You can try the Non-covalent interaction index (NCI) to find the interactions in each transition state and compare them ... Other option is the Quantum Theory of Atoms in Molecules (QTAIM), and both tools use a wfn file to make the topological analysis of the molecular electronic density ...

Jose-Zeferino Ramirez Ramirez Thanks for your reply.

I have already tried NCI, but rather than visualize non-covalent interactions in an optimized geometry; I need a quantification for that interaction. Is it possible to extract the value from the NCI plot?

For example, if there are two non-covalent interactions in my structure, which have represented by a green color (weak, attractive) in the NCI plot, how do we know that which interaction is stronger comparatively?

I haven't try QTAIM. Thanks for your suggestion. I will check it.

In Multiwfn (http://sobereva.com/multiwfn), not only NCI visualization analysis can be easily performed, but also it is possible to integrate the domain enclosed by NCI(RDG) isosurface to get value for quantitative discussion purpose. Please check Section 4.200.14.1 of Multiwfn manual on how to do that.

Using QTAIM to quantify the interaction is also viable and very popular. However, in many cases even if there exists non-negligible non-covalent interaction, there is no corresponding bond critical point. In this situation one has to employ RDG or IGM method to study the interaction.

While Professor Lu provided some valuable tools about portraying non-covalent interactions, you can also employ SAPT analysis using PSI4 package (freely available) to decompose non-covalent interactions into different physical components in two competitive TSs.

SAPT makes it possible to have the origin of non-covalent interactions in a quite quantitative manner (numerical values will be at hand).

Thank you very much for your useful replies. I will get back to you if there are any queries regarding these answers. Tian Lu Saeedreza Emamian Melek Hajji

Dear Prof. Tian Lu ,

I have done the quantification of non-covalent interactions in two transition states according to Multiwfn manual. In one transition state, there are 28 domains, and in another transition state, there are 30 domains. Then, I have calculated the sum of 'Average' values of 28 domains in one transition state and 30 domains in another transition state, and I got 0.49 for the first transition state and 0.55 for the second one. So, is it okay to conclude that the total non-covalent interactions in the second transition state are higher than the first one?

Vipin Raj K I don't know how you exactly calculated the values, the domains can be characterized in many different ways, for example, examining their total volumes, integrating a real space function in the domains and so on. Without more detailed information, such as the way of calculating these values as well as isosurface maps showing distribution of the 28 and 30 domains, I am unable to clearly give you a answer.

Dear Prof. Tian Lu ,

Thanks for your reply. I have correctly done what described in Multiwfn manual (section 4.200.14.1). I have followed each step shown for the first example, which is of phenol dimer (system 1 in the manual, page no. 641). Then I have got domains with corresponding grids (as shown in the manual page no. 642 for phenol dimer). See Pic_1 in attached files.

Then I have done the integration for all domains (option 2 in Multiwfn software), which results in an integral value, volume, and average corresponding to each domain. See Pic_2 in attached files.

Then I have added all the average values to get the total strength of non-covalent interactions in a transition state. (What I understood from the manual is that the average value is a better indicator for the strength of non-covalent interaction than integral value).

A point more crucial than the integral/average value or volume is the distribution of domains. If you tend to use such as integral of density in the domains to discuss interaction strength, you should first confirm that the domains in the two systems are comparable, for example, all the NCI domains occur in the interacting region and their natures are similar (i.e. all of them play attractive role, none of them corresponds to steric effect). This point can be examined by inspecting sign(lambda2)rho colored RDG isosurface map.

If indeed all of the 28 / 30 domains have similar feature and they are able to faithfully reveal the interaction, I think the "Integration result of all domains" will be somewhat able to be used to compare the relative interaction strength of the two cases.

Note that "added all the average values" is not meaningful, because average is not an extensive quantity but an intensive quantity, the latter is not additive.

Thanks, Prof. Tian Lu , for your valuable comments.

One quick question regarding Multiwfn. Is it possible to calculate the electron density at the bond critical point using Multwfn? I saw in some articles they plotted all the BCPs and gave the values of electron density at the BCPs and compare its strength approximately to explain the stability of one transition state compared to another.

Regarding NCI plot, I will first visualize individual domains (whether they are attractive or repulsive), then, I will select comparable attractive non-covalent interactions in two transition state and do the summation of integral values of all such domains only. I will get back to you if there are any further issues.

Using Multiwfn to calculate electron density at BCP is extemely easy, please check section 4.2.1 of the manual for example. Multiwfn is very good at AIM topology analysis.

Thank you very much, Prof. Tian Lu .

What about a quick NBO population analysis? Wiberg total bond indexes are extremely quick to calculate and quite structurally informative although not energetically informative.

Thank you, Joaquin Barroso-Flores Is it possible to get a bond index value for a non-covalent interaction? I thought it is only for a proper bond where the attraction between two atoms is due to the pairing of electrons.

Vipin Raj K the Wiberg bond index will pair all atoms so you get to decide which are covalently bonded. So a C-H bond will get a 0.999 bond index whereas a R-OH...OH2 might be say 0.5. Most indexes for far away atoms will be close to or effectively zero, those are the ones non interacting.

Joaquin Barroso-Flores Thank you. I will check it.

Felipe Silveira de Souza Schneider

Can NCIplot be used to find quantitative strength of NCI? Can it identify the electrostatic (between permanent multipoles) interaction or just the electron density fluctuation?

Prasanta Bandyopadhyay As I mentioned in my previous answer, Section 4.200.14.1 of Multiwfn manual illustrates how to integrate a given function within specific NCI isosurface to try to quantify the corresponding interaction. However, it is not possible to solely extract the energy of electrostatic interaction in the framework of NCI analysis, for this purpose you need to consider using energy decomposition analysis, such as the SAPT analysis in PSI4 and LMOEDA analysis in GAMESS-US. Multiwfn also supports energy decomposition analysis based on molecular forcefield, as illustrated in Section 4.21.1 of the Multiwfn manual.

Tian Lu I have used all the methods that you have said. I still have the similar querry, whether NCIplot can measure the purely electrostatic interaction (between permanent multipoles of the interacting monomers). If in a ideal situation, purely electrostatic interaction occurs, will it give any signature on the reduced density gradient?

Prasanta Bandyopadhyay Unfortunately, according to my understanding of your meaning, this is beyond the capacity of NCI plot method. The electrostatic component cannot be exactly isolated from the NCI plot result.

That is what I thought, Prof Tian Lu . Thank you very much.

To quantify all interactions (including non-covalent ones) at any stationary point, we use the energy decomposition analysis as implemented in ADF. We are able to quantify the electrostatic, Pauli repulsion, orbital interactions, and dispersion between fragments (i.e. two reactants).

For a trial version of ADF:

https://www.scm.com/free-trial/

For applications:

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