Subject: Re: CCL:Orbitals

From: "Jens Spanget-Larsen" <spanget$at$virgil.ruc.dk>
Date: Wed, 28 May 2003 17:07:23 +0100

E. Lewars:

> Are MOs physically real? This is a meaningful question only if there
> is some experiment or observation that could provide an answer _yes_
> or _no_.  Is there, at least in principle, such an experiment or
> observation?

I don't agree. For a many-electron system, one-electron wavefunctions 
are BY DEFINITION physically unreal. They can only be defined by 
neglecting certain very physical aspects, corresponding to a model 
where electron correlation effects are neglected. According to basic 
Physics, real electrons instantaneously correlate their individual 
movements, but electrons in orbitals don't. Electrons in orbitals are 
'quasi-particles', not 'real particles'.

> As J S-L points out, MOs are one-electron functions; does this mean
> that for hydrogenlike atoms they _do_ correspond to physical reality?

For an isolated hydrogen atom, the orbital wavefunctions, using the 
reduced mass and relativistic quantum mechanics, probably corresponds 
closely to what one might choose to consider as 'reality'. But in the 
end, the question becomes entirely philosophical; for example, no-one 
has ever observed an isolated atom.
 
> If MOs have no physical reality for multielectron species, why (a) is
> Koopmans' theorem useful, why (b) do photoelectron spectra match the
> predictions of MO energy-level diagrams, and why (c) does the Hueckel
> 4n+2 rule, which is based on MO diagrams, work? Of course, it is
> probably possible to formulate an MO-free electronic molecular theory
> that leads to the same predictions a-c, but I suspect that in some
> sense (but what sense?) MOs exist--occupied MOs; the meaning of a
> virtual MO is harder to see.

The MO concept is very useful, forming the basis for excellent models 
of chemical and spectroscopic behaviour. For example, if you adopt 
Koopmans' approximation (neglect of electronic correlation and 
reorganization effects on ionization), Koopmans' well-known theorem 
applies. This is frequently a very good model, largely because the 
different errors introduces by the adoption of Koopmans' 
approximation tend to cancel each other out. But sometimes Koopmans' 
approximation is a bad approximation, and Koopmans' theorem does not 
apply. Or in the other words: The MO picture of ionization is 
sometimes a good model, and sometimes it is not. 

In any case: MOs don't exist in the physical sense. But of course, 
you may say that they 'exist' in our minds!

Jens >--<

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JENS SPANGET-LARSEN         Office:         +45 4674 2710
Department of Chemistry     Fax:            +45 4674 3011
Roskilde University (RUC)   Mobile:         +45 2320 6246
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From: elewars <elewars_at_trentu.ca>
Date: Wed, 28 May 2003 15:14:17 -0400

2003 May 28

Hello,

Good points! Especially the idea that MOs are unreal _by definition_. If you
insist that an MO must be a one-electron function (I know this is in the usual
definition) then I suppose it could be "real" only for a hydrogenlike atom. For
these, as you imply, the exact solutions of the Schroedinger equation evidently
are physically real. As for the point about observing an isolated
system--Heisenberg and Platonic reality....that could lead one far afield,
perhaps.

EL
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Jens Spanget-Larsen wrote:

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