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sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,830

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Reply to metal-oxygen bonding analysis on CCL

Today I noticed there is a question on CCL:

In an NBO analysis I find I have a metal-oxygen bond which has a substantial "atom-atom overlap weighted NAO bond order" (~0.25).  These metal oxygen bonds also have a substantial MO bond order (~ 0.33).  However, there are no MO's describing the metal-oxygen bonds.

Either there is a bond and a combination of AO's to describe that interaction or there is no combination of AO's and there is no bond.  Can someone please help me understand this contradiction?

Since my reply may be useful for some Multiwfn users, I copy my reply here:

Regarding your question, I have a few opinions:

1 Do not focus on "Atom-atom overlap-weighted NAO bond order" and "MO bond order". In my viewpoint they do not have clear physical meaning, and in practice they are not as useful as the "Wiberg bond index matrix in the NAO basis" printed by NBO.

2 If the Wiberg bond index corresponding to this bond is not quite small, and you want to gain a deeper insight into it, you are suggested to use Multiwfn program to decompose the bond index as contributions from interactions between various natural atomic orbitals (NAOs), via this analysis you will make clear which kind of AO combination has relatively significant contribution. See Section 4.9.4 of Multiwfn manual for example of utilizing this analysis.

3 Usually, MO only has very loose relation with bonding, hence it is not useful to examine the bonding nature in terms of MOs. However, if you indeed prefer to examine contribution from MOs, you can use Multiwfn to perform the so-called "orbital occupancy-perturbed Mayer bond order" analysis, which is able to unveil contribution to Mayer bond order (which is similar with Wiberg bond index) from various MOs. Please check Section 4.9.1 of Multiwfn manual for example of performing this kind of analysis.

4 It is worth to note that localized molecular orbital (LMO) has very close relationship with chemical bonding, if you want to examine this bond from an orbital perspective, LMO analysis should be useful. LMO analysis is supported by Multiwfn, and "orbital occupancy-perturbed Mayer bond order" analysis can be performed based on LMO to easily reveal the LMO mostly contributed to a bond. Section 4.19.3 of Multiwfn manual presented a practical example.

5 Recently bond order density (BOD) was proposed in J. Phys. Chem. A, 124, 339 (2020) and has been supported by the latest version of Multiwfn. This method is able to graphically exhibit the electrons having contribution to delocalization index (which is essentially similar with Wiberg bond index), and natural adaptive orbitals (NAdOs) can be generated at the same time to provide a set of orbitals maximally contribute to the bond. This analysis may also be useful for you, see Section 4.200.20 of Multiwfn manual for example.