Chemistry student right here!
H3+ has two proposed structures: linear and cyclic. Upon analysis (using MO theory and other jargon) you can find that the cyclic structure is a little bit more stable than the linear structure.
Is that what you meant?

I don't think H3++ is stable either, but, mathematically it's easy to find a solution for, so I'm using it anyway for verification purposes.

Of course, not being stable, it's hard to find a name for : /

@Sid

I'm modeling the cyclic structure. As I mentioned in the OP, if there were 2 electrons, I would call it Trihydrogen cation. But, in the case of only one electron, is it still Trihydrogen cation? Trihydrogen dual cation? It must have a name and, if not, we should be able to make one up that makes sense.

oh, H3++... I thought you meant H3+.
Let's see... We could draw an analogy to how we name transition metal cations and call it H3 (2), pronounced "trihydrogen (two)". The number in parentheses stands for oxidation state. For practical purposes, you would probably just call it "trihydrogen two plus" though.

For what it's worth, the paper I'm comparing my results to says that you *may* be able to produce stable H3++ by photoinduced ionization of H3+. While interesting, they never refer to it by anything other than H3++, so it's ultimately unhelpful.

"trihydrogen two plus"

Thanks. Sounds a little silly, but that's the best I've got so far.

ok, i guess at low enough temperatures then even a tiny binding energy will be stable, and you can get the single electron shared between three protons. What use t would be is an entirely separate question, and not really relevant here...

But what is the binding energy? do you imagine an electron sitting in the middle (well in a cloud of possible positions with the middle as it's average) and have the three protons orbiting? each repelled by the others and closer to the electron so feeling a greater force of attraction than repulsion?? is that what is meant but the cyclic model?? (sounds more like a spherical model to me; ie having a spherical symmetry)

on an other side-note, what are you modelling it with?

The three atoms form the vertices of an equilateral triangle. I'm not exactly sure where the electron is, but it doesn't really matter, as all I'm trying to do is a non-self-consistent electronic structure calculation

"on an other side-note, what are you modelling it with?"

I'm not sure I can easily answer this question.

My work is based on the Density Functional Theory using the Kohn-Sham equations. I do a muffin-tin domain decomposition (Slater) and use Green's Functions (Self-energies) to calculate the discrete schrodinger equation H(E)Psi=EPsi.

yeah, the idea i'm imagining does make an equilateral triangle, though it it has any rotational modes then you'd get something like a sphere/circle...

the rotational modes being less stable i guess, intuitively, and i still have no idea how to do the math on that... poor me, i really don't deserve to call myself a computational physicist.

Hmm, i also know nothing about vibrational modes - like in linear molecules you can get a stretch in the molecule along the axis of the bond, that would make your equilateral triangle which expanded and contracted... no idea if that is possible, but it's a cool thought.

As for the electron, i'm pretty sure i'm right in saying that three protons don't just sit together in a nice pretty triangle without the electron, and the symmetry of the system forces the average position to be in the centre of that triangle - but as that centre point could be an anti-node of the wave equation it may not be occupied at all, thus the average in that case doesn't seem particularly important... it could also be a node, with a huge probability; but again my intuition fails and my quantum mechanics is very weak, so i've no idea how to either guess or calculate the solution.
(the case with two electrons is much more complicated and i wouldn't even be able to claim as little as i have)

"(the case with two electrons is much more complicated and i wouldn't even be able to claim as little as i have)"

Yes, which is why I'm doing verification with 1 electron first : )

Luckily, it works just fine with H and H2+, both of which do exist.

yeah, and looking at the wikipedia article, H3+ is stable in the interstellar medium, and thus pretty common in the universe. Which makes it pretty useful to understand, i guess. Once you figure out the H3++ that is :p

sounds really cool, pretty i can't imagine how i'd write a blog post about it...

i mean, a way to use it to educate, of at least interest people... Still i appreciate the thought food!

do you have the correct answer? i mean from spectroscopy of the ISM you should get data about the electronic, vibrational and rotational modes of H3+, (is that called Ramen spectroscopy, i was really bad at that class...) but if H3+ is common, and high energy photons have enough energy to ionize it, then you'd expect H3++ to also show up in the spectroscopy data if it is stable enough to survive any length of time...

or of course you could look in a lab... but i mean to ask, are you simulating to make a prediction of what should be seen, or trying to use a model to understanding the experimental data what has been seen?

Yeah, I don't know about all that. It's awfully low-level stuff to spark general interest.

I'm able to get answers with under 0.5% error compared to the analytic solutions for everything I've tested. Of course, I could be more accurate if I wanted to make a more refined mesh. I haven't compared to actual experimental results; I plan to for Benzene, though.

I don't have much interest in learning about things that have already been observed. I'm trying to make models that can be used to predict the behavior of new devices.

those analytical answers are approximations aswell right? i mean, the computation is some series with a limit and you only work it out to some number of terms to get the order of your error down...

Oh, I think I misunderstood you.

Yes, I know about what the correct answer should be based on a couple white papers.

