Absorption spectrum and exciton strengths

[yunho.ahn]

Dear Yambo community,

I've been calculating the optical spectrum of an organic charge transfer complex materials using GW-BSE by following tutorials.
I wanted to overlay the exciton strengths onto the calculated absorption spectrum to present individual exciton contributions shape the absorption spectrum.

One thing that I'm confused is that, as far as I understand, the exciton strength is the linear combination of the square of the dipole transition matrix elements between electron-hole pairs and the imaginary part of the dielectric function is derived from them, shouldn't the exciton strength be equal to or less than the imaginary part of epsilon? even though it's normalized.

But I got the exciton strength, which is larger than the corresponding imaginary epsilon (especially the first one). Could you help me understand why this might be the case?

Thank you in advance for your insights.

Best,
Yunho

[Daniele Varsano]

Dear Yunho,

One thing that I'm confused is that, as far as I understand, the exciton strength is the linear combination of the square of the dipole transition matrix elements between electron-hole pairs and the imaginary part of the dielectric function is derived from them

Correct! the dipoles are weighted with the corresponding BSE eigenvectors.

But I got the exciton strength, which is larger than the corresponding imaginary epsilon (especially the first one). Could you help me understand why this might be the case?

Please note the following:
1. The strength is the area beneath each peak of Im(eps) and not its height. The eps is obtained as convolution of Lorentzian function centered on each excitation, its intensity depends on the adopted smearing (broadening).

2. The strength in the output are normalized such that the largest value assumes the value 1. (The renormalization is reported in the exc file (Maximum Residual Value).

Best,

Daniele

[yunho.ahn]

Dear Daniele,

Thank you very much, now it's very clear for me!
I have more questions about the analysis (sorry for many questions.. this calculation is quite new for me..)

After calculating the optical spectra, I started to analyse the first exciton, as the strength is large. So I obtained 'o-3D_QP_298-360_BSE.exc_qpt1_weights_at_1' and 'o-3D_QP_298-360_BSE.exc_qpt1_amplitude_at_1'.

In 'o-3D_QP_298-360_BSE.exc_qpt1_weights_at_1', there are two transitions from 318 (VBM) to 320 and from 318 to 319 (CBM).

Q1.
For each transition, the corresponding Kv-q ibz and Kc q ibz span all four available k-points (QPkrange is from 1 to 4), so could I say this is a 'Charge-transfer exciton' rather than a 'Frenkel exciton'? And is this what is visualized by 'ypp_WF.in', right..? (as the spatial distribution of the exciton)

Q2.
How to calculate compositions? For example, in 'o-3D_QP_298-360_BSE.exc_qpt1_weights_at_1', the sum of weights of 318-320 transition is 0.553, so is it 55.3 %? and the oscillator strength for the whole exciton is the values obtained in 'o-3D_QP_298-360_BSE.exc_qpt1_E_sorted', right?
Because I'd like to tabulate each exciton in terms of: 'Excitation energy', 'Oscillator strength', and 'composition'...

Q3.
What does the last column of 'Energy [eV]' refer to in 'o-3D_QP_298-360_BSE.exc_qpt1_weights_at_1 ? And I'm also wondering how to interpret 'o-3D_QP_298-360_BSE.exc_qpt1_amplitude_at_1' file... so this presents the energies of the single-particle transitions.. but why are they lower than the exciton energies..?

I also attached the files..

Best regards,
Yunho