Category Archives: Literature

No, seriously, why can’t orbitals be observed?


The concept of electronic orbital has become such a useful and engraved tool in understanding chemical structure and reactivity that it has almost become one of those things whose original meaning has been lost and replaced for a utilitarian concept, one which is not bad in itself but that may lead to some wrong conclusions when certain fundamental facts are overlooked.

Last week a wrote -what I thought was- a humorous post on this topic because a couple of weeks ago a viewpoint in JPC-A was published by Pham and Gordon on the possibility of observing molecular orbitals through microscopy methods, which elicited a ‘seriously? again?‘ reaction from me, since I distinctly remember the Nature article by Zuo from the year 2000 when I just had entered graduate school. The article is titled “direct observation of d-orbital holes.” We discussed this paper in class and the discussion it prompted was very interesting at various levels: for starters, the allegedly observed d-orbital was strikingly similar to a dz2, which we had learned in class (thanks, prof. Carlos Amador!) that is actually a linear combination of d(z2-x2) and d(z2-y2) orbitals, a mathematical -lets say- trick to conform to spectroscopic observations.

Pham and Gordon are pretty clear in their first paragraph: “The wave function amplitude Ψ*Ψ is interpreted as the probability density. All observable atomic or molecular properties are determined by the probability and a corresponding quantum mechanical operator, not by the wave function itself. Wave functions, even exact wave functions, are not observables.” There is even another problem, about which I wrote a post long time ago: orbitals are non-unique, this means that I could get a set of orbitals by solving the Schrödinger equation for any given molecule and then perform a unit transformation on them (such as renormalizing them, re-orthonormalizing them to get a localized version, or even hybridizing them) and the electronic density derived from them would be the same! In quantum mechanical terms this means that the probability density associated with the wave function internal product, Ψ*Ψ, is not changed upon unit transformations; why then would a specific version be “observed” under a microscope? As Pham and Gordon state more eloquently it has to do with the Density of States (DOS) rather than with the orbitals. Furthermore, an orbital, or more precisely a spinorbital, is conveniently (in math terms) separated into a radial, an angular and a spin component R(r)Ylm(θ,φ)σ(α,β) with the angular part given by the spherical harmonic functions Ylm(θ,φ), which in turn -when plotted in spherical coordinates- create the famous lobes we all chemists know and love. Zuo’s observation claim was based on the resemblance of the observed density to the angular part of an atomic orbital. Another thing, orbitals have phases, no experimental observation claims to have resolved those.

Now, I may be entering a dangerous comparison but, can you observe a 2? If you say you just did, well, that “2” is just a symbol used to represent a quantity: two, the cardinality of a set containing two elements. You might as well depict such quantity as “II” or “⋅⋅” but still cannot observe “a two”. (If any mathematician is reading this, please, be gentle.) I know a number and a function are different, sorry if I’m just rambling here and overextending a metaphor.

Pretending to having observed an orbital through direct experimental methods is to neglect the Born interpretation of the wave function, Heisenberg’s uncertainty principle and even Schrödinger’s cat! (I know, I know, Schrödinger came up with this gedankenexperiment in order to refute the Copenhagen interpretation of quantum mechanics, but it seems like after all the cat is still not out of the box!)

So, the take home message from the viewpoint in JPC is that molecular properties are defined by the expected values of a given wave function for a specific quantum mechanical operator of the property under investigation and not from the wave function itself. Wave functions are not observables and although some imaging techniques seem to accomplish a formidable task the physical impossibility hints to a misinterpretation of facts.

I think I’ll write more about this in a future post but for now, my take home message is to keep in mind that orbitals are wave functions and therefore are not more observable (as in imaging) than a partition function is in statistical mechanics.

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I’m putting a new blog out there


As if I didn’t have enough things to do I’m launching a new blog inspired by the #365papers hashtag on Twitter and the naturalproductman.wordpress.com blog. In it I’ll hopefully list, write a femto-review of all the papers I read. This new effort is even more daunting than the actual reading of the huge digital pile of papers I have in my Mendeley To-Be-Read folder, the fattest of them all. The papers therein wont be a comprehensive review of Comp.Chem. must-read papers but rather papers relevant to our lab’s research or curiosity.

Maybe I’ll include some papers brought to my attention by the group and they could do the review. The whole endeavor might flop in a few weeks but I want to give it a shot; we’ll see how it mutates and if it survives or not. So far I haven’t managed to review all papers read but maybe this post will prompt to do so if only to save some face. The domain of the new blog is compchemdigest.wordpress.com but I think it should have included the word MY at the beginning so as to convey the idea that it is only my own biased reading list. Anyway, if you’re interested share it and subscribe, those post will not be publicized.

