Hydrogen anions - how do they form?

[sciFax]

TL;DR

I have only very recently been made aware of the existence of $H^-$ hydrogen anions, something which I had previously thought impossible. So how is this possible?

Having read a few Wiki articles on and around the subject, I am now somewhat aware of the means by which these $H^-$ anions acquire the extra electrons "donated" by e.g. ionized alkali atoms in stellar atmospheres, and the means by which they provide opacity.

What I don't understand is how it is possible for two negatively charged electrons to exist in stable "orbits/shells" around the single positively charged proton in the nucleus.

 

[Vanadium 50]

What I don't understand is how it is possible for two negatively charged electrons to exist in stable "orbits/shells" around the single positively charged proton in the nucleus.

Answer A - the two electron-proton attractions overcome the single electron-electron repulsion.

Answer B - just as you gain 13.6 eV when one electron falls into the potential generated by a proton, you gain 0.75 when a second electron falls in.

 

[sciFax]

@Vanadium 50 Your answer A is interesting, and will certainly lead me to look further into this. I still find it surprising that the positive charge of the central proton is not completely "balanced out" by the initial single electron of the neutral hydrogen atom. Would it be possible to have, say, three electrons in a hydrogen atom, or are two the maximum number permissible by the 1n electron shell?

Your answer B gives me further context in which to understand numbers seen in e.g. the Wiki hydrogen anion page where they mention an electron affinity of ~0.75 eV and an overall ground state energy of ~ -14.36 eV, being evidently the sum of 13.6 and 0.75 eV.

Thanks for your input!

 

[Vanadium 50]

Would it be possible to have, say, three electrons in a hydrogen atom

What does "possible" mean? It's possible to keep adding electrons until it becomes energetically unfavorable to do so, but I'm pretty sure that this always happens by N = 3. So it's possible to happen, but it just doesn't.

 

[sciFax]

What does "possible" mean?

Well, there's quite possibly a definite quantum mechanical or mathematical definition of the word "possible" in such a context, and speaking as a layman, I am definitely, and unfortunately, unaware of such a definition.

So, as a layman, I would probably reformulate my question in something like these terms: "do the rules of QM admit of such an eventuality that two or even more electrons could become attached to a proton/hydrogen nucleus", or "is there a solution to the schrödinger equation for the hydrogen atom which allows for the existence of, say, a hydrogen $H^-$ anion". Or other probably/possibly equally vague formulations expected to be burbled by a layman...

 

[etotheipi]

Answer A - the two electron-proton attractions overcome the single electron-electron repulsion.

I don't dare question @Vanadium 50, but shouldn't we be saying that for a given electron, the electron-proton attraction overcomes the electron-electron repulsion? My simple mind doesn't understand what it means to say the two electron-proton attractions overcome the electron-electron repulsion, when the interactions are between different pairs of particles.

 

[sciFax]

@etotheipi I think I understand in a non-technical what @Vanadium 50 's saying - I quite possibly have this wrong, but it's like the electrons are not actually in shells as such, but form "probabilistic clouds" around the proton, and can form localized pairs where each electron interacts with the proton, but don't "see" each other quite so well from the positions they may take in their own "cloud".

I don't have my Lego set with me right now, but I'm sure I could build something along these lines. Or maybe mud-pies would be more appropriate?

 

[Vanadium 50]

"do the rules of QM admit of such an eventuality that two or even more electrons could become attached to a proton/hydrogen nucleus", or "is there a solution to the schrödinger equation for the hydrogen atom which allows for the existence of, say, a hydrogen anion".

I believe the answer to your first question is "yes" and the second is "no".

 

[sciFax]

the second is "no"

Would that be a "no exact solution" no, or a "not even a perturbative numerical solution" no?

 

[ZapperZ]

I don't dare question @Vanadium 50, but shouldn't we be saying that for a given electron, the electron-proton attraction overcomes the electron-electron repulsion? My simple mind doesn't understand what it means to say the two electron-proton attractions overcome the electron-electron repulsion, when the interactions are between different pairs of particles.

If the two electrons are on the opposite sides of the proton at a given time, is the electron-electron repulsive force greater than, or less than the electron-proton attractive force? The electron-proton pair is at a distance r from each other, while the electron-electron pair are at a distance 2r from each other. Considering the Coulomb force drops as 1/r², you can easily answer that question.

