Linear interpolation of q-depedent dielectric function

[Ehsanulazim]

Hi,

In metallic systems, accurately computing optical properties—such as the dielectric function—often requires a dense sampling of q-points within the Brillouin zone. In my current work on bulk gold, I performed a DFT calculation in Quantum ESPRESSO using 6859 k-points, and subsequently used Yambo to obtain q-dependent dielectric functions based on these k-points.

I’m aware that Yambo offers an advanced technique known as the double-grid method, which allows for much denser q-point grid. However, in my case, applying the double-grid approach to bulk gold has not produced satisfactory results.

This led me to consider a different possibility: Since I already have the dielectric function data corresponding to 6859 q-points, would it be feasible to linearly interpolate this dataset in order to estimate the dielectric function at, say, 9000 k-points? In other words, could interpolation be used to approximate dielectric functions at additional k-points that weren’t included in the original DFT calculation?

I realize this idea might be unconventional or possibly naive, as I am still developing my understanding of DFT and many-body perturbation theory. Nonetheless, I would appreciate your opinion on whether such interpolation could be meaningful or physically justified.

Thank you for your time.


Best Regards
Ehsanul Azim
Masters student, Mechanical Engineering
University of Texas Rio Grande Valley (UTRGV)

[Daniele Varsano]

Dear Ehsanul,
yes, it makes sense. Anyway, from your post it is not clear at what level of theory you are calculating the dielectric function and if you need the macroscopic (G=G'=0) term (spectrum) or the complete GG' matrix.
If you are considering RPA level and only the macroscopic function is needed it is important you include a Drude term in the q=0 response, while for all the other q points intraband contribution are already included in the calculations.
If what you need it is just more resolution, interpolation should work properly.

If you are interested in GW corrections, you may have a look at this paper: https://journals.aps.org/prb/abstract/1 ... 107.155130
Here, some useful approximations are described.

We have implemented a new fully ab initio technique for dealing with metals including Drude term in an ab initio way, this is not yet available, but a paper will be published soon, and the method will be then released.

Best,

Daniele

[Ehsanulazim]

Hi Professor,

Thank you so much for your response.

To clarify, I am working within the framework of linear response theory under the Independent Particle Approximation (IPA). In my study, I require the dielectric function at both q → 0 and finite q-points, as the theoretical model I’m working on demands a dense sampling of q-dependent dielectric functions.

For bulk gold (Au), I am currently using a 3×3×3 supercell, resulting in 6,859 q-points. However, for improved resolution and integration accuracy, I need dielectric function data for more than 20,000 q-points. My energy range of interest spans from 0 to 2 eV, meaning that for each q-point, I need both the real and imaginary parts of the dielectric function within that energy window.

This leads me to a conceptual question: if linear interpolation could be applied reliably, why do we resort to more advanced and computationally intensive methods such as the double-grid technique? As I understand, Yambo extracts q-dependent dielectric functions using wavefunction data from Quantum ESPRESSO at each q-point. But instead of repeating such calculations, could wensimply interpolate the dielectric functions from the available data?

Thank you once again for your time and guidance.

Best Regards
Ehsanul Azim
Masters student, Mechanical Engineering
University of Texas Rio Grande Valley (UTRGV)

[Daniele Varsano]

Dear Ehsanul,

double grid method has been introduced to spped BSE calculations, see e.g.: D. Kammerlander, S. Botti, MAL Marques, A. Marini, C. Attaccalite
Physical Review B 86 (12), 125203 (2013)

Best,
Daniele