# Very low frequency optical response calculation

Hello all,

I am trying to calculate the optical response at very low frequencies using ABINIT, and the photon frequency of interest is around 10 GHz, which is about 1.5e-6 Ha of energy. I noticed that this is well below the example in the optic tutorial (broadening, domega, maxomega and tolerance are set to the appropriate order of magnitude).

The optic job can still be completed, but it gives a result that is essentially a horizontal line (linear response function). I tried to calculate it over a wider energy range (~1 Ha) and it looks like its overall characteristics are close to the experimental results, and in the region where the energy is close to 0, it is also close to the horizontal line mentioned above.

What I want to know is whether this is because the optical response function is inherently closer to a constant in the low-frequency region, or whether some numerical accuracy limitation causes the possible characteristics on such a fine energy scale to be smoothed out?

Hi Iavas,

10GHz is super low frequency, below even IR or certainly optical ranges.

• Optic only considers electronic transitions → optical spectroscopy
• IR+Raman modes are vibrational so follow the DFPT tutorials to get that range (THz typically).
• Depending what features you want at 10GHz they may be accessible from DFT, or not. This might be rotational excitations, or slow magnetic or other modes. Don’t know really, but you have to have the right theory for the physics you want to reproduce.

Matthieu

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Hi Matthieu,

I am interested in the dielectric function of a semiconductor in this frequency range. DFPT provides a method for calculating the dielectric constant of an insulator, but I am not sure if the dielectric function of a semiconductor in such a low-frequency range will behave like a constant or still show some peaks and valleys.

Hi @iavas, the optic utility uses the “sum-over-states” approach to compute the optical response (see eq. 46 of this paper). In this formalism, in order to get a non-zero response at a given frequency \omega, you need to have two states (1 occupied and 1 inoccupied such that f_{mn}\neq 0) whose difference in energy \omega_{nm} is close to \omega (otherwise the denominator \omega_{mn}-\omega can kill any optical response from those states). In a semi-conductor, if \omega is well below the gap, your response will be very close to 0 by definition for the imaginary part and a constant for the real part. Note that 10GHz << 1meV therefore, you’d need a semi-conductor with super small gap to see any interesting structures at that scale.

Hello @fgoudreault thanks for your explanation. I just get some measurements and it looks like it does behave close to a constant in this frequency range, much higher frequencies are required to produce frequency-dependent behavior.