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,