to_one) v2plot2D=v2plot2D/v_max
Best,
Daniele
Dr. Daniele Varsano
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/

 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
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
University of Cambridge
 Daniele Varsano
 Posts: 2719
 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
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
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/
S3CNR Institute of Nanoscience and MaX Center, Italy
MaX  Materials design at the Exascale
http://www.nano.cnr.it
http://www.maxcentre.eu/