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In a hypothetical (?) Og2+235 we would have a simple sigma bonding orbital occupied by one electron (leading to a bond order of 1/2). But how to take into account the giant repulsion of the two nuclei? Generally how are nucleis taken into account for energy calculations from molecular orbitals in MO theory? So far I've always read about the electrons but very few about the nuclei in the system.

Same in He23+, half bond order but very large repulsion. My intuition says that He21+ should be more stable, even if both have the same bond order.

Where in the framework of MO theory is exactly that taken into account? How does nuclei repulsion change the MO energy scheme?

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    $\begingroup$ Oh, no, not again ;> For diatomics you get +2, tops. Some absurd charge is out of question. $\endgroup$
    – Mithoron
    Nov 29, 2022 at 21:55
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    $\begingroup$ Apply the common sense of classical electrostatics and you would see that the monotonous steep slope of potential energy of nuclei cannot be disturbed by very tiny bump caused by interaction of electrons. $\endgroup$
    – Poutnik
    Nov 29, 2022 at 21:55
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    $\begingroup$ @FlawC en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation - calculating MOs first involves the assumption that that the nuclei are stationary (have fixed positions) and then optimising the electron wavefunction. The nuclear repulsion term is not ignored in the overall energy, but it is just a constant (for a given set of nuclear positions). $\endgroup$ Nov 29, 2022 at 22:11
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    $\begingroup$ @FlawC Short answer: never. Long answer: what you need to do is to plot the energy of such a compound as a function of bond length. (You can google 'hydrogen bond energy curve' for an example of what this looks like for H2.) Now, your curve for $\ce{Og2^{235+}}$ would be so biased towards large distances, and the 'dip' in the curve would be so small, that it can hardly be considered a molecule. To be technical, it wouldn't admit a vibrational state which is required for something to be considered a molecule. goldbook.iupac.org/terms/view/M04002 So there is no bond at any length. $\endgroup$ Dec 1, 2022 at 1:48
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    $\begingroup$ That said, the original question isn't silly at all (although I guess you did choose a rather extreme example). I would love to write a proper answer, but it's very late where I am now. Feel free to ping me again tomorrow and maybe I can get round to it. $\endgroup$ Dec 1, 2022 at 1:50

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I would not bet on it. We apparently can't even get $\ce{He2^{3+}}$, let alone higher single-electron diatomic ions. From Wikipedia:

$\ce{He2^+}$ was predicted to exist by Linus Pauling in 1933. It was discovered when doing mass spectroscopy on ionised helium. The dihelium cation is formed by an ionised helium atom combining with a helium atom: $\ce{He^+ + He -> He2^+}$.[1]

The diionised dihelium $\ce{He2^{2+}} (1Σ_g^+)$ is in a singlet state. It breaks up $\ce{He2^{2+}->2 He^+}$ releasing 200 kcal/mol of energy. It has a barrier to decomposition of 35 kcal/mol and a bond length of 0.70 Å.[1]

Thus even with only two positive charges the helium dimer is prone to breaking up due to electrostatic repulsion. Although the dication above is metastable, we should expect the stability to only become worse with an additional positive charge and only one bonding electron instead of two.

A simple classical electrostatic calculation is instructive. Suppose you have a negative charge and two positive charges, the latter equidistant from the negative charge on opposite sides. The net force is attractive if all charges are one unit, but this net attraction is lost if we give two or more (and certainly 118!) units to both positive charges. The true quantum mechanical calculation is of course much more complicated, but can give only less favorable results because as the positive nuclear charges approach the electron cloud cannot stay fully between them. Thereby $\ce{H2^+}$ is predicted to be the only single-electron homonuclear diatomic ion that remains bound.

Cited Reference

  1. Grandinetti, Felice (October 2004). "Helium chemistry: a survey of the role of the ionic species". International Journal of Mass Spectrometry. 237 (2–3): 243–267. Bibcode:2004IJMSp.237..243G. https://doi.org/10.1016/j.ijms.2004.07.012.
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