Posts Tagged ‘energy difference’

Molecule orbitals as indicators of reactivity: bromoallene.

Thursday, September 1st, 2016

Bromoallene is a pretty simple molecule, with two non-equivalent double bonds. How might it react with an electrophile, say dimethyldioxirane (DMDO) to form an epoxide?[1] Here I explore the difference between two different and very simple approaches to predicting its reactivity. bromoallene

Both approaches rely on the properties of the reactant and use two types of molecule orbitals derived from its electronic wavefunction. The first of these is very well-known as the molecular orbital (MO), which has the property that it tends to delocalise over all the contributing atoms (the “molecule”). MOs are often used in this context; the highest energy occupied MO is thought of as being associated with the most nucleophilic (electron donating) regions of the molecule and so such a HOMO would be expected to predict the region of nucleophilic attack. The second is known as the natural bond orbital (NBO), which is evaluated in a manner that tends to localise it on bonds (the functional groups or reaction centres) and atom centres. What do these respective orbitals reveal for bromoallene? 

The MOs
HOMO, -0.3380 HOMO-1, -0.3692 au
Click for 3D

Click for 3D
Click for 3D

Click for 3D
The NBOs
HONBO, -0.3769 HONBO-2, -0.3898
Click for 3D

Click for 3D
Click for 3D

Click for 3D

The table above shows the energies (in Hartrees) of the four relevant orbitals. The less negative (less stable) the orbital, the more nucleophilic it is. The (heavily) delocalized HOMO is located on the C=C bond bond carrying the C-Br bond, Δ1,2 alkene, but it also has a large component on the Br. The more stable HOMO-1 is located on the C=C bond located away from the Br, the Δ2,3 alkene and also with a (different type of) component on the Br.

In contrast, the HONBO is located on the Δ2,3 alkene and it is the HONBO-2 that is on the Δ1,2 alkene. Both these orbitals have very little “leakage” onto other atoms, they are almost completely localised.

Well, now we have a problem since these two analyses lead to diametrically opposing predictions! So what does experiment say? A recent article[1] addresses this issue by isolating the initially formed epoxide from reaction with DMDO and characterising it using crystallography. But here comes the catch; such isolation only proved possible if the allene was also substituted with large sterically bulky groups such as t-butyl or adamantyl. And the isolated product was the Δ1,2 epoxide. So does that mean that the MO method was correct and the NBO method wrong? Well, not necessarily. Those large groups play an additional role via steric effects. To factor in such effects one has to look at the transition state model for the reaction rather than depending purely on the reactant properties. And the steric effects in this case appear to win out over the electronic ones.[1]

The Klopman[2]-Salem[3] equation (shown in very simplified, and original, form below for just the covalent term) casts some light on what is going on. This term is a double summation over occupied/unoccupied (donor-acceptor) orbital interactions, involving the coefficients of the orbitals (the overlap integrals in effect) in the numerator and the energy difference between the occupied/unoccupied orbital pair as denominator.

KS1

Performing such a double summation is rarely attempted; instead the equation is reduced to just one single term involving the donor of highest energy and the acceptor of lowest energy, ensuring the energy difference is a minimum and hence the term itself is (potentially) the largest in the summation. There is still the issue of the orbital coefficients, and here we get to the crux of the difference between the use of MOs and NBOs. You can see by inspection that the two π-MOs for bromoallene have different coefficients on the two atoms of interest, the two carbons of the double bond. One really has to evaluate the size of this term in the summation by using quantitative values for the respective coefficients and to very probably include the further terms in the summation for any other orbitals which also have significantly non-zero coefficients on these two atoms. But with the NBOs, the localisation procedure used to derive them has reduced the coefficients to just the carbon atoms and effectively no other atoms; all the other terms in the double summation in effect do drop out entirely. So with NBOs, the only number that matters is the energy difference between the occupied/empty orbitals (the denominator). But since the acceptor (the electrophile, DMDO in this case) is the same for both regiochemistries, things reduce even further to just comparing the donor energies for the two alternatives (Table above). The higher/less stable of these will have the greater contribution in the Klopman-Salem equation.

This little molecule teaches the important lesson that electronic and steric effects both play a role in directing reactions, and in this system they may well oppose each other. Simple interpretations based on reactant orbitals may give only a partial and even potentially misleading answer.

