# Why was helium hydride ion HeH$^+$, not hydrogen H$_2$, the first molecule formed in the early universe? [duplicate]

Why was helium hydride ion HeH$$^+$$, and not hydrogen H$$_2$$, the first molecule formed in the early universe?

How did NASA scientists confirm it?

https://www.nasa.gov/feature/the-universe-s-first-type-of-molecule-is-found-at-last

Molecular chemistry in the early universe requires species with bound electrons. Helium hydride is the first molecule to form because neutral helium atoms, formed about 120,000 years after the big bang, could combine with plentiful protons; but it was another 260,000 years until significant numbers of neutral hydrogen atoms formed, and it is only once these are present that there is a route to forming H$$_2$$.

Details:

Helium has a much higher ionisation energy than hydrogen and therefore starts to recombine at higher temperatures (about 7000 K at redshifts of $$\sim 2500$$, compared with 3000 K and a redshift of 1100 for hydrogen). Thus in the primordial gas of hydrogen and helium, it is the helium that recombines first. There is therefore a period of time in the early universe, $$120,000 < \tau < 380,000$$ years, in which almost all the hydrogen is ionised, but most of the helium is in the form of atoms.

The two react to form helium hydride $${\rm He} + {\rm H}^{+} \rightarrow {\rm He H^+}$$

As you might expect, the concentration of this molecule is low, because the temperatures were still high enough to easily radiatively disassociate it - about 1 part in $$10^{21}$$ at $$z \sim 2000$$ (Stancil et al. 1998; Galli & Palla 2013).

This is the first molecule to be produced with any important level of abundance. Note, this appears to be a somewhat arbitrary definition, since it is also claimed (e.g. Lepp et al. 2002), that He$$_{2}^{+}$$ formed the first molecular bond, via He$$^+ +$$ He, but was too weakly bound to survive in any concentration (the concentration peaks about 100 times lower than HeH$$^+$$ according to Galli & Palla 2013).

It is also possible to form small quantities of $$H_2$$ at $$z> 2000$$ via the reaction of a hydrogen atom with another in an excited state: H + H$$^* \rightarrow$$ H$$_2$$; but of course, although the hydrogen molecule is much more strongly bound than HeH$$+$$ (the dissociation energy of $$H_2$$ is 4.5 eV, versus about 1.8 eV for HeH$$^+$$), there is very little atomic hydrogen present and this reaction requires not one, but two hydrogen atoms to get together. It is not until H atoms recombine in quantity some 260,000 years later that hydrogen molecules are formed in various gas phase processes and H$$_2$$ becomes the dominant molecular species.

• But doesn't $\mathrm{H}$ have much higher binding energy than the association energy of $\mathrm{HeH}^+$? Shouldn't atomic hydrogen form earlier than this ion? – Ruslan Feb 23 '20 at 7:43
• @Ruslan It appears to be just a question of concentrations. Yes, I believe there is more atomic hydrogen than helium hydride, but helium hydride is the first molecule produced in any noticeable quantity. The concentrations are still very small. See edit. – ProfRob Feb 23 '20 at 9:14
• @Ruslan note that the first creation of H$_2$ also requires a reaction between TWO hydrogen atoms, and thus on the square of the hydrogen atom concentration. – ProfRob Feb 23 '20 at 11:25

Edited. HeH+ was formed before H2 because it has the lowest electronic energy of the two. Although its dissociation energy is slightly smaller (3.6 eV) than that of H2 (4.5 eV), it's the total electronic energy that favours its formation.

• Any references to the actual values of the binding energies? It seems strange that a highly reactive ion of a noble-gas-atom-based molecule would have higher binding energy than a quite common molecule. – Ruslan Feb 14 '20 at 11:33
• This answer is unclear because the answer uses pronouns without their antecedents: you use the word "it" five times in thirty-six words, twice to mean "the reason" and three times (I think) to mean "the HeH+ molecule." Furthermore the answer is substantially incomplete, because the answer does not consider the changes in the chemistry of the early universe as it cooled; the answer by Rob Jeffries is much more convincing. – rob Feb 23 '20 at 16:57
• @rob Apologies. I was writing about HeH+, the subject of the thread. The answer does not pretend to be the full story and much more can be said about our universe but it, the answer, gives the essential reason why it, HeH+ , the positively charged Helium hydride molecular ion, was formed first. More complete answers are also nice of course. – my2cts Feb 23 '20 at 17:24
• The edited version (v4) is completely unclear to me. Precisely what energy is being referenced here, and how does a lower such energy make it easier for the molecule to exist? – Emilio Pisanty Feb 23 '20 at 22:18
• @EmilioPisanty Let me clarify. The nuclear potential, kinetic and electron repulsion energy of the electrons. It, I mean the potential plus kinetic energy of the electrons, may appear an esoteric concept for physicists. My argument is that after He+, He and H, HeH+ has the lowest such electron binding energy, per electron. – my2cts Feb 24 '20 at 1:00