Subject: Orbitals yet again

From: "Phil Hultin" <hultin=at=cc.umanitoba.ca>
Date: Mon, 7 Feb 2005 10:01:29 -0600

Two comments:

Dr. Sukumar points out that the discussion has veered away from the Nature
paper that stimulated it.  I also have noted that the discussion has
neglected the specifics of Villeneuve et al's paper.  There is a lot of talk
about whether they have actually imaged the difference between N2 and N2+,
but it appears to me that their technique is NOT a difference method at all.
I can't claim to understand everything about their method, and I do feel
very uncomfortable about statements they make about spectroscopic signals
being generated by the interference of two wavefunctions (which are
undeniably human-created and non-physical things).

Having said this, I return to my original posting: if Villeneuve et al have
NOT imaged an orbital as they claim (and I believe that strictly speaking
such an image is indeed a QM impossibility), then just what is the physical
origin of the spectroscopic data that they present?  It is fine to deny that
an orbital image is possible, based on theory.  Unless the critics are
claiming that the observation by Villeneuve et al is a fabrication (which
nobody seems to be saying, thank heaven), I really would like to see their
point-by-point explanation of just what actually was observed in
Villeneuve's experiment, or how the processing of the raw data gave rise to
an invalid conclusion.

As I understand it, a series of spectra of very high overtones arising from
the laser stimulation of N2 molecules in a set of defined rotational states
with respect to the plane of laser polarization were acquired.  They assert
that this technique selectively excites only the highest-energy electrons in
the sample, which they equate with the HOMO electrons.  The spectra were
found to vary as a function of the rotational orientation of the molecules.
A standard tomographic technique was used to obtain a 3-dimensional plot of
something that the authors assert is the electronic state that gave rise to
the spectral signal.  They quote literature sources to support this claim.
Finally, they note that the topology of this 3-D plot is strikingly similar
to an HF-derived graph of the expected HOMO.

I do not see any point at which the orbital model was used to process the
raw data, but this may be because I have not tracked down the literature
supporting the idea that overtone spectra of this kind do give information
about the electron density of a single state.

The second comment is this:

Dr. Sun remarked:

"Dr. Hultin is speculating whether some physical properties of electronic
structure can lead to some information of WFs. This is surely possible for
H.

However, such an activity distinguishes from any experimental observation,
as it is conducted in reference to the pictures in your mind. It is not
based on any physical interacting relationship. WFs are not experimental
observable whatever, simply because they are not the choice of the nature
but humans. The choices of the nature are electrons, their motion (or
density distribution), and the space they occupy. The reverse construction
of WFs for multielectron systems would be extremely hard and is impossible
to me (or I am not quite sure)."

I quite agree that we are not able to deduce a rigorous mathematical
formulation to describe an observation of one among many electrons (if that
is indeed possible).  But I do not think that the only information of
interest is that which can be treated mathematically. Yes, WFs are human
creations and do not have physical reality.  Nevertheless, the inability of
humans to come up with an equation in no way limits our ability to observe
electronic behaviour within the limits of uncertainty.  Just as we can
deduce the concept of a Newtonian trajectory from our observations of balls
in motion, surely we can deduce something orbital-like if we observe that
electron density is concentrated in specific regions of space?  We have the
tools to mathematically describe a Newtonian trajectory, and we do not have
such tools to handle the behaviour of electrons, true.  Does this mean that
we cannot conceptually recognize that there is some systematic behaviour of
electrons?  I hope not.

Also, I have remarked that it is possible albeit unlikely that some of our
ab initio mathematical treatments have captured some of this systematic
behaviour, at least superficially.  I do not say that this IS so, I merely
note that it is a possibility.  Does this mean that WFs are "real"?
Absolutely not.  If it were the case that HF or some other theory gave
correspondence to observable electronic behaviour, it would not necessarily
mean that the mechanics of our calculation must reflect the details of how
that behaviour arises.

Dr. Philip G. Hultin

Associate Professor of Chemistry,

University of Manitoba

Winnipeg, MB

R3T 2N2

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