References

  1. D. Christopher Braddock, A. Mahtey, H.S. Rzepa, and A.J.P. White, "Stable bromoallene oxides", Chemical Communications, vol. 52, pp. 11219-11222, 2016. https://doi.org/10.1039/c6cc06395k
  2. G. Klopman, "Chemical reactivity and the concept of charge- and frontier-controlled reactions", Journal of the American Chemical Society, vol. 90, pp. 223-234, 1968. https://doi.org/10.1021/ja01004a002
  3. L. Salem, "Intermolecular orbital theory of the interaction between conjugated systems. I. General theory", Journal of the American Chemical Society, vol. 90, pp. 543-552, 1968. https://doi.org/10.1021/ja01005a001

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Bond stretch isomerism. Did this idea first surface 100 years ago?

Tuesday, February 9th, 2016

The phenomenon of bond stretch isomerism, two isomers of a compound differing predominantly in just one bond length, is one of those chemical concepts that wax and occasionally wane.[1] Here I explore such isomerism for the elements Ge, Sn and Pb.

In one earlier post, I noted a form of bond stretch isomerism that can arise from a Jahn-Teller distortion ending in two different geometries in which one or more pairs of bonds swap short/long lengths. Examples include substituted cyclo-octatetraenes[2] and octahedral d9-Cu(II) complexes.[3] A more interesting seminal possibility was implied by G. N. Lewis a century ago when discussing the arrangement of electrons in a (carbon-carbon) triple bond.[4]

lewis1
*It took ~50 years to prove this assertion wrong.[5]

In a commentary, I reported the results of a search of the crystal structure database for the geometries associated with RX≡XR systems (X= C, Si, Ge, Sn, Pb). Here I focus the search[6] specifically for X=Sn,Ge; this version of bond stretch isomerism also allows angles to change (= rehybridisation at atoms) in order to provide a mechanism for a barrier separating the two forms.

For X=Sn, note the presence of up to three clusters, although the relatively low number of hits makes the statistics less certain.

  1. The hotspot cluster centered around angles of 125° and a Sn-Sn distance of ~2.6Å.
  2. Another with angles of <100° and Sn-Sn distances of ~3.3Å.
  3. A third with angles of <100° and Sn-Sn distances of 2.8Å, which may or may not be a genuine unique form of bonding.

This pattern was commented on in 2010 by Power[7], whose group synthesized most of the examples in the hits above.‡ A plot of compounds with Ge-Ge bonds reveals both similarity with (two, possibly three clusters) and difference from (the clusters are closely spaced in terms of the Ge-Ge bond length, but separated in terms of angle) Sn.†

GeGe

Time for some computations (which at least will remove random errors in the geometry). I selected the only known example of an RPb-PbR compound[8] as a seed and put it through a B3LYP+D3/Def2-TZVPP calculation (with 172 atoms and 2920 basis functions, this is a relatively large calculation!), which reproduces the known structure pretty well (table).

QIMQUY

So what about another bond stretch isomers? The Pb=Pb variation is indeed a stable minimum around 28.0 kcal/mol above the known structure, which seems to put this form out of experimental reach (with this ligand/aryl group at least). With Sn for the same aryl ligand, the energy difference is smaller (~15.8 kcal/mol for this ligand; Powers reports other systems where the energy difference may be only ~5 kcal/mol). Judging by the distribution of the 13 hits recovered from the CSD search, both bond stretch isomers may be accessible experimentally. The calculations show that the GeGe bond isomers are much closer in energy than SnSn (for this ligand). For all three metals however, the calculated difference in the metal-metal length for the two isomers is ~0.45 – 0.52Å. This strongly suggests that whereas the SnSn plot above is demonstrating bond length isomerism, the GeGe plot may not be; at least not of the same type that the calculations here are revealing (via the Wiberg bond orders).

System Relative energy XX distance RXX angle Wiberg bond order DataDOI
Pb=Pb +28.0 2.767 118.7 1.666 [9]
Pb-Pb 0.0 3.215 (3.188)[8] 93.7 (94.3)[8] 0.889 [10]
Sn=Sn +15.8 2.640 123.1 1.911 [11]
Sn-Sn 0.0 3.126 95.5 0.892 [12]
Ge=Ge +0.5 2.263 125.2 2.138 [13]
Ge-Ge 0.0   2.777 99.7 0.866 [14]

