Subject: HYBRIDIZATION NOT "REAL";V. FOCK

From: Guido Raos <[email-masked]>
Date: Tue, 12 Sep 2000 12:27:47 +0000

The discussion about the reality of hybrid orbitals reminds me a lot 
of the one on the reality of molecular orbitals, which was on this 
list a few weeks ago.

I believe we all agree that no orbitals can ever be observed. For 
this reason, some would then go on to argue that orbitals (of any 
kind: hybrids, canonical or localized MO's, natural orbitals, 
Kohn-Sham orbitals...) should be banned from our discussion of 
chemical phenomena. I do not share this view. The userfulness of the 
orbital concept should be judged from its "effectiveness" and 
"economy" in the explanation of particular phenomena. In 
particular, the canonical Hartree-Fock orbitals and energies help the 
discussion of photoelectron spectra and of a number of symmetry 
selection rules. However, hydrid orbitals do a much better job when 
it comes to chemical bonding.

Incidentally, what "chemical" insights have been gained from 
"exact" quantum chemical calculations (full CI, diffusion Monte 
Carlo, and the like)? Often, approximate methods are much better at 
producing some understanding of particular chemical phenomenona.
If I remember correctly, Dirac (quoted by Feynman) once said: "I 
understand an equation, if I don't have to solve it in order to know 
what the solution is going to look like". I think this applies 
also to our case: just replace "equation" with "molecular structure", 
and "solve it" with "run a Gaussian job".

Coming back to the hydrids, I agree with Alan Shusterman that 
Coulson's discussion provides an excellent starting point:

> "The previous discussion has brought out clearly the very wide
> context in which hybridization seems to be relevant. We must not,
> however, allow ourselves to believe that it represents any real
> 'phenomenon', any more than resonance between different structures
> such as the covalent and ionic ones of a polar bond may be called a
> 'phenomenon'. But we can at least say:
> 
> (a) that hybridization is the most efective way of preserving the
> concept of a localized bond with perfect pairing of orbitals on the
> two atoms of the bond;
> 
> (b) that it is a restricted form of resonance, so that a residual
> resonance, due to alternative schemes of pairing, still exists."

Since then, one major advance has come from the applications of the 
GVB method of Goddard and the spin-coupled method of Gerratt, Cooper 
and Raimondi. Building on the Coulson-Fisher wavefunction for H_2, 
they both generalize and bridge the gap between MO and VB theories on 
a "one electron per orbital" basis.  I shall not dwell on the 
differences between these methods. In simple cases, such as CH_4, 
they give very similar answers. The eight valence electrons turn out 
to be localized. Four of them are found on the hydrogens in distorted 
1s H orbitals. The other four orbitals are centered on the carbon, 
and they are strikingly similar to Pauling's sp^3 hybrids.
The point is that the shape of the orbitals in not given "a priori" 
(as in the classical VB treatment), but it is a _unique_ outcome of 
the energy minimization. The N-electron spin-coupled wavefunction is 
_not invariant_ under some unitary/linear transformation of the 
orbitals (as the Hartree-Fock wavefunction: a principle exploited in 
the construction of localized MO's).

Sorry for the lengthy message. Thanks for the attention.

Guido.

------------------------------------------------------
Dr. Guido Raos
Dipartimento di Chimica, Politecnico di Milano
Via L. Mancinelli 7, I-20131 Milano, Italy
E-mail: [email-masked], [email-masked]
phone: +39-02-2399-3051       fax: +39-02-2399-3080

---

From: Eric Scerri <[email-masked]>
Date: Tue, 12 Sep 2000 09:30:40 -0800

Guido Raos writes,

>it comes to chemical bonding.

etc.

--------------------------

I am surprised to see this argument even needs to be presented to 
this forum given the prevalence of all kinds of very successful 
orbital methods in computational chemistry.

Of course orbitals are supremely useful even though they are not 
'real'.  Did anyone seriously propose banning orbitals from 
discussion of chemical phenomena just on the grounds that they are 
not real?  I should add that I am a relative newcomer to this list. *

Does that someone not accept that the use of the square root of minus 
one is also very useful in many branches of mathematical physics, 
chemistry and engineering regardless of the lack of 'reality' of the 
square root of minus one as opposed to -1?

I hope this will not lead to a discussion of whether numbers are 
'real' although this might also prove interesting.  The question has 
a long tradition in philosophy and philosophy of mathematics and
many believe that numbers ARE real objects although not observable of course.

This leads me to the earlier comment, by Oscar Ventura, who suggested 
that the whole discussion on orbitals etc. could be simplified by 
just taking "real" to mean observable.  Such a 'Marxist' approach has 
some appeal but I believe is far too crude for the kinds of issues 
under discussion even without drifting off into philosophy of 
mathematics.

For example quarks are considered to be 'real' particles in 
elementary particle physics but the theory itself now ensures that 
they cannot be directly observed.  This may be a perverse aspect of 
modern particle theory but it cannot be swept aside too easily.

eric scerri

* I joined CCL after A. Hocquet mentioned my article "Have Orbitals 
Really Been Observed?'  which is due to appear in Journal of Chemical 
Education.