This is analogous to a triplet state where the two electrons have symmetric spins with respect to each other, but antisymmetric spatial components, meaning they are as far away from each other as possible (thus, opposite side from one another).

Zz.

 

[Vanadium 50]

ould that be a "no exact solution" no, or a "not even a perturbative numerical solution" no?

You're splitting hairs - hairs that can't be split at B level. If I told you the third electron doesn't form a bound state but the (e-,H-)scattering amplitude shows a pole, would that help you?

 

[sciFax]

If I told you the third electron doesn't form a bound state but the (e-,H-)scattering amplitude shows a pole, would that help you?

As you can probably guess, not very much. Nonetheless, I glanced through this and found it to be ... interesting. Probably a million miles away from what you were talking about.

 

[symbolipoint]

Without even making any attempt to justify or give any quantum mechanics accounting, hydrides do exist and some are used as reagents; for example, Sodium Borohydride.

note: My understanding on this could be faulty. The hydrogen is present in such compound with a negative charge but the anion is the borohydride anion.

 

[Fred Wright]

Dear sciFax,
I think you can better understand @Vanadium 50 and @ZapperZ comments if you consider the resonant scattering of electrons by atoms. This paper, https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1963.0128, from 1963, considers Hydrogen in particular.

 

[Vanadium 50]

I don't think that's a B level paper. I don't think there may even be a B level answer beyond what has been said.

 

[TeethWhitener]

Would it be possible to have, say, three electrons in a hydrogen atom,

The electron affinity of helium is estimated at -0.5 eV, meaning it’s energetically unfavorable by that amount to bind an electron to helium. And the situation will probably be worse for H^-, since you’re trying to bind two negatively charged objects.

 

[sciFax]

The electron affinity of helium is estimated at -0.5 eV, meaning it’s energetically unfavorable by that amount to bind an electron to helium.

And there's a shoe-in for those unfamiliar with (or have forgotten, since it's so long ago!) QM - a simple phrase like "energetically unfavorable" says more than "the (e-,H-) scattering amplitude shows a pole" would, any day. A B-level question needs a B-level answer.

So, one can play with the idea of energetic unfavorability, go back and read the Wiki articles with that in the back of one's mind and maybe - possibly - move a little forwards in trying to understand/encompass the idea of hydrogen anions.

 

[sciFax]

Dear sciFax,
I think you can better understand @Vanadium 50 and @ZapperZ comments if you consider the resonant scattering of electrons by atoms. This paper, https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1963.0128, from 1963, considers Hydrogen in particular.

Thanks for the link to the paper. It's a tad above my pay-level, but nonetheless makes interesting reading.

 

[Vanadium 50]

It's a difficult discussion to decide if something is impossible or "possible but just doesn't happen". Probably impossible.

If you like the energetic argument, you probably will like the charge argument. It's easy to bind an electron to a positively charged proton. It's harder but still possible to bind an electron to a neutral hydrogen atom. It's harder still (and doesn't happen) to bind an electron to a negatively charged H- ion. So far as I know there are no stable isolated 2- ions, but if there were, it would be harder still to stick yet another electron on one.

 

[snorkack]

Look at it from this aspect: on classical side, a dielectric object will acquire induced dipole in field of a charge, that will attract the charge.

But from this classical approach, a hydrogen atom as polarizable dielectric should have equal attraction to a proton and an electron.

 

[DrDu]

Hi,
a relatively accessible summary of the understanding of the hydride ion was given by Hylleraas and can be found here:
http://adsabs.harvard.edu/full/1964ApNr...9..345H

He also gives a quite simple approximate wavefunction which yields a very good approximation.

 

[sciFax]

Hi,
a relatively accessible summary of the understanding of the hydride ion was given by Hylleraas and can be found here:
http://adsabs.harvard.edu/full/1964ApNr...9..345H

He also gives a quite simple approximate wavefunction which yields a very good approximation.

Thank you for this - it gives a nice historical perspective on the question of whether the $H^-$ anion could exist.

Also interesting to note that some physics "big names" like Bethe and Chandrasekhar had also turned their attention to the anion.