No doubt the particular bond length form is being facilitated by the nature of the ligand and the steric interactions therein imparted, both repulsive AND attractive. These interactions can be visualised via NCI (non-covalent-interaction) plots (click on the image to obtain a rotatable 3D model). First Pb-Pb followed by Pb=Pb. Note how in both cases, the PbPb region is enclosed in regions of weak attractive dispersion interactions, which however avoid the "hemidirected" inert Pb lone pairs.[15]

Pb-Pb Pb=Pb

So in the end we have something of a mystery. There is evidence from crystal structures that at least two bond-stretch isomers of RSnSnR compounds can form, but the calculations indicate that the Sn=Sn form is significantly higher in energy (although not impossibly so for thermal accessibility). Conversely, the Ge=Ge equivalent is very similar in energy to a Ge-Ge form with a significantly longer bond length, but there seems no crystallographic evidence for such a big difference in bond lengths. Perhaps the answer lies with the ligands?

It seems particularly appropriate on the centenary of G. N. Lewis' famous paper in which he clearly notes the possibility of three isomeric forms for the triple bond, to pay tribute to the impact his suggestions continue to make to chemistry.

‡The individual entries can be inspected via the following dois: [16],[17],[18],[19],[20],[21],[22],[23],[24],[25]

†You can view individual entries via the following DOIs: [26],[27],[28],[29],[30],[31],[32],[33],[34],[35]

