Dear Tian,
I performed calculations based on your instruction.
Interestingly, there is not any significant difference between two values. Indeed, whether employing the approach I described in "My answer is:" or using "user-defined function #91", the values generated for d_g(IGMH,inter) are identical up to 5 decimal places.

Once again, too many thanks for your kind attention.

Sincerely,
Saeed

Dear Tian,
Too many thanks for your kind attention to prompt reply with highly valuable and informative comments.
I will download the newest version and perform according to your nice instruction.

Sincerely,
Saeed

The method described in #3 is the most rigorous way of evaluating delta_g(IGMH,inter) without any approximation, please use it.

I have updated Multiwfn 3.8(dev) on Multiwfn website today, now Delta_g(IGMH,inter) has been added as 91th user-defined function. To obtain this quantity at BCP, you should:

(1) Set "iuserfunc" in settings.ini to 91.
(2) After loading input file into Multiwfn, enter main function 1000 (a hidden function), select option 16 to define two fragments.
(3) Use topology analysis module to find BCPs as usual.
(4) Use option 7 in topology analysis module to check properties of CPs of interest, the printed "user-defined function" is just the delta_g(IGMH,inter) between the two fragments.

Dear Tian,
My answer is:
When we deal with a BCP associated with a non-covalent interaction, the contribution of intramolecular interactions can safely be ignored and, thus, the computed d_g(IGMH) at such a BCP can totally be related to the intermolecular contribution; d_g(IGMH, inter). Are you agree with my statement?

Sincerely,
Saeed

Dear Tian,

Please, if possible, kindly let me know what is the easiest way to compute exact value of Delta_g(IGMH,inter) at the BCP of an NCI between two interacting fragment using Multiwfn?

In advance, too many thanks for your kind attention.

Sincerely,
Saeed