No, H and H2+ can be solved mathematically exactly.

H3++ is a numerical solution, but accurate within DFT, as far as I understand the paper.

Well, I mean, sure. My final answer is going to be limited by machine error, but there's a difference between having an analytic solution with only so much precision and having a numerical solution which is inexact before you even plug in for the variables.

yeah, i mostly understand, but i still think this stuff is really cool, at least when one comes to the conclusion that sometimes systems get so complex you can't work out an analytical solution, and then that nobody can work it out and thus all the maths you ever learned don't contain enough little tricks to simplify it enough, and that nobody knows any better tricks... which is when physicists start inventing new mathematics, (at least that's what newton did, or did he steal calculus from Leibniz?)

and then you realise it doesn't matter, because whether you measure, model or work out an analytic solution, you end up with an error... (and the analytic solution has infinite non-trivial steps, so before computers we had to do these things on paper by hand...)

now that is something i'd like to be able to explain to people and try to make interesting...

As it turns out, almost every interesting problem can't be solved analytically. Luckily, this is OK for two reasons

1) Similar, non-interesting problems can be solved analytically and can serve as good starting points.

2) Numerical Analysis is very fun.

3) Computer processing power is no longer a rate-limiting step.

heh

I thought of a 3rd reason while typing.

Well, I guess this answers that question:

H. Medel-Cobaxin, "About non-existence of the molecular ion H3++"

http://arxiv.org/abs/0805.1796

someone show me how to make LSD :P

My organic chemistry professor taught the synthesis of XTC as course material. Good times.

that looks like a really cool paper, and i know that it would go way over my head... (though i think i understood the abstract, oddly enough)

i guess the H3+ has a more stable 2-electron orbital, along with the extra negative charge. I still want to know how you tell me the life-time of the 'non-existant' H3++, i mean, it may be unstable, but how do you work out the ΔE of the bound state, to figure out how long it will last before breaking down into whatever lower state happens to be available? (i'm guessing a good model is still useful, but i don't know about experimental results...)

"3) Computer processing power is no longer a rate-limiting step." +1

I skimmed this thread a few times the past couple of days, and maybe I missed it, but why are you researching H3++, and how'd you get the lucky job of doing so??

This is interesting work, abge. I am afraid that I cannot offer much to the discussion as my physical chem profs were so mathematically incompetent, they couldn't finish any problem in class, and I was certainly too lazy back then to teach myself the material. =P

@dub

I'm not researching H3++, per se. I'm designing a method from first-principle to solve arbitrary nanoelectronic structures problems. I just so happened to find a paper that gave "good" results for H3++, so I was going to include it in my paper as proof of concept. Although, my results for H3++ aren't nearly as good as they are for H or H2+ and, since it's not even a real molecule, I may drop it all together.

@abge, you said that H2+ can be solved analytically.

-This is the part where I reveal I have a master's degree in theoretical chemistry and allow for a short, but meaningful pause-

That's true, it's some pretty ingenious mathematics, but by analogy H3++ should also be analytically solvable right? It has only one degree of liberty if you assume an equilateral triangle, just like H2+ does, and - also equivalently - just a single electron.

Okay clock's ticking GL.

*degree of freedom.

lol

I was getting bad results for H3++ because my atoms were making an isosceles, not equilateral triangle. Fucking geometry.

@red

TBH, I'm not sure. It doesn't help that I don't have access to the paper that is sited for the exact value.

However, I will say this: Solving the Schrodinger equation for 3 atoms is not at all trivial. How would you propose to do it? Within DFT, you can use Plane Waves (approximations), LCAO (approximations), or some sort of linearized muffin-tin scheme (approximations).

Do you know of an analytic form for the 3-body schrodinger equation? I don't.

Oh, and thanks all for the questions. This turned into a nice practice for my proposal : )

Can I help you on the access thing?

Perhaps.

Can you get this paper?

J.W.Johnson and R.D. Poshusta, International Journal of Quantum Chemistry 11, 885 (1977).

I can find it here

http://onlinelibrary.wiley.com/doi/10.1002/qua.560110515/abstract

but my university doesn't subscribe to this publication.

Can't seem to get it either, I'll ask my professor tomorrow, don't worry.

Thanks, but don't kill yourself trying to get it. I'd be interested to see how they calculate it, but, ultimately, it's not that important.

hey there. funny to see that the percentage of nature scientist is much higher here then in the world out there ^^

i didnt had the access as well. but with old papers its often like this.
but you could try asking the authors (if still existing) or people who now sit at the same institute.

years ago one had to write a postcard to get access to a paper. so try it the medium old way and write an email ;)

Your lucky, i could get the paper

Where to send it? the webdipmod mail adress?

Thanks!

Can you send it to [email protected]

Oh wow I managed to get it too.

I sent it to you. The University of Melbourne does have a large subscription :)

Thanks!

I'll let ya'll know what I find out.

okay so you already got it.
University of Cottbus not, but this paper we got ;D