References

  1. J.A. Labinger, "Bond-stretch isomerism: a case study of a quiet controversy", Comptes Rendus. Chimie, vol. 5, pp. 235-244, 2002. https://doi.org/10.1016/s1631-0748(02)01380-2
  2. J.E. Anderson, and P.A. Kirsch, "Structural equilibria determined by attractive steric interactions. 1,6-Dialkylcyclooctatetraenes and their bond-shift and ring inversion investigated by dynamic NMR spectroscopy and molecular mechanics calculations", Journal of the Chemical Society, Perkin Transactions 2, pp. 1951, 1992. https://doi.org/10.1039/p29920001951
  3. W. Zhang, L. Chen, R. Xiong, T. Nakamura, and S.D. Huang, "New Ferroelectrics Based on Divalent Metal Ion Alum", Journal of the American Chemical Society, vol. 131, pp. 12544-12545, 2009. https://doi.org/10.1021/ja905399x
  4. G.N. Lewis, "THE ATOM AND THE MOLECULE.", Journal of the American Chemical Society, vol. 38, pp. 762-785, 1916. https://doi.org/10.1021/ja02261a002
  5. F.A. Cotton, "Metal-Metal Bonding in [Re<sub>2</sub>X<sub>8</sub>]<sup>2-</sup> Ions and Other Metal Atom Clusters", Inorganic Chemistry, vol. 4, pp. 334-336, 1965. https://doi.org/10.1021/ic50025a016
  6. H. Rzepa, "Crystal structures containing Sn...Sn bonds", 2016. https://doi.org/10.14469/hpc/249
  7. Y. Peng, R.C. Fischer, W.A. Merrill, J. Fischer, L. Pu, B.D. Ellis, J.C. Fettinger, R.H. Herber, and P.P. Power, "Substituent effects in ditetrel alkyne analogues: multiple vs. single bonded isomers", Chemical Science, vol. 1, pp. 461, 2010. https://doi.org/10.1039/c0sc00240b
  8. L. Pu, B. Twamley, and P.P. Power, "Synthesis and Characterization of 2,6-Trip<sub>2</sub>H<sub>3</sub>C<sub>6</sub>PbPbC<sub>6</sub>H<sub>3</sub>-2,6-Trip<sub>2</sub> (Trip = C<sub>6</sub>H<sub>2</sub>-2,4,6-<i>i</i>-Pr<sub>3</sub>):  A Stable Heavier Group 14 Element Analogue of an Alkyne", Journal of the American Chemical Society, vol. 122, pp. 3524-3525, 2000. https://doi.org/10.1021/ja993346m
  9. H.S. Rzepa, "C 72 H 98 Pb 2", 2016. https://doi.org/10.14469/ch/191856
  10. H.S. Rzepa, "C 72 H 98 Pb 2", 2016. https://doi.org/10.14469/ch/191873
  11. https://doi.org/
  12. H.S. Rzepa, "C 72 H 98 Sn 2", 2016. https://doi.org/10.14469/ch/191881
  13. H.S. Rzepa, "C 72 H 98 Ge 2", 2016. https://doi.org/10.14469/ch/191882
  14. H.S. Rzepa, "C 72 H 98 Ge 2", 2016. https://doi.org/10.14469/ch/191883
  15. M. Imran, A. Mix, B. Neumann, H. Stammler, U. Monkowius, P. Gründlinger, and N.W. Mitzel, "Hemi- and holo-directed lead(<scp>ii</scp>) complexes in a soft ligand environment", Dalton Transactions, vol. 44, pp. 924-937, 2015. https://doi.org/10.1039/c4dt01406e
  16. Jones, C.., Sidiropoulos, A.., Holzmann, N.., Frenking, G.., and Stasch, A.., "CCDC 892557: Experimental Crystal Structure Determination", 2012. https://doi.org/10.5517/ccyys5t
  17. Phillips, A.D.., Wright, R.J.., Olmstead, M.M.., and Power, P.P.., "CCDC 187521: Experimental Crystal Structure Determination", 2002. https://doi.org/10.5517/cc6942p
  18. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771267: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwklt
  19. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771268: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkmv
  20. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771270: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkpx
  21. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771271: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkqy
  22. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771272: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkrz
  23. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771274: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkt1
  24. Fischer, R.C.., Pu, Lihung., Fettinger, J.C.., Brynda, M.A.., and Power, P.P.., "CCDC 624216: Experimental Crystal Structure Determination", 2007. https://doi.org/10.5517/ccnyk04
  25. Pu, Lihung., Phillips, A.D.., Richards, A.F.., Stender, M.., Simons, R.S.., Olmstead, M.M.., and Power, P.P.., "CCDC 221953: Experimental Crystal Structure Determination", 2004. https://doi.org/10.5517/cc7fysc
  26. Sasamori, Takahiro., Sugahara, Tomohiro., Agou, Tomohiro., Guo, Jing-Dong., Nagase, Shigeru., Streubel, Rainer., and Tokitoh, Norihiro., "CCDC 1035078: Experimental Crystal Structure Determination", 2014. https://doi.org/10.5517/cc13r2mk
  27. Sidiropoulos, A.., Jones, C.., Stasch, A.., Klein, S.., and Frenking, G.., "CCDC 749451: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cct4vvm
  28. Shan, Yu-Liang., Yim, Wai-Leung., and So, Cheuk-Wai., "CCDC 1019495: Experimental Crystal Structure Determination", 2015. https://doi.org/10.5517/cc136vy3
  29. Sugiyama, Y.., Sasamori, T.., Hosoi, Y.., Furukawa, Y.., Takagi, N.., Nagase, S.., and Tokitoh, N.., "CCDC 297827: Experimental Crystal Structure Determination", 2006. https://doi.org/10.5517/cc9zxbh
  30. Stender, M.., Phillips, A.D.., Wright, R.J.., and Power, P.P.., "CCDC 180660: Experimental Crystal Structure Determination", 2002. https://doi.org/10.5517/cc61zry
  31. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771273: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwks0
  32. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771269: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwknw
  33. Peng, Yang., Fischer, R.C.., Merrill, W.A.., Fischer, J.., Pu, Lihung., Ellis, B.D.., Fettinger, J.C.., Herber, R.H.., and Power, P.P.., "CCDC 771266: Experimental Crystal Structure Determination", 2010. https://doi.org/10.5517/cctwkks
  34. Jones, C.., Sidiropoulos, A.., Holzmann, N.., Frenking, G.., and Stasch, A.., "CCDC 892556: Experimental Crystal Structure Determination", 2012. https://doi.org/10.5517/ccyys4s
  35. Jones, C.., Sidiropoulos, A.., Holzmann, N.., Frenking, G.., and Stasch, A.., "CCDC 892555: Experimental Crystal Structure Determination", 2012. https://doi.org/10.5517/ccyys3r

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Oxime formation from hydroxylamine and ketone: a (computational) reality check on stage one of the mechanism.

Sunday, September 23rd, 2012

The mechanism of forming an oxime from nucleophilic addition of a hydroxylamine to a ketone is taught early on in most courses of organic chemistry. Here I subject the first step of this reaction to form a tetrahedral intermediate to quantum mechanical scrutiny.

