Category Archives: History of science

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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#RealTimeChem – Happy birthday DNA!


What a happy coincidence -if indeed it was- that #RealTimeChem week happened to coincide with the sixtieth anniversary of the three seminal papers published in Nature on this day back in 1953, one of which was co-authored by J. Watson and F. Crick; of course I mean the publication for the first time of the structure of deoxyribose nucleic acid, or DNA, as we now call it.

You can get the original Nature papers from 1953 here at: http://www.nature.com/nature/dna50/archive.html (costs may apply)

Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid 737

J. D. WATSON & F. H. C. CRICK
doi:10.1038/171737a0

Molecular Structure of Nucleic Acids: Molecular Structure of Deoxypentose Nucleic Acids 738
M. H. F. WILKINS, A. R. STOKES & H. R. WILSON
doi:10.1038/171738a0

Molecular Configuration in Sodium Thymonucleate 740
ROSALIND E. FRANKLIN & R. G. GOSLING
doi:10.1038/171740a0

Nature’s podcast released two episodes (called ‘pastcast’) to celebrate DNA’s structure’s birthday, one of them is an interview with Dr. Raymond Gosling who in 1953 worked under Dr. Rosalind Franklin at King’s College London in diffractometry of biological molecules. If you haven’t listened to them you can get them here at nature.com/nature/podcasts. Of course, the history around the discovery of DNA’s structure is not without controversy and it has been long argued that the work of Franklin and Gossling didn’t get all deserved credit from Watson and Crick. In their paper W&C acknowledge the contribution of the general nature of DNA from the unpublished results by Franklin’s laboratory but that is as far as they went, they didn’t even mention photo 51 which Crick saw at Wilkins laboratory, who in turn got it from Gossling at Franklin’s suggestion. Still, no one can deny that the helical structure with which we are now familiar is their work, and more importantly the discovery of the specific pairing, which according to Gossling was a stroke of genious that probably couldn’t have happened in his own group, but without Franklin’s diffraction and Gossling’s crystallization  there was little they could do. Details about the process used to crystallize DNA can be heard in the aforementioned podcast, along with an inspiring tale of hard work by Dr. Gossling. Go now and listen to it, its truly inspiring.

For me it was not the story of a helix, that I was familiar with; it was the story of the specific pairing of two hélices
– Dr. Raymond Gosling

Famous Photo 51 by Dr. Rosalind Franklin and Raymond Gosling (Source: Wikipedia)

The iconic Photo 51 by Dr. Rosalind Franklin and Raymond Gosling (Source: Wikipedia)

Above, the iconic Photo 51 taken by Franklin and Gossling (have you ever noticed how most scientists refer to Franklin just as Rosalind but no one refers to Watson as James? Gender bias has a role in this tale too) To a trained crystallographer, the helical symmetry is evident from the diffraction pattern but going from Photo 51 to the representation below was the subject of hard work too.

Modern DNA representation (Source: Wikipedia)

Modern DNA representation (Source: Wikipedia)

There are million of pages written during the last 60 years about DNA’s structure and its role in the chemistry of life; the nature of the pairing and the selectivity of base pairs through hydrogen bond interactions, an interaction found ubiquitously in nature; water itself is a liquid due to the intermolecular hydrogen-bonds, which reminds us about the delicate balance of forces in biochemistry making life a delicate matter. But I digress. Millions of pages have been written and I’m no position of adding a meaningful sentence to them; however, it is a fascinating tale that has shaped the course of mankind, just think of the Human Genome Project and all the possibilities both positive and negative! DNA and its discovery tale will continue to amaze us and inspire us, just like in 2011 it inspired the Genetech company to set a Guiness World Record with the largest human DNA helix.

Genetech SF, Cal. USA (Source worldrecordacademy.com)

Genetech SF, Cal. USA (Source worldrecordacademy.com)

Happy birthday, DNA!

Institute of Chemistry Library flood – UNAM


If a mind is a terrible thing to waste, then wasting a collective mind is an even more terrible thing. During the past weekend the library at the institute of chemistry suffered a flood caused by a broken pipe just above it, which incidentally happens to be the lab were I used to work as an undergrad student. When it comes to scientific journals, our institute still relies a lot on paper issues for the oldest numbers; we can order them online but it’s just easier to Xerox it at the library if you really need to read that old reference.

