The strongest bond in the universe!

The rather presumptious title assumes the laws and fundamental constants of physics are the same everywhere (they may not be). With this constraint (and without yet defining what is meant by strongest), consider the three molecules:



N≡N (H-N≡N)+ (H-N≡N-H)2+
NN length, Å 1.0967 1.0915 1.0795
NN stretch, cm-1 2418.8 2356.4 




ELF NN basin


3.57 4.31 4.59
QTAIM ρ(r)/∇2ρ(r) 0.714/-3.38 0.690/-3.07 0.700/-2.96
aValue for hydrogen mass of 10,000 bValue for hydrogen mass of 0.001.

The series explores the effect of protonating dinitrogen (generally considered as strong as a diatomic bond gets).

  1. Firstly, one notes that the N-N distance decreases with mono and then diprotonation, the second protonation having the greater effect. Is shorter stronger?
  2. What about the NN stretching vibration? Here one encounters an annoying feature of vibrations; the modes are not always pure. Thus whilst in N2 itself, there is only one normal mode, and it is as pure as they get, by the time we have di-protonated, we have three stretching modes, two involving H-N and one N-N. They mix and none can now be considered a pure N-N stretch. Thus in H2N2, the highest wavenumber mode of 3024 is a mixture of H-N and N-N, and likewise the 2226 mode, albeit in different proportions. So a trick has to be played. If the mass of each hydrogen is increased to 10,000, modes involving these super-heavy atoms no longer mix with any other mode. Now, the N-N mode becomes pure, and its value is 2688, a significant increase on nitrogen itself. The monoprotonated form also shows a lesser increase.
  3. The ELF disynaptic basins for the three molecules also steadily increase their populations. Electrons that were previously in the terminal nitrogen lone pairs now creep into the N-N region instead, and hence make the bond stronger. The population does not reach six (the nominal value for a triple bond), since the H-N regions still contain more than 2 electrons. But ELF matches the previous two results.
  4. QTAIM measures the electron density ρ(r) at the bond critical point. Here different behaviour is seen, with ρ(r) lower for the monprotonated, and the diprotonated form intermediate between the other two. Perhaps absolute electron densities measured at a single point do not measure bnd strengths after all. The Laplacian, ∇2ρ(r) steadily decreases along the series.

So is the NN bond in HNNH2+ the strongest bond in the universe? Almost certainly. OK, so bonds with higher formal bond orders (Cr2 for example) exist, but they come nowhere near HN≡NH2+, which is crowned champion.

Oh, by  the way, another article (DOI: 10.1063/1.1576756) claimed the title in 2003,  but  I make the claim for a stronger bond here!


7 Responses to “The strongest bond in the universe!”

  1. Henry Rzepa says:

    In the above post, I linked to an article claiming that the fine structure constant varies according to where in the universe it is measured. What I noticed about this article is that six blogs have already picked up on this, and all have commented in the form of trackbacks. It is an interesting second layer of peer review that perhaps we should adopt more of in chemistry?

  2. Henry Rzepa says:

    I used a “trick” to purify the normal vibrational modes of the molecules. The trick was to make the mass of H so different from that of the N that the two modes do not mix. In the case above, the mass of H was made much larger than N. In fact, upon reflection, the correct answer is to make the mass of the H much lighter, not heavier. This means all N-H streching is factored out, since the ultra light H just rides on the N. The three wavenumbers become: 2418.8, 2451.5, 2567.7. The conclusion remains unchanged. I also note that this latter treatment is equivalent to the use of compliance constants, which was the method adopted in DOI: 10.1063/1.1576756

  3. […] the paramagnetism of dioxygen, and the triple bonded nature of dinitrogen (but never mentioning the strongest bond in the universe!). Rarely is diberyllium mentioned,  and yet by its strangeness, it can also teach us a lot of […]

  4. Henry,

    What about O2 2+ dication? Is it a worthy contender? It is isoelectronic to nitrogen and its O-O bond of 1.073 Å had been claimed to be the shortest bond between two 2nd row atoms.

    Dications are remarkable species. I had outlined “paradoxes and world records” associated with their electronic structure and reactivity in a 2003 Chem. Rev. paper (

  5. Henry Rzepa says:

    I did have a go earlier at O4; i.e. (-)O-O(+)=O(+)-O(-). The result is at 10042/20256 The central O-O length is 1.59Å.

  6. Henry Rzepa says:

    At the same level as the calculations reported above (CCSD/aug-cc-pvtz) O2(2+) has a bond length of 1.0401Å and a vibrational wavenumber of 2337 cm-1. The handle for the calculation is 10042/20261. At the higher CCSD(T) level, the length is 1.050Å and the wavenumber 2185 cm-1 (10042/20262) I think this makes the bond shorter. Whether the force constant is is larger than the NN one in HNNH (2+) remains to be evaluated (the wavenumber is down, but the mass of the oxygen is up).

    Just for fun, FO(3+), isoelectronic with O2(2+), comes out with a bond of 1.165Å and a wavenumber of 941 (CCSD(T)/aug-cc-pvtz)

    And to complete this, NO(+) emerges as 1.069Å and 2356 cm-1 (CCSD(T)/aug-cc-pvtz).

  7. Mark Penick says:

    Some baffled astronomer somewhere may be looking at a series of lines with a spacing of about 2451 cm-1 and wondering what they are. I say this because your hypothetical hydrogen of 0.001 amu is almost the mass of a positron! What is the stretching freq of N2-e+ [“proton” mass of 0.00054462 amu]? This molecule may be visible from here…

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