  1. The first decision is to decide which atom of the hydroxylamine acts as the nucleophile. Reaction 1 shows the oxygen and reaction 2 the nitrogen. The text books will tell you that nitrogen nucleophiles are better than oxygen ones. This is because nitrogen is less electronegative than oxygen (it has a smaller nuclear charge) and so binds its single lone pair less tightly than oxygen does its two lone pairs. Sometimes the Klopman-Salem equation is invoked, which tells you that the reactivity is directly proportional to the overlap between the donor MO and the (empty) acceptor MO, and inversely proportional to the energy gap between these two orbitals. Nitrogen wins out because its lone pair is “larger” and hence overlaps better, and because its donor MO energy is higher than oxygen and hence the energy gap between it and the π* C=O acceptor is lower. 
  2. Reality check: We need to construct a suitable transition state for both possibilities, and then compare their free energies. There is a choice of choosing a stepwise pathway (the one shown in all the text books) in which the bond from N or O to C is formed in an initial step, and then followed by a step often just labelled PT to transfer the proton using solvent molecules. These two steps can also be conflated into a single concerted mechanism involving a 6-membered ring transition state. Quantum mechanically, this latter option has the advantage of avoiding any great build up of charge separation at any stage in the mechanism, but has the disadvantage that the entropic loss at the transition state is greater (although “borrowing” a water molecule from a bulk solvent for this purpose is easier than doing so from an infinite distance away).
    1. Shown below is a ωB97XD/6-311G(d,p)/SCRF=water calculation of the transition state for N-attack. It has a dipole moment of 6.2D, which is really quite small, and far from that expected for the zwitterionic intermediate shown in the stepwise mechanism (that would be between 15-30D).

      Cyclic transition state for N-attack. Click for animation of transition mode.

    2. The intrinsic reaction coordinate shows a concerted reaction with quite a small barrier. It is small because the nitrogen is in fact a super-nucleophile, its nucleophilicity has been augmented over that of a simple amine by a so-called α-effect from the adjacent two pairs of lone pairs on the oxygen activating the nitrogen lone pair by lone-pair repulsions. 
    3. The gradient norm along the coordinate also shows an almost synchronous reaction. The only blip occurs at around IRC +1.3, and this corresponds to the transfer of a proton from NH to a water molecule. An earlier proton transfer from water to the carbonyl oxygen was essentially synchronous with formation of the N-C bond. This synchronicity is what helps avoid any large build up of charge separation. For this reason, I cannot help but feel that the text books could absorb this lesson and show a cyclic concerted reaction mechanism as a probable alternative to two stepwise processes.
  3. Next, O-attack. The IRC for this isomeric mode shows a significantly higher barrier compared to N (the computed relative free energies show the O to be higher by 8.3 kcal/mol than the N) and smaller exothermicity. It reveals even greater synchrony of the two proton transfers with the O-C bond formation. So we have a reality check of the text-books on this point in the form of an energy difference, which is always useful.

    O-attack. Click for animation of reaction mode.
  4. Now that our proton transfers are involved in the mechanism, it is time to take a closer look at the geometry of these transfers. On this point, the text books tell us that the most favourable geometry for a proton transfer is having the proton co-linear with the two oxygens. Whilst this is largely true for the geometries shown above, the resulting 6-membered ring as a result adopts a triangular shape, which is not ideal for the bond angles. This could be solved by incorporating a second water molecule, to give us model 3 shown above.
    1. A second water molecule can be placed in two alternative positions. The first simply solvates the 6-ring transition state. The second actively participates via an enlarged 8-membered ring transition state. It turns out that the latter is lower by 4.5 kcal/mol in free energy, largely due to the far better bond angles and the almost exactly linear proton transfers now possible.

      O-Transition state with two water molecules, one merely hydrogen bonding to the 6-ring (magenta arrow).

      O-Transition state with two water molecules, both part of a cyclic transition state.
    2. So the following is our best model. It is 10.4 kcal/mol lower in free energy than the isomeric O-attack transition state. The timing of the bonds shows that N-C formation coincides with the first proton transfer to the carbonyl oxygen, followed by an O to O proton transfer and finally N to O. The dipole moment at the transition state is 5.9D, revealing little explicit charge separation.

      N-attack via an 8-ring transition state. Click to view animation of reaction mode.

It is worth concluding this exploration by reiterating that the models above are not complete. A bulk solvent would allow (statistical) participation of more than just two solvent molecules, and the dynamics of such a (very complex) process has yet to be explored. But I hope what you see here is a bit closer to “reality” than many a text-book author has when they illustrate their books.

doi:10042/a3uxl

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Driving the smallest car ever made: a chemical perspective.