This morning the librarians were appalled when noticed not only the huge puddle on the floor but all the books and scientific journals that were dripping water from the shelves. The broken pipe has been fixed and the water on the floor has been mopped. It is now the books the ones that suffer the aftermath of this accident. Not only saving the information was important; wet paper is a great culture media for fungi which in turn could pose a health threat to all users. The administrative staff immediately got to work in recruiting academics and students to help the drying process: “Heal a book!“, they informally called it. Everyone grabbed an item and with the help of industrial blow dryers – the kind we use in chemistry labs to dry wet glassware – and an extraordinary amount of paper towels, each person got to dry the journals page by page.

I got an item that corresponded to the British journal New Scientist, which consisted of about fifteen issues from the year 1980. When I noticed the title in my hand I wanted to switch it. Should we save first those journals with the highest impact factor? or should we work on those that are most relevant to our own research? Should we throw away Chemical Abstracts now that the whole database is online? After all, New Scientist is a magazine which summarizes research that has already been peer reviewed and published; it is journalistic work, not peer reviewed science. But I was afraid to look pedantic so I got to work on drying it.

Kudos to the library staff on organizing in promptu “Heal a book!”

Students as well as the academic and administrative staff drying journals

Each person had their own technique. Some journals had their binding covers still in good shape so they were placed open standing on the floor in front of fans. Some placed paper towels carefully between pages and after a while they would remove them and then use the blow dryer. I thought that if I heated the edges of the paper and thus dried them, capillarity would drive the moisture in the innermost part of each page outwards. Didn’t quite work, at least not in a pragmatic time scale, so I went back to page by page.

I’m glad I did so. That way I was able to find some real pieces of history which could make any scientist nostalgic. For example: I took these photos with my iPod, and if you are by any chance reading this piece on an iPhone, you must find the following  picture about Swedish research endearing.

An ancient iPad or an edgy ‘Etch-a-Sketch‘?

Yes, online doodling games were already a thought back in 1980!

Are you subscribed to this blog? That means you got a notification by e-mail. So what? No big deal! Well, back in 1980 Britain was getting excited over a new form of comunication called the ‘Electronic Mail’ (available only at a couple of post offices). Besides, you wouldn’t have been able to get that message nor read this post on an HP Matrix Machine (you can’t even find a decent link in google about it nowadays!)

But scientists are not all about working, we like games too! So how about purchasing a ‘Hungarian Magic Cube‘ or a ‘Chess Computer‘?

An 80’s sensation!

E-chess

We also love a juicy piece of gossip. For instance, did you know that John Maddox was a controversial editor for Nature back in the 70’s who, as a student, went into chemistry because if he’d gone into physics he could’ve been drafted by the army in WWII to work on radars? Well me neither. But it seems that we should have known who he was, and now we do.

Sir John Maddox

There were many pieces of science news that nearly kept me in the library all night, if not for the fact that I had to drive 50 miles from Mexico City to my place in Toluca, but the one that captured my attention more than any other was the news of a European dream envisioned more than three decades ago; a dream from a group of scientists about looking for answers, like any other group of scientists, answers that are fundamental for the understanding of our universe and the understanding of matter, back when some of the biggest questions hadn’t even been fully posed, this group of visionaries agreed on taking the necessary steps to build an enormous subatomic-particle Supercollider for the European Center for Nuclear Research, better known as CERN.

The announcement of grand things to come

Back in 1980 I was already alive but I was only two years old. I could barely talk and had no idea what the word ‘future‘ meant, let alone what I’d become when it reached me. Now, even if I’m not a particle physicist I get excited about the news regarding the finding of the Higgs Boson and even if I’m not an astronomer I also get excited about pictures from the Curiosity Rover on Mars. I am a scientist. One out of hundreds of thousands or perhaps even millions, and this is part of my collective memory, the memory of the work of those who paved the road for us, those giants upon whose shoulders we struggle day by day to stand with dignity and against all odds. But here is the thing: those giants are actually made of dwarfs, millions of them; millions of us. Thousands and thousands of papers written, reviewed and published; papers that collectively gather the scientific experience summed up in rigorous experiments both successful and failed.

Preserving the information in those wet journals is important despite the fact you can get them all online. I hope one day a bored chemistry grad student goes to the library and browses old issues of New Scientist and other journals just for fun; they’ll go for a trip down a collective Memory Lane which will remind them that if they can dream it in the present, they can make it come true in the future.

2011, The International Year of Chemistry (IYC 2011)


IYC 2011In April 2006, during a IUPAC Executive Committee meeting, the idea for an international year of was first discussed. From that meeting a IUPAC committee was appointed to work along with UNESCO in the creation of the event and finally during 2008, the year 2011 was officially designated the International Year of Chemistry (IYC 2011); additionally 2011 marks the 100th anniversary of the Nobel Prize awarded to Madame Marie Curie so the IYC 2011 will also be devoted to celebrate the contributions of women to science in general and not only to chemistry. Furthermore, 2011 is also the 100th anniversary of the founding of the International Association of Chemical Societies so the benefits of international scientific cooperation will also be highlighted.

