Posts Tagged ‘physicist’

Are close H…H contacts bonds?

Friday, October 7th, 2011

The properties of electrons are studied by both chemists and physicists. At the boundaries of these two disciplines, sometimes interesting differences in interpretation emerge. One of the most controversial is that due to Bader (for a recent review, see DOI: 10.1021/jp102748b) a physicist who brought the mathematical rigor of electronic topology to bear upon molecules. The title of his review is revealing: “Definition of Molecular Structure: By Choice or by Appeal to Observation?”. He argues that electron density is observable, and that what chemists call a bond should be defined by that observable (with the implication that chemists instead often resort to arbitrary choice). Here I explore one molecule which could be said to be the focus of the differences between physics and chemistry; cis-but-2-ene.

Two possible conformations of cis but-2-ene.

The structure of this system has been determined by electron diffraction to exhibit a H…H distance of ~2.1Å as in (a), DOI: 10.3891/acta.chem.scand.24-0043. Why is this of interest? Because a rotational alternative, shown as (b) could result in a significantly longer H…H distance (~ 2.6Å). Now bear in mind that the van der Waals radius of hydrogen is estimated at ~1.2Å, and that two hydrogens will be most strongly attracted by dispersion forces when separated by ~2.4Å. As they get closer, that attraction will be counterbalanced by a repulsion, which will eventually win out. Structure (b) does not benefit from H…H dispersion attractions, but are the hydrogens in structure (a) too close to do so as well?

Well, let us adopt Bader’s approach, and look at the topology (QTAIM) of the electronic distribution in structure (a). The features to concentrate on are the purple dots, which in this analysis have been named bond critical points (BCP)  and the single yellow sphere, which is a ring critical point (RCP). There are two other types of critical points, which I will call nuclear attractors (NACP) and cage points (CCP). The total occurrences of all these critical points is determined by a topological theorem (Poincare-Hopf), which states that NACP-BCP+RCP-CCP=1. You can see below that the H…H region is indeed connected by a bond critical point (none of the other purple dots are controversial). To a physicist, this is a real feature of the (observable or in this instance the calculated) electron density. In effect, it is a topological bond. Unfortunately, chemists like to think of bonds as entities which result in stability; a bond contributes to the stability of a molecule (and an anti-bond, should such exist, to instability). Hence aromaticity (=stability) vs anti-aromaticity (=instability). Chemists, by choice, might prefer not to call the H…H region a bond because it is probably not contributing to the stability of the molecule. Of course, the two camps are arguing about different things; the topology of the electron density ρ(r) vs the energy of the molecule.

QTAIM topological analysis of cis but-2-ene. Click for 3D.

Somewhat ignored in this discussion up to this point has been the yellow dot, the RCP. Firstly, notice how close it is to the H…H BCP. Secondly, notice from the Poincare-Hopf relationship that if you remove BOTH of these points, the theorem is still satisfied; a BCP and a RCP are said to be capable of annihilating each other (much like and electron and a positron might). So perhaps a chemical picture might emerge if you choose to consider BOTH points together, rather than just the BCP?

I have done so below using the NCI (non-covalent interaction) procedure (which I have commented on in many other posts here). The NCI surface is shown below, embedded within the NCI surface as purple dots are the BCP and RCP discussed above. Now, the NCI method cleverly attempts to ascertain whether a region is attractive or repulsive, and it colour codes the surface accordingly. In the below, blue is deemed attractive, and red repulsive. We immediately see that the H…H BCP is embedded in an attractive region, but the adjacent RCP is embedded in a repulsive region. Whatever attraction the BCP might be experiencing is negated by the repulsion the RCP has. The two cancel (annihilate). Taken together, the H…H region is probably repulsive (ways of quantifying how NCI regions integrate are being investigated and will be discussed in a future post). Perhaps this manner of looking at it satisfies both the physicists and the chemists?

The NCI surface for cis but-2-ene. Click for 3D.

Well, not quite. A chemist would still ask why structure (a) is preferred over structure (b), if the wider H…H region is not deemed attractive (I call it a region rather than a bond in a probably futile attempt to avoid controversy). Actually, the answer might be in how the two methyl groups each interact with the other part of the molecule, the alkene, and how that might depend on their orientation with respect to the alkene. But that analysis is for another post!