How to read (and perhaps even write) a scientific paper


This post was inspired by this other one, featured in WordPress’ Freshly Pressed section, on how should non-scientist read a scientific paper.  While the approach presented therein is both valid and valuable, I’d like to address the way I think a scientist should read a paper, given the fact that we need to read a lot of them at all times. Each scientist has their own reading style, not to mention their own writing style, and while my CV could indicate I don’t know how to do neither one, here I present to you my scientific-paper-reading style which I consider to be the most suitable for me.

I’d like to start by emphasizing that I dive into scientific literature in a bona fide fashion. That is not to say I’m totally naive or even gullible, but even when science is all about questioning and casting doubt onto all sorts of claims, we can’t re-develop every bit of science we need. At a certain point we must start *gasp* believing trusting other scientists’ claims. Reading in what I call bona fide is not mutually exclusive with critical reading. This sort of scientific trust is earned, to a degree, mostly by two indicators: Author’s preceding reputation at the time of publication of any given paper as well as the journal’s. Both indicators aren’t without controversy and flaw.

The way I read a paper is the following: I start with the Abstract, then follow with the Conclusions, then the Results section, sometimes I read the details of the methodology and seldom read the Introduction. Let me explain.

I read the abstract first because I read in bona fide as I hope the authors wrote the paper in bona fide. If properly written, the abstract should include all the relevant information as to what was done, why, and how but also point to the knowledge derived from it all: Their conclusions! and that is why I follow with that section. I’m interested in knowing what the authors learned and ultimately want me to learn about their study. Once again I’m reading in bona fide, so I hope they weren’t tempering their results to fit their preconceptions, that all experiments were thoroughly self-judged, validated, correlated, referenced and controlled. Recently, my sister Janet, who is a physicist working on her PhD in neuroscience, told me about some friends of hers who never (shall I say, never have I ever?) read the conclusions as to not becoming biased by the authors. To me it seems like too much work having to scrutinize every piece of data again in order to come up with my own conclusions when authors, collaborators, people on the hallway down the lab (optional), referees and editors (vide infra) have already (hopefully) done it (properly). Still I put on my scientist badge and question everything I critically read in the results section trying thus to understand how did the authors reached their conclusions and asking myself if I could come up with something entirely different. No? OK, how about something slightly different? Still no? Well, do I agree with the authors on their findings and their observed results? And so on. I like thinking that my critical reading process resembles the Self Consistent Field method which iteratively reaches the best wavefunction for a set of certain given conditions, but it never reaches the exact one.

The methodology section is a bit tricky, specially when it comes to computational chemistry. Back when I was a grad student, working in an inorganic chemistry lab, I’d only read the methodology if I had any plans of reproducing the experiment, other than that I didn’t care too much if reagents were purchased from Aldrich or Fluka or if the spectrophotometer was a Perkin Elmer one, I just expected authors to have purified their reagents prior to usage and calibrated all spectrophotometers. Now in computational chemistry I read about the methods employed, which functional and what basis set were used and why were they selected are my most frequent questions, but the level of theory is usually stated in the abstract. I also take a look at what methods were used to calculate which properties; these questions are important when we have to validate our trust in the results in front of us.

Finally, I seldom read the introduction because, if the paper is relevant to my own research, I don’t need to read why is important or interesting, I’m already sold on that premise! that is why I’m reading the paper in the first place! If both me and the author act in bona fide, we both already know what the state of the art is, so lets move on because I have a ton of other papers to read. Hence, I read the introduction only when I’m trying to immerse myself in a new field or when reading something that seems interesting but which has little to do with my area of expertise. There is another reason why I almost never read introductions and that is that, even when I try to work in bona fide, there are a lot of people out there who don’t. Twice have I received the reviews from a mysterious referee who believes it would serve the work a great deal to cite two, maybe three, other papers which he or she lists for your convenience, only to find out that they all belong to the same author in each case and that they are not quite entirely related to the manuscript.

In the title of this post I also try to address the writing of a scientific paper, although I’m not an authority on it, I think today’s key phrase is bona fide. So to young and not so young scientists out there I’d ask you to write in bona fide, please. Be concise. Be convincing. Be thorough and be critical. This is science we are doing, not stamp collecting. It shouldn’t be about getting all sorts of things out there, it is about expanding the knowledge of the human race one paper at a time. But we are humans; therefore we are flawed. More and more cases of scientific misconduct are found throughout the literature and nowadays, with the speed of blogging and tweeting, we can point at too many of them. The role of bloggers in pointing this frauds, of which I’ve written before here, is the subject of recent controversy and possibly the topic of a future post. We are all being scrutinized in our work but that shouldn’t be an excuse to make up data, tinker or temper with it, to push our own personal agendas or to gain prestige in an otherwise wild academic environment.

I for one may never publish in Science or Nature; I may never be selected for any important prize, but even the promise of achieving any of those is not worth the guilt trip of lying to an entire academic society. I try then, to always remember that science is not about getting the best answers, but about posing the right questions.

What is your own style for reading papers? Any criticism to my style? How different is the style of a grad student from that of a researcher?

As usual thanks for reading, rating and commenting!

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