The International Year of Chemistry represents a great opportunity to celebrate, highlight and raise awareness about the extraordinary achievements of chemistry and how it has mold the way we live. The IYC 2011 motto is “Chemistry- Our life, our future”. To me this motto reflects how chemistry will help to solve the current problems our planet is going through (from global warming to alternative energy sources); I work at a research center that is ultimately supposed to be devoted to research in sustainable chemistry, so the appeal is huge! The main goal of the IYC 2011 is to increase the public appreciation of chemistry by reaching out for the general public (in the end, us chemists are already interested in chemistry) in a wide variety of activities that will range from conferences to hands-on experiments and other forms of interactive performances for people of all ages. Everyone can get actively involved by just visiting the official website (see below)

We live in times where science surrounds us yet people fear it, distrust it, argues it without foundations, school boards in first world countries dare to promote religious-like factoids in education. It is our duty as scientists to raise awareness about the importance of chemistry to the technological and cultural advancement of the human race, at least so next time some TV ad announces a chemicals-free product people raise their eyebrows.

Like every well respected institution around the world, here at UNAM we are organizing a series of events directed to celebrate the International Year of Chemistry. I’m already trying to organize a visit for some of the most brilliant people I had the pleasure and honor to meet and work with at Babes-Bolyai in Romania, hopefully we’ll build some academic bridges between our two institutions. Also a series of books on different aspects of chemistry (from the very scientific to the more philosophical kind) will be published by our university.

I encourage you to promote the events in your local scientific community, but also to raise awareness within your non-scientist friends. I will sign all my emails, twits, blog posts and Facebook updates with something like ‘2011, International Year of Chemistry’. What about you? Chemists of the world: Get involved!

Thanks for reading!

2011, International Year of Chemistry
http://www.chemistry2011.org

Pauling hybridization model


Is the C atom in methane sp3 hybridized because it’s tetrahedral or is it tetrahedral because it’s sp3 hybridized? It’s funny how many students think to this date that the correct answer is the latter; specially those working in inorganic chemistry. I ignore the reason for such trend. What is true is that most chemistry teachers seem to have lost links to certain historical facts that have shaped our scientific discipline; most of those lay in the realm of physics, maybe that’s why.

What Linus Pauling, in a very clever way, stated was that once you have a set of eigenvectors (orbitals) of the atomic Hamiltonian any combination of them will also be an eigenvector (which is normal since one of the properties of Hermitian operators is that they are linear); so why not making a symmetry adapted one? Let’s take the valence hydrogenoid orbitals (hydrogenoid being the keyword here) and construct a linear combination of them, in such a way that the new set transforms under the irreducible representations of a given point group.  In the case of methane, the 2s and 2p orbitals comprise the valence set and their symmetry-adapted-linear-combination under the Td point group constitutes a set of new orbitals which now point into the vertexes of a tetrahedron. Funny things arise when we move to the next period of the table; it has been a controversy for a number of years the involvement of empty d orbitals in pentacoordinated P(V) compounds. Some claim that they lay too high in energy to be used in bond formation; while others claim that their involvement depends on the nature (electronegativity mainly) of the surrounding substituents.

In many peer reviewed papers authors are still making the mistake of actually assigning a type of hybridization to set of valence orbitals of an atom based on the bond angles around it. Furthermore, it is not uncommon to find claims of intermediate hybridizations when such angles have values in between those corresponding to the ideal polyhedron. Symmetry is real, orbitals are not; they are just a mathematical representation of the electron density distribution which allows us to construct mind images of a molecule.

Linus Pauling is one of my favourite scientific historical figures. Not only did he build a much needed at the time bridge between physics and chemistry but he also ventured into biochemistry (his model of an alpha-helix for the alanine olygopeptide became the foundation to Watson & Cricks later double  helix DNA model), X-ray diffractometry, and humanities (his efforts in reducing/banning the proliferation of nuclear weapons got him the Nobel Peace Prize long after he had already received the Nobel Price in Chemistry). He was a strong believer of ortho-molecular nutrition, suggesting that most illnesses can be related to some sort of malnutrition. Linus Pauling and his book On the Chemical Bond will remain a beacon in our profession for the generations to come.

 

Disclaimer: The question above, with which I opened this post, was taken from an old lecture by Dr. Raymundo Cea-Olivares at UNAM back in the days when I was an undergraduate student.

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