Dear Tian,
Too many thanks for your kind attention to guide me with your perfect and very valuable comments.

Sincerely,
Saeed

Goto https://www.tc.uni-koeln.de/PP/clickpse.en.html. If for an element there are two PP core-sizes, then usually they should be regarded as small and large-core versions. If there are three, then they may respectively correspond to small, medium and large versions. You can easily guess the shells represented by PP according to the total number of electrons replaced with PP and shell structures of elements.

As an example, from the website you can find there are ECP28MDF and ECP10MDF for Br, the former is large core, the corresponding PP basis set explicitly represents valence electrons of 4s, 4p; the latter is small core, the outermost valence electrons (4s, 4p) and subvalence electrons (3s, 3p, 3d) are explicitly represented.

Thank you very much.
Could you also please let me know your comments on 1?

See review of SAPT DOI: 10.1002/wcms.1452 and references cited in it.

Dear Tian,

1- Many many thanks for the kindness you always kindly gift me making me guide with so valuable comments.
In addition to your valuable comments, please let me know if you know a detailed and evident reference regarding this topic. It seems I should pay much more attention to this issue and, thus, I am looking for the straightforward and complete lecture/text book/etc by which one gets understanding how the small-, medium-, or large-core shell is defined and regarded to an element.

2- It seems the results of DFT-SAPT are not so sensitive to the precision of "grac_shift" value. Do you agree?

3- I would be highly grateful if you introduce me a good lecture/tutorial in which asymptotically behaviour of DFT-SAPT functional  is graphically presented (2-D plot of energy vs. distance or something like this) and shows how the "grac_shift" quantity corrects such behaviour (mathematical equations). Previously, I have had such a nice reference but, unfortunately, I cannot find that right now.

Please, in advance, accept my highest apology for taking your so valuable time.

Sincerely,
Saeed

Usually, if only the electrons in the outer-most shell is considered, it is large core. While if subvalence electrons are also considered, it is small or medium core. If there is a medium core version of a PP, then small core referes to the case that only electrons of inner-most core shells are represented by PP.

You can simply take as much as decimal places as possible, at least there's no harm in that.

Dear Tian,

When a given atom uses PP basis set, Gaussian takes a specific number of electrons as core electrons. For instance, using aug-cc-pVDZ(+PP) basis set for Iodine atom, Gaussian indicates that 25 electrons out of total 53 electrons are taken as valence electron for Iodine. In consequence, 53-25=28 and, one can conclude that the number of core electrons in Iodine approximated by a PP basis set is 28. The question (which is in my mind for a long time) is that this 28 electron should be regarded as small-core, medium-core, or large-core? Commonly, after computing the number of core-electrons as shown for Iodine, how one reliably should identify small-, medium-, or large-core size regarding the core electrons in a desirable atom?

Moreover, please also let me know how much a given "grac_shift" value in the DFT-SAP should be accurate. Indeed, while some researchers consider only two digits after the decimal point (XX.YY), other ones take 4-5 digits after the decimal point (XX.YYYY or XX.YYYYY) for a given "grac_shift" value.

In advance, many thanks for your kind attention and highly valuable guidance.

Sincerely,
Saeed