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Dear friends,

Recently I did some Raman spectrum calculations. In the result analyses, I strongly feel that the Raman intensity in my systems is closely related to the band gap. Actually, early work [Physica C 341, 2267 (2000) and J. Phys. Chem. B 110, 12860 (2006)] has suggested similar trend.

Right now, I hope to figure out (based on ab initio calculation) which bands contribute most to the 1st-order change of dielectric susceptibility tensor. (maybe some kind of finite difference calculation). Could you enlighten me?

Sincerely,
Guangfu Luo

Dear friends,

I think I find out the solution. To relate the Raman intensity to band structure, we can turn to the other first-principles way of calculating dielectric function: the sum-over-states or band-to-band-transition method.

The dielectric function at zero frequency, epsilon(0), by sum-over-states is equal to the clamped-ion dielectric function by using DFPT [if the local field effects are not crucial]. Specifically, epsilon(0), which equals the real part of epsilon at zero frequency, is related to the imaginary part of epsilon (Im-epsilon)through the Kramers-Kronig formula, and the contribution of Im-epsilon decreases with 1/omega. Therefore, generally epsilon(0) is dominated by the first local maximum of Im-epsilon, which is directly related to the band gap.

I did several finite atomic displacement tests and confirmed the consistence between results by using the DFPT and sum-over-sates approaches.

Sincerely,
Guangfu Luo