The even more mysterious N≡N triple bond in a nitric oxide dimer.

Previously, I pondered about the strange N=N double bond in nitrosobenzene dimer[1] as a follow up to commenting on the curly arrow mechanism of the dimerisation.[2] By the same curly arrow method, one can produce the below, showing how the simpler nitric oxide radical could potentially dimerise to a species with a N≡N triple bond!^† This involves a total of six electrons entering the N-N region, and hence raises the question of whether these all move in a single concerted/synchronous bond forming reaction, or whether they might go in (asynchronous) stages. Here are some calculations[3]) which might shed some light on this aspect.

The structure[4] of a nitric oxide dimer was shown in 1982 to have a very long (rather than short) N-N bond length of 2.237Å and a theoretical analysis[5] showed it to be a weak complex with a very complex wavefunction showing multi-reference character.

Firstly, an IRC-based reaction path (method: uωB97XD, scrf=(cpcm,solvent=water) guess=(mix,always) def2tzvpp to allow either an open shell biradical to form and also to encourage any ion pair formation). As you can see, the (total) energy goes up to a very  shallow transition state (with a tiny reverse barrier) to form a biradical  with 2> 0.628. This species, as noted existing in a very shallow energy well, has an N-N bond length of 1.725Å.

The bonding for this species is complex (analysis for a later post), but the calculated biradical spin density below shows the unpaired electrons are in the π-system (click on the image to get a 3D rotatable model).

Further contraction of the N-N length results in an IRC energy potential to a transition state with a N-N length 1.294Å across a further barrier of ~12 kcal/mol (ΔE; ΔG 13.6 kcal/mol). The overall barrier from two nitric oxide molecules is ΔG 31.0 kcal/mol with the overall thermochemistry summarised in the table. Basically, this barrier is unsurmountable at normal temperatures and the reverse barrier of ΔG 6.7 kcal/mol ensures that the N≡N triple bonded species shown above is not likely stable and will not be observed experimentally.^‡ However this product is NOT a biradical but a normal closed shell singlet molecule.[6]

So to answer my first question, the six electrons appear to move in two stages, firstly two electrons form a weak N-N bond and then a further four electrons contract this to a triple bond. Their motion is effectively concerted, but asynchronous.

Now for a NEDA energy decomposition analysis[11]

Electrical (ES+POL+SE) :  -9414.608
   Charge Transfer (CT) :  -1363.597
       Core (XC+DEF-SE) :  10782.725                      
  Total Interaction (E) :      4.520 kcal/mol.

Normally NEDA total interaction energies are -ve, but this one is positive! So the triple bond dissociation energy is not merely small, but actually negative. That is a weak triple bond and as the title implies, a very mysterious bond. In some aspects however it is conventional. Thus calculated r_NN 1.114Å and ν_NN 2604 cm^-1. However partial occupancies of NBO antibonding BD* orbitals results in a calculated Wiberg bond order of only 1.01; there is still a great deal of mystery left about this species! Probably what is fairly certain is that the closed shell single-reference wavefunction used here is not appropriate for a full explanation and more complex multi-reference procedures would have to be used to get a more complete picture of this strange non-existing^‡ little molecule. It may even be that such procedures remove the small reverse barrier noted above, thus preventing the molecule from even existing in an energy well.

^†This species does not appear to have been previously discussed or suggested, according to SciFinder/CAS.
^‡Might it exist at very high pressures in water?

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References

1. H. Rzepa, “The mysterious N=N double bond in nitrosobenzene dimer.”, 2025.
2. H. Rzepa, “Mechanism of the dimerisation of Nitrosobenzene.”, 2025.
3. H. Rzepa, “N2O2 as strong dimer TS as biradical cis, G = -259.785500”, 2025.
4. S.G. Kukolich, “The structure of the nitric oxide dimer”, Journal of the American Chemical Society, vol. 104, pp. 4715-4716, 1982.
5. N. Taguchi, Y. Mochizuki, T. Ishikawa, and K. Tanaka, “Multi-reference calculations of nitric oxide dimer”, Chemical Physics Letters, vol. 451, pp. 31-36, 2008.
6. H. Rzepa, “N2O2 as strong dimer? G = -259.796140, STABLE wavefunction!”, 2025.
7. H. Rzepa, “Nitric oxide monomer, G = -129.917471 *2 = -259.834942”, 2025.
8. H. Rzepa, “N2O2 as strong dimer singlet trans biradical state G = -259.807165”, 2025.
9. H. Rzepa, “N2O2 as strong dimer triplet state G = -259.808649 DG 16.5”, 2025.
10. H. Rzepa, “N2O2 as strong dimer? bent G = -259.796140”, 2025.
11. E.D. Glendening, and A. Streitwieser, “Natural energy decomposition analysis: An energy partitioning procedure for molecular interactions with application to weak hydrogen bonding, strong ionic, and moderate donor–acceptor interactions”, The Journal of Chemical Physics, vol. 100, pp. 2900-2909, 1994.