Thursday, November 10th, 2011

Fascination with nano-objects, molecules which resemble every day devices, is increasing. Thus the world’s smallest car has just been built. The mechanics of such a device can often be understood in terms of chemical concepts taught to most students. So I thought I would have a go at this one!

A molecular car (from 10.1038/nature10587)

The car comprises a single (relatively small) molecule, shown above as the authors represented it. The motion along a surface comprised of copper atoms is driven by light as fuel coupled with encouragement from an STM probe. The distance travelled in a straight line was about 6nm in ten steps (note the nanodistance), although the average speed for the complete journey is not recorded. It is probably safe to say it was not recorded using a speed camera!

The car rattling along a copper surface (grey).

The chemistry is shown below. The car has four wheels (the fluorene units) which rotate about an C=C double bond axle using light as the fuel (a configurational change). The component labelled helix inversion can also be described by the chemical name atropisomerism, a topic I dealt with earlier with the example of Taxol and which is a conformational change.

The nitty-gritty of the car's engine.

These two processes are used to rotate the wheels in the sequence shown below (after which the wheels return to their starting point).

The four stages of powering the car (from 10.1038/nature10587)

I set out to build the car by optimising the 3D geometry of the molecule. This so that I could view the device from any direction (not just the one represented in the diagrams above). I also felt it important to estimate the change in energy of the car as the wheels rolled (something not touched upon in the original article). A good place to start would be to raid the supplementary information associated with the article. This comprises a PDF document and four movies. As it happens, none of these contain 3D coordinates for the molecule. Well, in truth this is not unusual, and I am used to such absence by now. Ah well, I would start from the top diagram, which is a schematic 2D representation of the molecule. As you can read in this post, such representations can often be illusory, or even contradictory. One is indeed lucky if they are free of ambiguity. Thus:

  1. The stereogenic centres are fine, they are labelled (R) and (S), and they provide an important aspect of the mechanism for allowing the motions of the four wheels to be coordinated such that the car drives in a straight line. Much is made of this aspect in the article.
  2. It is the atropisomerism that starts to cause problems. Here the diagram contains emboldened bonds carved into a benzene ring. This convention was first proposed by Hubert Maehr in 1985, but his intended use has since been much abused. As I fear it is here. Although it is difficult to be certain, the benzo groups in the car are annotated with several Maehr-like emboldened bonds, and a few non-Maehr wedged bonds as well. It is all meant to indicate perspective, and probably not intended in the Maehr sense at all.
  3. That latter feeling is reinforced when the benzo groups of the fluorene unit are annotated with dashed bonds replacing the single bonds in the Kekule resonance structure. Normally, a C- – -C is taken to indicate a breaking, or transition bond, but here it is again just an attempt at perspective (and a new addition to the bond menagerie).

Well, it is possible to build a 3D model armed with these instructions (although it has to be done visually, with constant comparisons with the space fill representations in the article).

  1. Here is my take on the starting point for the car:

    The initial conformation of the molecular car. Click for 3D.

  2. The car starts its journey by a light-driven rotation of the C=C bonds to form an isomer (about 8 kcal/mol higher according to my estimate using PM6).

    Car after step 1, double bond isomerisation. Click for 3D.

  3. There is then an STM-induced helix inversion, or atropisomerism. The two benzo groups are induced to swap over, much in the manner of bi-phenyls. The energy at this point is identical to the starting position. It is worth noting that the molecule was not returned to this position by reversing the first C=C rotation, but by two quite different operations (light and STM-electrons). I presume this was done to ensure the wheels turn in a constant direction, and do not simply flip back and forth randomly.

    Car after step 2, helix inversion. Click for 3D.

  4. A final light-induced twist of the double bond (the energy is again about 8 kcal/mol higher than the start point)

    Car after step 3, double bond isomerism. Click for 3D.

  5.  and another  STM-induced helix inversion returns the car to ~0.6nm on from its starting position.
So to understand nanotechnology and nano-sized objects, all you need is a good training in introductory chemistry! But a plea please to nano-scientists. Could you please include 3D coordinates for your wonderful machines. Movies are fine, but to really see what is going on, I would suggest you need proper 3D models (not least because you can then use these immediately to test my assertions about the energies of the various conformations).
Oh, I cannot resist observing that the group reporting this work probably do not ride motorcycles!

Postscript: The optimised ωB97XD/6-31G(d) geometries for the two poses of the car are to be found at 10042/to-10227 and 10042/to-10219  The  total energy difference is  15.5 kcal/mol (compared with 8 at the  PM6 level).

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