One of the more controversial components of Bader’s Atoms-In-Molecules (AIM) theory is the contention that there is a one-to-one correspondence between the existence of a bond critical point and the existence of a chemical bond. I discuss this matter in my book and also in these posts (1 and 2). Lane and co-workers now examine this relationship with regard to hydrogen bonds.¹

They examine the topological structure of the electron density of the series 1,2-ethanediol 1, 1,3-propanediol 2, and 1,3-butanediol 3. They find a bond critical point (bcp) between the hydrogen of one hydroxyl group and the oxygen of the second hydroxyl group for the two large compounds 2 and 3. This forms a ring, and a ring critical point is located as well. However, for 1 they find no bond critical point associated with what might be the intramolecular hydrogen bond in 1. For all three diols, the OH stretching frequencies are diminished relative to monoalcohols. So geometrically and spectroscopically there appears to be a hydrogen bond, but rigorous application of Bader’s notion of bonding says that there is no “bond” in 1.

Lane and coworkers go on to show that the electron density in the three diols is really topologically identical, just differing in a matter of degree. They conclude that the existence of a bond critical point should not be the sole arbiter of bonding, but one of the criteria that can be utilized to assess bonding.

While I am not at all in conflict with this conclusion, the paper contains some issues that need be addressed. First off, “bonding” is not a concept of either-or, rather there is a continuum of bonding. Hydrogen bonding should not at all be confused with covalent or ionic bonding – it is dramatically weaker and so one might consider whether the bcp criteria is applicable at all. The authors really fall into this trap stating “… the absence of a BCP should not necessarily be considered evidence as to the absence of a chemical bond (emphasis mine).” Do we want to consider a hydrogen bond as a chemical bond?

I think the key element overlooked in this study is the strength of the “hydrogen bond”. While not determined in the study, undoubtedly the hydrogen bond strength increases in the order 1 < 2 < 3. What is really to be gained by arguing there is or is not a “hydrogen bond” in all or some of these three molecules? The ring-like conformation is the lowest energy conformation for all three. This is driven by some electrostatic attraction between the OH dipole of one hydroxyl group for the dipole of the second hydroxyl group. When do we want to call this attraction a hydrogen bond? What do we gain by not doing so for all three? If we understand that there is an energy continuum of hydrogen bonding, from weak to weaker, doesn’t that provide enough of a model to interpret and predict chemical structure and behavior?

References

(1) Lane, J. R.; Contreras-García, J.; Piquemal, J.-P.; Miller, B. J.; Kjaergaard, H. G. J. Chem. Theor. Comput. 2013, 9, 3263-3266, DOI: DOI: 10.1021/ct400420r.

InChIs

1: InChI=1S/C2H6O2/c3-1-2-4/h3-4H,1-2H2
InChIKey=>LYCAIKOWRPUZTN-UHFFFAOYSA-N

2: InChI=1S/C3H8O2/c4-2-1-3-5/h4-5H,1-3H2
InChIKey=YPFDHNVEDLHUCE-UHFFFAOYSA-N

3: InChI=1S/C4H10O2/c5-3-1-2-4-6/h5-6H,1-4H2
InChIKey=WERYXYBDKMZEQL-UHFFFAOYSA-N

A long sought-after data point critical to the non-classical cation story has finally been obtained. The elusive x-ray crystal structure of a norbornyl cation was finally solved.¹ The [C₇H₁₁]⁺[Al₂Br₇]^– salt was crystallized in CH₂Br₂ at low temperature (40 K). This low temperature was needed to prohibit rotation of the norbornyl cation within the crystal (the cation is near spherical and so subject to relatively easy rotation within the crystal matrix) and hydride scrambling among the three carbons (C₁, C₂, and C₆) involved in the non-classical cation structure.

