It may be not new for the community so I believe I will get a quick response on my query.
It is know that for some CDW systems, say some TMDs the phonon softening can be removed by using a large smearing value.
I have seen many papers using degauss=0.02 and with that value, there is an acoustic branch which softens which indicates CDW instability in the system. Could someone explain

Why the instability disappears with large smearing value? Is there a direct relation between CDW and smearing?

Does phonon-softening always represent CDW instability or this is specific to some TMDs?

What is safe value of degauss that someone could use?

Does the smearing value affect the superconducting properties, say Tc and SC gap?

Hoping for a quick reply. Don't need to answer all of them. Anyone could answer any of the questions.
Thank you
Shubham

Except for the last question, I will answer the questions quickly as they are less relevant to EPW.

Q: Why the instability disappears with large smearing value? Is there a direct relation between CDW and smearing?
A: To account for instability stemming from CDW in calculations, reproducing the Fermi surface with high resolution might be necessary. Although the smearing mentioned here is different from smearing in momentum space, applying energy smearing could result in the loss of crucial information, such as the Fermi surface's shape. Some studies suggest a connection between CDW and the nesting of the Fermi surface, though this remains a topic open to debate. Nevertheless, there's a possibility for conditions to inadvertently eliminate instability. It's crucial not to neglect ensuring reliable computational results through convergence tests. The threshold for convergence testing varies depending on what you want to calculate lastly. If softening occurs, there may also be a need to calculate phonon frequencies during the testing phase.

Q: Does phonon-softening always represent CDW instability or this is specific to some TMDs?
A: No. The cause of phonon instability may be other than CDW instability.

Q: What is safe value of degauss that someone could use?
A: All input parameters vary depending on what you want to calculate lastly, so there are no such things as 'safe' values. For instance, if you want to describe phenomena that occur only at low temperatures, you will often need a high-resolution momentum sampling. It's necessary to set appropriate smearing for each momentum sampling. Generally, the higher the resolution of the momentum sampling, the lower the required smearing value.

Q: Does the smearing value affect the superconducting properties, say Tc and SC gap?
A: Yes, it can affect the superconducting properties. It's possible that phonon frequencies with strong electron-phonon interactions are sensitive to the smearing value. In such cases, it's necessary to carefully verify convergence.

Thank you so much for the detailed explanation. I would like to mention that my ultimate goal is to calculate Tc. And I checked with different smearing values (degauss) in QE calculations (phonon calculations) results into different Tc in NbSe2. I think this is because there is phonon-softening and there are imaginary frequencies present in the phonon spectra for this particular system. So, I want to know how one could say that we use a larger smearing value, avoid the phonon smearing, and calculate the Tc. Is that a correct practice? This practice has been used in the following Refs.:
1. PHYSICAL REVIEW B 99, 161119(R) (2019),
2. S. Das et al. https://doi.org/10.1038/s41524-023-01017-4

I want to know for this particular example (NbSe2) only. Is increasing degauss is the correct approach to evaluate appropriate Tc?

When conducting DFT calculations, the fundamental premise, in my opinion, is to model electronic systems at absolute zero temperature since DFT is primarily a formalism for describing the ground state. If you adhere to this principle, smearing should be regarded as a parameter associated with convergence. However, in certain scenarios, such as when attempting to simulate systems at elevated electron temperatures, one may opt for the Fermi-Dirac occupation function for smearing. Analogously, if you accept that using a large smearing artificially simulates the occupation at a non-zero temperature, using it to eliminate imaginary modes may seem reasonable. Nonetheless, you should clearly understand that the disappearance of imaginary modes stems from a different logic than finite-temperature phonon calculations that take into account anharmonic effects, which are actively developed nowadays.

Personally, I have not utilized the Fermi-Dirac distribution function for smearing in pw.x for phonon calculations. While I can appreciate its use as an approximation, I don't regard it as a generally applicable approach. It's just a practical workaround for CDW. If you choose to employ a large smearing to eliminate imaginary modes in TiSe2, please do so at your own discretion and risk. Particularly when writing a paper, it might be necessary to justify the obtained results by comparing them with the results published in previous studies.