## Coulomb matrix elements in the wanner function basis set

Run-time issues concerning Yambo that are not covered in the above forums.

Moderators: Daniele Varsano, andrea marini, Conor Hogan, myrta gruning

### Coulomb matrix elements in the wanner function basis set

Dear Yambo Developers,
I am parameterizing a tight-binding hamiltonian. The system is a polymer on top of graphene.
I did the electronic structure with QuantumEspresso and I interpolated the band structure with Wannier90.
I have the 1-body part of the Hamiltonian in the Wannier basis set, namely <i|H|j> where i and j are Wannier Functions.
I also have the WannierFunctions in real space.

Now, I want to include the 2-body part of the Hamiltonian to get parameters concerning the exciton (e.g. binding energy).
So, I would like to calculate with Yambo the four center integrals in the Wannier basis set: <i j|e^2/r| k l> where i,j,k,l are WannierFunctions.
The important point here is that the coulomb matrix elements must be in the Wannier function basis set.

Is there an easy way to do that with Yambo?
I don't mind to modify the code to get the matrix elements that I need.

Angelo Ziletti
--------------------------------
angelo.ziletti@gmail.com
Phd candidate
School of Physics
UCD - University College Dublin
ziletti

Posts: 2
Joined: Tue Oct 09, 2012 9:12 am

### Re: Coulomb matrix elements in the wanner function basis set

Dear Angelo,

you can make Yambo print the matrix elements of the screened interaction writte in the Kohn-Sham k-basis. Then, by knowing the coefficients of the expansion of the Wannier states in extended states you should be able to recosntruct the matrix elements you need.

Do you thik this is enough ? In this case I can tell you where to look for these state.

You could even make Yambo to calculate the matrix elements in the Wannier basis.

Andrea
Andrea MARINI
Istituto di Struttura della Materia, CNR, (Italy)

andrea marini

Posts: 447
Joined: Mon Mar 16, 2009 4:27 pm

### Re: Coulomb matrix elements in the wanner function basis set

Dear Andrea,

I think that the best solution for me would be to calculate directly the screened matrix elements in the Wannier functions basis.
However, I don't know how complicated it is to implement this procedure in Yambo.

If it is very complicated, I can use the matrix elements in the Kohn-Sham basis and apply a unitary transformation to get the matrix elements in the Wannier functions basis.

So, I have 2 questions:
1) how can I calculate the screened matrix elements in the Wannier functions basis?
2) how can I print the screened matrix elements in the Kohn-Sham basis?

Best,
Angelo Ziletti
-------------------------------
angelo.ziletti@gmail.com
Phd Candidate
School of Physics
UCD - University College Dublin
Ireland
ziletti

Posts: 2
Joined: Tue Oct 09, 2012 9:12 am