You can combine some methods into getting a weak interactions.

I use Natural Bonding Orbitals theory to calculate this interactions, with emphasis in Wiberg Indexes (knowing also that a weak interaction is below 0.1 and a hydrogen bond is below 0.3) and also topological analysis using Non Covalent Interactions. With this you can analyze and have an idea if you have a weak or a strong interaction between molecules, or even intramolecular ones.

I don't suggest using bond order to study typical weak interactions, except for the rare cases that covalent interaction play significant role, such as very short, strong H-bonds.

There are numerous better ways of characterizing weak interactions than bond order, for example, AIM analysis, NCI analysis, electrostatic potential analysis, vdW surface penetration analysis, energy decomposition analysis and so on, most of them are supported by Multiwfn. If you have interest, you may consult the brief review in Section 4.A.5 of Multiwfn program manual (http://sobereva.com/multiwfn)

Thank you very much for your guidance. I've already performed NCI analysis, but I couldn't identify whether the "green regions" are weakly attractive or weakly repulsive. Can I distinguish these interactions?

The green ones refers as a weak interactions, the best example I can give are like VDW interactions, only steric. That refers the green ones, there are nor attractions nor repulsions if you want to explain ligthly. Another way to analyze is that is equally attractive and repulsive, but this sounds weird. I can tell you that is a weak attraction

Hi Yu Ozawa,

Based on your question, you want to calculate a bond order for weak interactions, or some people called "bonding".

There are several ways to calculate bond order, and some of them are slightly different in terms of numbers. However, in conceptual, there is a real, physical, distinction between them.

For example:

- Natural Bond Orbital (NBO): 

 It is the most popular one, but I personally, do not recommend to use it, as Stone shows NBO is useless in regard of charge-transfer for f intermolecular interactions (here is the DOI link for more details:  DOI: 10.1021/acs.jpca.6b12930).

- Natural resonance theory (NRT): 

It is also another method that used a lot for such interactions.

- Mayer bond order (MBO): 

I cannot remember if it can be used for all types of intermolecular interactions. You should check this. However, here is the link shows the MBO for water dimer:

doi:  10.1038/srep22099 

- AIM delocalization index (DI): 

It is very known and I think it is already explained above.

- Fuzzy Atom Bond Order (FBO):

This method, I think, is more general than DI method, i.e. DI is a special case of the FBO. 

Note that these methods, especially the last three methods are mainly considered the overlap matrix elements.

This means these methods are mainly taking into account the sharing populations, covalent contribution, in the interactions.

The intermolecular interactions are the controversial topic and of course, there are others. Unfortunately, I do not have time to briefly cover everything here.

If I remember there was a study of comparison between different methods for calculating BOs. Once I find it, I will attache it here.

All the best!

Khidhir