Getting good exciton binding energy from bad band gap

[xueshanxihua]

Dear all,

I'm calculating the absorption spectrum of CuCl with Yambo.

The band gap of CuCl observed in experiments is about 3.4 eV, but PBE only gives Eg~0.6 eV, this is of course entirely normal for DFT. To build the BSE Hamiltonian, I used scissor operator ΔE=2.8 eV to mimic the "real" quasiparticle transitions, and calculated the static screened Coulomb potential W from PBE band structure. However, after diagonalizing BSE Hamiltonian, surprisingly I find the exciton binding energy to be 130 meV, very similar to its experimental value 190 meV.

Although it's a good news to obtain comparable result against experiments, I'm still puzzled that why we can get such "good" binding energy with the screened potential calculated from such "bad" electronic structure. I.e., the PBE band gap is one order of magnitude smaller than the experimental value, but the exciton binding energy obtained from PBE screened potential is rather similar with the experimental value.

So, I want to know whether the such kind of results are reasonable. Also, how can we understand the good performance of PBE in calculating binding energy, or is it just a coincidence in CuCl ?



Thank you,

[Daniele Varsano]

Dear Zeyu,
what you did it is the standard way when doing GW/BSE at first iteration of Hedin equation.
More explicitly, Sigma=GoWo where W is calculated by using DFT energies and wavefucntions. Next the BSE kernel is built by using the screening at the same level (i.e. DFT energies).
In your case, you did not calculate the quasi-particle correction but you have considered a scissor operator.
By the way, if you want to check the impact of the gap in the calculation of the screening for the binding energy you can consider to add the same scissor also in W (this is what is usually called eigenvalue self-consistent GW) where the qp equation is iterated updating the qp energies both in G and W and then the BSE is calculated by considering the screening with the converged QP energies.
In Yambo, this can be taken into account by adding a scissor also in W.
You can do that by adding in your input file the variable:

Code: Select all

% XfnQP_E
 0.000000 | 1.000000 | 1.000000 |        # [EXTQP Xd] E parameters  (c/v) eV|adim|adim
%

similarly on what you did with KfnQP_E (scissor for the BSE kernel).

Best,
Daniele

[xueshanxihua]

Dear Zeyu,
what you did it is the standard way when doing GW/BSE at first iteration of Hedin equation.
More explicitly, Sigma=GoWo where W is calculated by using DFT energies and wavefucntions. Next the BSE kernel is built by using the screening at the same level (i.e. DFT energies).
In your case, you did not calculate the quasi-particle correction but you have considered a scissor operator.
By the way, if you want to check the impact of the gap in the calculation of the screening for the binding energy you can consider to add the same scissor also in W (this is what is usually called eigenvalue self-consistent GW) where the qp equation is iterated updating the qp energies both in G and W and then the BSE is calculated by considering the screening with the converged QP energies.
In Yambo, this can be taken into account by adding a scissor also in W.
You can do that by adding in your input file the variable:

Code: Select all

% XfnQP_E
 0.000000 | 1.000000 | 1.000000 |        # [EXTQP Xd] E parameters  (c/v) eV|adim|adim
%

similarly on what you did with KfnQP_E (scissor for the BSE kernel).

Best,
Daniele

Dear Daniele,

Really appreciate your quick reply and suggestions, so it seems I need more tests to find the best approach describing this system.

Actually, what I really wonder about is why the large underestimation of band gap is not reflected in the binding energy. But anyway, I think it's not something that can never happen, is it ?