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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, R3T 2N2 http://umanitoba.ca/chemistry/people/hultin |