Your very nice and informative comments are highly appreciated. Please let me say that, at least, in the current project I am studying the IBSI values based on the IGMH (rather than the promolecular approach) have a better and more satisfying correlation with the interaction strength and also these values are all below 0.15 indicating non-covalent interactions in the systems considered, in complete agreement with values of Rho at BCPs.

Sincerely yours,
Saeed

1 Usually this is correct

2 Please note that IBSI implementation in Multiwfn is somewhat different to the IBSI original paper. I suggest calculating some systems to confirm this point.

Best,

Tian

Based on this fact that our given inter-fragment interaction is covalent (very strong) or non-covalent (weak), one should pay attention to, respectively, sobEDA or sobEDAW. It seems there are two nice ways to characterize the interaction type: 1) Computing value of Rho at the BCP of interaction. In this sense, a Rho value less that 0.1 a.u. reveals a non-covalent interaction while a value greater than 0.2 a.u. specifies  a covalent interaction; 2) computing value of IBSI index (loading .wfn or. chk file-->9--->10--->1--->4) between two interacting atoms. An IBSI value below 0.15 and greater than 0.15 characterizes a non-covalent and covalent interaction, respectively (based on the scale proposed by the authors of IBSI original paper).
If possible, please let me know whether my statements are correct or please correct my probable mistakes.

Sincerely,
Saeed