The role of dispersion in large systems is increasingly recognized as critical towards understanding molecular geometry. An interesting example is this study of acene dimers by Grimme.¹ The heptacene and nonacene dimers (1 and 2) were investigated with an eye towards the separation between the “butterfly wings” – is there a “stacked” conformation where the wings are close together, along with the “open” conformer?

The LPNO-CEPA/CBS potential energy surface of 1 shows only a single local energy minima, corresponding to the open conformer. B3LYP-D3 and B3LYP-NL, two different variations of dealing with dispersion (see this post), do a reasonable job at mimicking the LPNO-CEPA results, while MP2 indicates the stacked conformer is lower in energy than the open conformer.

B3LYP-D3 predicts both conformers for the nonacene dimer 2, and the optimized structures are shown in Figure 2. The stacked conformer is slightly lower in energy than the open one, with a barrier of about 3.5 kcal mol^-1. However in benzene solution, the open conformer is expected to dominate due to favorable solvation with both the interior and exterior sides of the wings.

open

stacked

Figure 1. B3LYP-D3/ef2-TZVP optimized structures of the open and stacked conformations of 2.

References

(1) Ehrlich, S.; Bettinger, H. F.; Grimme, S. "Dispersion-Driven Conformational Isomerism in σ-Bonded Dimers of Larger Acenes," Angew. Chem. Int. Ed. 2013, 41, 10892–10895, DOI: 10.1002/anie.201304674.

InChIs

1: InChI=1S/C60H36/c1-2-10-34-18-42-26-50-49(25-41(42)17-33(34)9-1)57-51-27-43-19-35-11-3-4-12-36(35)20-44(43)28-52(51)58(50)60-55-31-47-23-39-15-7-5-13-37(39)21-45(47)29-53(55)59(57)54-30-46-22-38-14-6-8-16-40(38)24-48(46)32-56(54)60/h1-32,57-60H
InChIKey=OYVUURMCCBPDLI-UHFFFAOYSA-N

2: InChI=1S/C76H44/c1-2-10-42-18-50-26-58-34-66-65(33-57(58)25-49(50)17-41(42)9-1)73-67-35-59-27-51-19-43-11-3-4-12-44(43)20-52(51)28-60(59)36-68(67)74(66)76-71-39-63-31-55-23-47-15-7-5-13-45(47)21-53(55)29-61(63)37-69(71)75(73)70-38-62-30-54-22-46-14-6-8-16-48(46)24-56(54)32-64(62)40-72(70)76/h1-40,73-76H
InChIKey=FTSMWBVFVPAXOB-UHFFFAOYSA-N

The singlet and triplet carbene is the topic of Chapter 4, especially sections 1 and 2. The ground state of methylene is the triplet, with one electron in the σ-orbital and one electron in the π-orbital, with the spins aligned. The lowest singlet state places the pair of electrons in the σ-orbital, and this state is about 9 kcal mol^-1 higher in energy than the triplet. The next lowest singlet state has one electron in each of the σ- and π-orbitals, with the spins aligned. The singlet state with both electrons in the π-orbital is the highest of these four states, some 60 kcal mol^-1 above the ground state triplet.

Hoffmann and Borden now pose the question “Can the doubly occupied π carbene (¹A₁-σ⁰π²) be the ground state with appropriate substitution?” The answer they find is yes!¹

The trick is to find a combination of substituents that will raise the energy of the σ-orbital and lower the energy of the π-orbital. The latter effect can be enhanced if the π-orbital can be a part of an aromatic (6e^–) ring.

Two of the best possibilities for identifying a ground state ¹A₁-σ⁰π² carbene are 1 and 2. The CASSCF/6-31G(d) optimized geometries of these two are shown in Figure 1. In 1, the nitrogen lone pairs act to destabilize the σ-orbital, while the aldehyde group acts as a withdrawing group to stabilize the π-orbital. The result is that the ¹A₁-σ⁰π⁶ state of 1 is predicted to be about 8 kcal mol^-1 more stable than the triplet state, as per CASPT2 and CCSD(T) computations.

An ever greater effect is predicted for 2. Here the nitrogen lone pairs adjacent to the carbene act to destabilize the σ-orbital. The empty π-orbital on B lowers the energy of the carbene π-orbital by making it part of the 6-electron aromatic ring. The ¹A₁-σ⁰π⁶ state of 2 is predicted to be about 25 kcal mol^-1 more stable than its triplet state!

1

2

Figure 1. CASSCF/6-31G(d) optimized geometries of the ¹A₁-σ⁰π⁶ states of 1 and 2.

References

(1) Chen, B.; Rogachev, A. Y.; Hrovat, D. A.; Hoffmann, R.; Borden, W. T. "How to
Make the σ⁰π² Singlet the Ground State of Carbenes," J. Am. Chem. Soc. 2013, 135, 13954-13964, DOI: 10.1021/ja407116e.

InChIs

1: InChI=1S/C5H2N2O2/c8-1-4-5(2-9)7-3-6-4/h1-2H
InChIKey=QDSVROXEBBWIOO-UHFFFAOYSA-N

2: InChI=1S/C3H3BN2/c1-4-2-6-3-5-1/h1-2,4H
InChIKey=MQJXDZBYOSOLST-UHFFFAOYSA-N

What is the closest non-bonding H^…H distance within a single molecule? The world record had been 1.617 Å in a pentacyclodecane.¹ This record now appears to be broken by the preparation of the disilane 1.² The ¹H NMR and IR suggest the interior hydrogens are very close. The x-ray structure of 1 indicates a very short Si-Si distance of 4.433 Å, a distance that must accommodate two S-H bonds, typically about 1.48 Å and the H^…H non-bonded distance, which might be as short then as 1.47 Å! The crystal is unfortunately not large enough for a neutron diffraction study, which would enable precise location of the hydrogens.

1

However, computations can help here, and they suggest a H^…H separation of only 1.57 Å: this is the distance obtained with B3PW91/6-311+G(2d,p), M062x/6-311+G(2d,p) and MP2/6-31G(d). The M062x/6-311+G(2d,p) structure is shown in Figure 1.

Figure 1. The M062x/6-311+G(2d,p) optimized structure of 1.

Any ideas for a compound with an even shorter non-bonded H^…H distance?

References

(1) Ermer, O.; Mason, S. A.; Anet, F. A. L.; Miura, S. S. "Ultrashort nonbonded hydrogen^…hydrogen distance in a half-cage pentacyclododecane," J. Am. Chem. Soc. 1985, 107, 2330-2334, DOI: 10.1021/ja00294a023.

(2) Zong, J.; Mague, J. T.; Pascal, R. A. "Exceptional Steric Congestion in an in,in-Bis(hydrosilane)," J. Am. Chem. Soc. 2013, 135, 13235-13237, DOI: 10.1021/ja407398w.

InChI

1: InChI=1S/C39H32S3Si2/c1-7-19-34-28(13-1)25-40-31-16-4-10-22-37(31)44-38-23-11-5-17-32(38)41-26-29-14-2-8-20-35(29)43(34)36-21-9-3-15-30(36)27-42-33-18-6-12-24-39(33)44/h1-24,43-44H,25-27H2
InChIKey=SBEUQCUCKCNPCC-UHFFFAOYSA-N