h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I know this has probably been done, but what I wanted to do was calculate the wavefunctions of the H2+ molecule, without using the born-oppenheimer approximation. Then I could create a superposition state in which just electronic degrees of freedom are excited. Then I could let the system evolve, and watch the energy transfer to the nuclear degrees of freedom.

I was thinking of using a plane wave basis set for all the particles. This way the internuclear separation (bond length) can change for different excited electronic states. Any thoughts?

Sorry, but I'm not a theoretical chemist. So, no idea there.

You want to 'see' or 'calculate' the H2+ spectrum? I think H2+ is completely solved innit? IIRC, some people have observed even the faintest couplings and lamb-shifts on hydrogen, dunno about H2+ though.

HELL

Err...magic!!!

It's definitely more that I want to "see" than calculate. I know you can solve for the electronic levels of H2+ analytically using the born-oppenheimer approximation. 1st off, I want to try solving a system without that approximation. The easiest system would be H2+. Someone has probably done this calculation one way or another; I just want to do it to learn.

Second, I'm more interested in observing the superposition state evolve from S1 v=0 to S1 v>>0, and possibly back again. I'm not that concerned about seeing the spectrum, so much as the wavefunction evolve.

Like you wanna watch the wavepackets moving along the potential surface n'stuff? You can try to use SCF, or the likes for different geometries and interpolate... For theexcited state people use Carr Parinello simulations, open-shell whatever stuff. I usually fall catatonic in the theoretician's seminars... And they're usually off by 3eV anyways...

Good luck. (I might ask my theoretician for some good clues...)

HELL

Is this that work function thing where the number of e electrons released is proportional to the frequency of light and not the intensity!!!

basically, yes I want to watch them move along the potential. I'll look up car-parinella.

Lady Admiral - yes, it is related to that. What you're describing is called the photoelectric effect, in which electrons are ejected from a metal sample. Whether or not they are removed depends on the frequency, as you point out, not the intensity. In this case, instead of completely removing the electron, we're just going to give it a little nudge so it starts moving around, and then watch it. We expect that it will affect the nuclei that it is bound to, and they'll start moving too.

*whispers to Lady Admiral*

They're talking pretty theoretical (PhD level and beyond) physics here. Unless you have degree level quantum theory knowledge you'll not really be able to contribute to this one.
Heaven knows I can't.
All I know is that H2+ is a three body problem (two nuclei and 1 electron) and it is therefore not possible to solve the trajectories of everything simultaneously. Hence assumptions and approximations are used in attempts to try and get near to the real answers. What dave wants to do is *not* use the Born-Oppenheimer approximation.

This assumes that nuclear, electronic, vibrational, rotational and translational energy levels are independent and can be solved separately. That is, the wavefunction is the product of each of these
(Psi = Psi(nuc)*Psi(elec)*Psi(vib)*Psi(rot)*Psi(trans))

The selection rules of spectroscopy are largely based on this approximation which in fact is not so true leading to so-called "forbidden" transitions being seen in various forms of spectroscopy.

If you don't use it you will (hopefully) get a more accurate wavefunction but the maths will be a *lot* harder...

ty Orcus, that's a pretty nice explanation. Hopefully I'll be able to get the computer to do most of the maths

Actually Orcus, I was hoping to still keep the wavefunctions separable. I was going to change the dimension of the Hilbert space (I think that is the right terminology). So, a basis function would look like:
|psi(R1)i>|psi(R2)j>|psi(r)k>

where R1 is nuclues 1, R2 is for nucleus 2, r is for the electron.
i,j,k refer to the energy level/index of the basis states for each particle.

So then more basis functions would be:

|psi(R1)(i+1)>|psi(R2)j>|psi(r)k>
|psi(R1)i>|psi(R2)(j+1)>|psi(r)k>
|psi(R1)i>|psi(R2)j>|psi(r)(k+1)>

If I decide to use N basis states for each particle, then the number of matrix elements goes as N^3!!!! This is kind of a problem, and probably why this method isn't used.

Now, if I can come up with a way to block diagonalize, perhaps through suitable choice of basis functions, maybe it would be more tractable.

dave

all y'all, please check this out if you can:

A3600901

Why did you delete it?

well, because it quickly became out of date - I was revising so much with people in RL that the hootoo one wasn't close. And also because I submitted it and it's done anyway. Sorry.

Oh, well, anyway it served its purpose.

Darn it, I saw it but didn't have time to read...

I must say though, one comment I was going to add was :

for heaven's sake don't put research proposals in such a pulbic place...

(a) Because others will steal it if they see it and claim it as their own (dirty business we're in sometimes).

(b) Because anything you post on h2g2 immediately becomes intellectual copyright of the BBC as per the house rules.
OK one who is in the know probably won't see
it here but nevertheless the risk is there.

good point about the intellectual property ... that's one I was vaguely worried about, but not nearly as much as should have been.

About the theft...I didn't want to sound like an *ss, but that was one reason I took it down. I guess if I were to ever have to do it I could post it on my website, and then have people email me, then I could send them the site. If people are interested in reading it for fun or suggestions I could do that. What do you think?