The authors report a number of different structures, all very similar, depending on slight differences in the crystals used. However, the important features are consistent with all of the structures. The cation is definitely of the non-classical type (see Figure 1) with the basal C₁-C₂ bond length of 1.39 Å similar that in benzene and long non-classical C₁-C₆ and C₂-C₆ distances of 1.80 Å. These distances match very well with the MP2(FC)/def2-QZVPP optimized distances of 1.393 and 1.825 Å, respectively.

Figure 1. X-ray structure of norbornyl cation.

References

(1) Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation," Science 2013, 341, 62-64, DOI: 10.1126/science.1238849.

Circulenes are molecules where a central ring is composed of fused benzenoids. Corranulene can also be named [5]circulene and coronene is [6]circulene. In a previous post I discussed the topology of the circulenes. This earlier work suggested that [8]annulene 1 would have a saddle-shape. This hypothesis has now been confirmed with the synthesis of the substituted [8]circulene 2 by Wu and co-workers.¹

The x-ray structure does show a saddle geometry for 2. The central 8-member ring is tub-shaped, even more puckered that cyclooctatetraene (COT) itself, though the bonds in 2 are nearly of equal length. The bond lengths involving the central carbon atoms appear consistent with an [8]radialene-type structure.

The ωB97X-D/6-31G** optimized geometries of the parent compound 1 and the synthesized compound 2 are shown in Figure 1. These computed structures are very similar to each other, along with being very similar to the x-ray structure of 2.

1

2

Figure 1. ωB97X-D/6-31G** optimized geometries of 1 and 2.
(Don’t forget that you can click on these structures – and any other structure on my blog – to interactively manipulate and visualize them, something worth doing here!)

The computed NICS(0) (at HF/6-31+G* – I would really rather have seen these computed with some density functional, preferably at ωB97X-D/6-31G**) values for the six-member rings of both 1 and 2 are negative, ranging from -8.9 ppm to -4.0 ppm, indicating aromatic character. The NICS(0) value at the center of the 8-member ring is +9.8 ppm in 1 and +12.2 ppm in 2. The authors argue that this value cannot discriminate the 8-member ring from that in COT (NICS(0) = 1.98 ppm, the expected value for a non-aromatic ring) and [8]radialene (NICS(0) = -1.2 ppm, also an expected value for a non-aromatic ring). However, they are silent on whether this might actually imply some antiaromatic character to the 8-member ring, which would be consistent with the equivalent bond lengths around the ring.

The authors note that there should be a second isomer of 2 resulting from a flip of the tub. Variable temperature NMR does not show any change in the spectrum, though with a different substituted [8]circulene they do see some coalescence, suggesting a large flipping barrier of at least 20 kcal mol^-1. A computational search for this flipping/inversion might be interesting as the transition state is likely to not be planar.

References

(1) Feng, C.-N.; Kuo, M.-Y.; Wu, Y.-T. "Synthesis, Structural Analysis, and Properties of [8]Circulenes," Angew. Chem. Int. Ed. 2013, 52, 7791-7794, DOI: 10.1002/anie.201303875.

InChIs

1: InChI=1S/C32H16/c1-2-18-5-6-20-9-11-22-13-15-24-16-14-23-12-10-21-8-7-19-4-3-17(1)25-26(18)28(20)30(22)32(24)31(23)29(21)27(19)25/h1-16H
InChIKey=BASWMOIVIHXTRC-UHFFFAOYSA-N

2: InChI=1S/C96H80/c1-49-17-33-65(34-18-49)81-73-57(9)58(10)75-83(67-37-21-51(3)22-38-67)85(69-41-25-53(5)26-42-69)77-61(13)62(14)79-87(71-45-29-55(7)30-46-71)88(72-47-31-56(8)32-48-72)80-64(16)63(15)78-86(70-43-27-54(6)28-44-70)84(68-39-23-52(4)24-40-68)76-60(12)59(11)74(82(81)66-35-19-50(2)20-36-66)90-89(73)91(75)93(77)95(79)96(80)94(78)92(76)90/h17-48H,1-16H3
InChIKey=DEKWLSGHBADDAQ-UHFFFAOYSA-N