# When should I include semi-core electrons in DFT calculations?

Many DFT codes use pseudopotentials (for the core electrons) and basis set functions (for the valence electrons) in order to solve the Schrodinger equation. This because simulates each electron wavefunction is very costly.

I found works where the authors generate the pseudopotentials dividing the core electrons in electrons from the inner core and electrons for the external core (called semi-core). These semi-core electrons were also considered as "valence" electrons.

When should I include semi-core electrons in DFT calculations?

• Could you be more specific about your question in the main body? Could you cite some of the papers you mentioned using semi-core electrons? May 1, 2020 at 2:06

I am quoting from the book Materials Modelling Using Density Functional Theory: Properties and Predictions by Feliciano Giustino

How do we decide which wavefunctions should be considered ‘core’ and which ones ‘valence’ states? As a rule of thumb, in the context of DFT calculations the ‘valence’ corresponds to the outermost shell of the atom in the periodic table; for example, for tungsten we would have 6s25d4. However, there are cases where one might need to include more electronic states in the set of ‘valence electrons’. For example, in the case of bismuth it is important to describe on an equal footing both the nominal valence shell, 6s26p3 , and the ‘semi-core’ shell, 5d10. In practice the distinction between core and valence is not a strict one, and depends on the level of accuracy that one is trying to achieve. When in doubt, an inspection of the spatial extent of all the atomic wavefunctions represents the first point of call for identifying core and valence states.

Many DFT codes use pseudopotentials (for the core electrons) and basis set functions (for the valence electrons) in order to solve the Schrodinger equation. This because simulates each electron wavefunction is very costly.

The key of KS-DFT is to solve the Kohn-Sham equation. Basically, there are four main classifications in terms of the used basis. You may take a look at this post:When are atomic-orbital-basis (rather than plane-wave) methods appropriate in periodic DFT?. In general, the electrons are partitioned into core and valence electrons and the core electrons are treated with pseudopotential method only when you use the plane-wave basis. The reason is that the wavefunction of the core electrons are oscillating strongly and there are many nodes closed to nuclei, which means you should use many plane waves to expand it and hence lead to prohibitive computational cost.

When should I include semi-core electrons in DFT calculations?

This assumes that you are using a plane-wave type Kohn-Sham solver, such as VASP, in which the partition of valence and core electrons is decided when generating pseudopotential. There are two situations you need to include semi-core electrons (maybe I am missing some situations):

• If you want to study the spectral properties of core electrons, you should use the pseudopotential with the inclusion of semi-core electrons.

• If you want to perform GW calculations, you will use the pseudopotential with semi-core electrons.

Hope it helps.

• You don't need plane-waves to use pseudopotentials; similar guidelines also apply to several real space grid codes like GPAW. Feb 22, 2021 at 16:31
• @SusiLehtola If you use the plane-wave basis, then you must use pseudopotentials. That's my point.
– Jack
Feb 23, 2021 at 0:21

You are making an approximation by including the semicore states in the pseudopotential. Like the name suggests, semicore states aren't really core states; they lie higher up in energy so they may not always be spectators.

To decide whether to include the semicore states, you should compare the results of calculations with and without the semicore states in the valence. If both procedures lead to the same result, this means the semicore states don't play an important role in your study. If including the semicore states changes the results, it means that you should include them in the calculation, since the frozen-core approximation does not hold for them.