I calculated the triplet-singlet splitting of M-M multiple bond systems. I found that for some particular system, the bond length of double bond (triplet state) is close to the triple bond (singlet state), or even shorter. Mayer bond order of the triplet state is 1.6 and singlet state is 1.4, but the molecular orbitals shows obviously the singlet state has three counteracted overlap of d-d orbitals, while the triplet have two. So, I am very confused and don't know how to explain. I am not good at analysing bond orders, please give me some advice?
It is important to analyze bonding, non-bonding and anti-bonding contributions from the canonical orbitals. The lower bond order does imply considerable antibonding and/or non-bonding contributions. Frequently small overlap integrals are over-estimated by visual inspection of MO plots.
In short, the triplet state may have less antibonding contributions and thus shows a higher bond order and shorter bond distance.
Thanks, Dear David Scheschkewitz. I agree with you, I wonder that whether the small overlap orbitals would be deemed to bongding. Possible that the three bonding with small overlap of orbitals will due to long distance than that of two strong bonding.
Trying to count overlapping orbitals can sometimes work but often it is not a reliable way to get accurate bond orders. Maybe you could compute the DDEC6 bond orders to determine if the effect is real. Mayer bond order, especially if computed based on Mulliken population analysis, can be sensitive the setup (basis sets, exchange-correlation method, etc.) DDEC6 bond orders are more robust.
See the following paper for details: T. A. Manz, "Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders," RSC Advances, 7 (2017) 45552-45581 (http://dx.doi.org/10.1039/C7RA07400J ).
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