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Gravitational fields and asymmetric synthesis

Saturday, November 20th, 2010

Our understanding of science mostly advances in small incremental and nuanced steps (which can nevertheless be controversial) but sometimes the steps can be much larger jumps into the unknown, and hence potentially more controversial as well. More accurately, it might be e.g. relatively unexplored territory for say a chemist, but more familiar stomping ground for say a physicist. Take the area of asymmetric synthesis, which synthetic chemists would like to feel they understand. But combine this with gravity, which is outside of their normal comfort zone, albeit one we presume is understood by physicists. Around 1980, chemists took such a large jump by combining the two, in an article spectacularly entitled Asymmetric synthesis in a confined vortex; Gravitational fields and asymmetric synthesis (DOI: 10.1021/ja00521a068). Their experiment was actually quite simple. They treated isophorone (a molecule with a plane of symmetry and hence achiral) with hydrogen peroxide and then measured the optical rotation.

Asymmetric synthesis of Isophorone oxide

Conventional wisdom is that the oxygen can be delivered with equal probability to either face of the alkene, resulting in a racemic (equal) mixture of the two enantiomers of the epoxide. But if one enantiomer is formed in slightly greater amount than the other, the reaction is said to proceed asymmetrically, and the product will exhibit an optical rotation. Normally, such asymmetry is induced by carrying out the reaction in the presence of a chiral molecule or catalyst. Light too can be chiral, but these brave chemists decided to use gravity. More specifically, the earth’s gravitational field. In the Northern Hemisphere. The reaction was conducted in a centrifuge in three ways. With the spun tube horizontally, and then vertically spinning clockwise or anticlockwise. The first of these produced product which exhibited no optical rotation within experimental error (e.g +0.2 ± 0.3 mdeg). The second gave results with a positive rotation (e.g. 12.8 ± 0.3 mdeg) and the third a negative rotation (-2.2 ± 0.2 mdeg). They considered that the reaction was occurring in e.g. a clockwise vortex constituting a P-helix (the vortex in other words was chiral) interacting with the earth’s coriolis force.  They speculated (but did not do the experiment) that the reverse effect would be seen in the Southern Hemisphere. Their paper concluded with the grand speculation that prebiotic organic synthesis could have been partially asymmetric as a result of being conducted in a chiral gravitational field (nothing like aiming high!).

Shortly after this was published, a rebuttal appeared (DOI: 10.1021/ja00544a051) penned not by a synthetic chemist but a physicist. In truth, most of the four-paragraph article presents arguments few chemists are familiar with (and probably do not understand). Only one sentence, the very last, made the impact (and it sounds as if it was added as a throw-away afterthought). It simply stated that the magnitude of the earth’s field (in so-called natural units) suggested that a parameter ω related to the spinning velocity was ~10-21 and that the corresponding value that would be required to induce the asymmetry observed (which can be computed from e.g. ΔG = -RT Ln K) was 10-14. Put in rather plainer English, the earth’s magnetic field was seven orders of magnitude too weak to have the effect claimed for it. That last sentence on its own pretty much sunk the theory, and it is no longer thought that gravitational fields can induce asymmetry in reactions. I tell this story (which, as it happened thirty years ago is now largely forgotten), since seven orders of magnitude is quite a large mismatch! Chemists rarely have the opportunity to be so spectacularly wrong when they propose a theory. In reality, even two orders of magnitude is unusual.

It’s when you approach factors of say less than one order of magnitude (the nuances) that arguments about which interpretation is correct may break out. So which category might the subject of this post belong to? As I there noted, it’s all about whether the two carbon atoms separating carbon dioxide and cyclobutadiene in a crystalline lattice by a distance of 1.5Å are interacting by a covalent bond, or a van der Waals attraction. In terms of energies, most chemists agree that these differ by around two orders of magnitude. This, I suggest, does not come into the category of nuance!

For a nice review of asymmetric synthesis under physical fields, see here.

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