Dear Sujeeth Kumar D ,

The short answer

We (often) need to use pseudopotentials for DFT calculations because they dramatically decrease the number of plane waves we need to expand the wave function. Pseudopotentials don't give ecutrho and ecutwfc per say. These energy cutoffs are related to how many plane waves we would like to use, which depends not only on the pseudopotentials but also on the level of accuracy we would like to obtain in our DFT calculations. The higher the energy cutoff, the more accurate the calculation. The specific information we get from pseudopotential files is v_{ext} in the KS equations (https://en.wikipedia.org/wiki/Kohn%E2%80%93Sham_equations), which takes into account electron-nuclei interactions.

The long answer

Pseudopotentials are often used in conjunction with plane wave basis sets. It takes a very large number of plane waves to expand the wave functions of core electrons because they are highly oscillatory near nuclei. Pseudopotentials essentially replace the core electrons and true potential (Z/r) with a smoother, effective potential that produces atomic, valence electron wave functions with less oscillatory behavior while preserving the key features of the all-electron, atomic, valence electron wave functions such as their eigenvalues, values outside the cutoff radius (which separates the core and valence region), etc. There are many other pseudopotential optimization constraints lumped into this "etc." giving rise to a number of different pseudopotential types, e.g. norm-conserving and ultrasoft.

For an general introduction to pseudopotentials, I recommend appendix E of this book by Feliciano Giustino:

https://www.amazon.com/Materials-Modelling-Density-Functional-Theory/dp/0199662436/ref=asc_df_0199662436/?tag=hyprod-20&linkCode=df0&hvadid=312090128349&hvpos=1o1&hvnetw=g&hvrand=5502795901564709233&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003941&hvtargid=pla-524703217081&psc=1

For an introduction to norm-conserving pseudopotentials, I recommend this paper by my PhD advisor, Andrew Rappe:

Article Designed nonlocal pseudopotentials for enhanced transferability

For an introduction to ultrasoft pseudopotentials, I recommend this paper by David Vanderbilt:

Article Soft Self-Consistent Pseudopotentials in a Generalized Eigen...

I hope that this was helpful. Please let me know if you have any questions.

Best,

Rob

Dear Sujeeth Kumar D ,

The short answer

We (often) need to use pseudopotentials for DFT calculations because they dramatically decrease the number of plane waves we need to expand the wave function. Pseudopotentials don't give ecutrho and ecutwfc per say. These energy cutoffs are related to how many plane waves we would like to use, which depends not only on the pseudopotentials but also on the level of accuracy we would like to obtain in our DFT calculations. The higher the energy cutoff, the more accurate the calculation. The specific information we get from pseudopotential files is v_{ext} in the KS equations (https://en.wikipedia.org/wiki/Kohn%E2%80%93Sham_equations), which takes into account electron-nuclei interactions.

The long answer

Pseudopotentials are often used in conjunction with plane wave basis sets. It takes a very large number of plane waves to expand the wave functions of core electrons because they are highly oscillatory near nuclei. Pseudopotentials essentially replace the core electrons and true potential (Z/r) with a smoother, effective potential that produces atomic, valence electron wave functions with less oscillatory behavior while preserving the key features of the all-electron, atomic, valence electron wave functions such as their eigenvalues, values outside the cutoff radius (which separates the core and valence region), etc. There are many other pseudopotential optimization constraints lumped into this "etc." giving rise to a number of different pseudopotential types, e.g. norm-conserving and ultrasoft.

For an general introduction to pseudopotentials, I recommend appendix E of this book by Feliciano Giustino:

https://www.amazon.com/Materials-Modelling-Density-Functional-Theory/dp/0199662436/ref=asc_df_0199662436/?tag=hyprod-20&linkCode=df0&hvadid=312090128349&hvpos=1o1&hvnetw=g&hvrand=5502795901564709233&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003941&hvtargid=pla-524703217081&psc=1

For an introduction to norm-conserving pseudopotentials, I recommend this paper by my PhD advisor, Andrew Rappe:

Article Designed nonlocal pseudopotentials for enhanced transferability

For an introduction to ultrasoft pseudopotentials, I recommend this paper by David Vanderbilt:

Article Soft Self-Consistent Pseudopotentials in a Generalized Eigen...

I hope that this was helpful. Please let me know if you have any questions.

Best,

Rob

Thank you so much for your valuable answer as well for articles.

Dear Suujeeth,

Theoretically pseudopotentials and density functional theory are two completely different things. Density functional theory is a popular way to cope with many particle effects, particularly exchange-correlation phenomena. This approach is still not completely understood, but there are a lot of practical schemes, yielding usable answers. Used properly a true density functional requires all of the charge distribution.

The pseudopotential method is an approximate technique to reduce the numerical effort to determine the energies and wave functions, by neglecting cleverly the bound states, necessary to account for the singularity caused by the nuclei. Since the pseudopotential technique is an approximate one, it ignores a large part of the total charge density.

For practical reasons the two methods you mention and want to combine, are popular to do practical calculations. Unavoidably you have to make errors to do so, but for many problems this is acceptable. It simply depends on the type of problem you are working on.

C.M.J. Wijers whilst I agree with much of what you say, it isn't true that the pseudopotential technique "ignores a large part of the total charge density". The core states are treated with the same density functional as the valence states, and the non-linear exchange-correlation interaction between the core and valence states is also treated properly. Indeed, the properties of the core states may be recovered with a type-1 PAW reconstruction, which is how core-level spectra are typically modelled. Of course there are approximations involved, principally the "frozen core approximation", but the core density is treated properly within that framework.