Fullerenes can undergo the Diels-Alder reaction with some specificity: the diene preferentially adds across the bond shared by two fused 6-member rings over the bond shared by the fused 6- and 5-member rings. Garcia-Rodeja and colleagues have examined the analogous Diels-Alder reaction of cyclopentadiene with five curved aromatic compounds, 1-5.¹

The computations were performed at BP86-D3/def2-TZVPP//RI-BP86-D3/def2-SVP. Representative transition states for the addition of cyclopentadiene with 3 over the 6,6-bond and 5,6-bond are shown in Figure 1.

5,6-bond

6,6-bond

Figure 1. RI-BP86-D3/def2-SVP optimized transition states for the reaction of cyclopentadiene with 3.

For the reactions of cyclopentadiene with 2-5 the reactions with the 6,6-bond is both kinetically and thermodynamically favored, while with 1 the 6,6-bond is kinetically preffered and the 5,6-adduct is the thermodynamic product. As the molecules increase in size (from 1 to 5), the activation barrier decreases, and the barrier for the reaction with 5 is only 1.4 kcal mol^-1larger than the barrier with C₆₀. The reaction energy also becomes more exothermic with increasing size. There is a very good linear relationship between activation barrier and reaction energy.

Use of the distortion/interaction model indicates that the preference for the 6,6-regioselectivity come from better interaction energy than for the 5,6-reaction, and this seems to come about by better orbital overlap between the cyclopentadiene HOMO and the 6,6-LUMO of the buckybowl.

References

(1) García-Rodeja, Y.; Solà, M.; Bickelhaupt , F. M.; Fernández, I. "Reactivity and Selectivity of Bowl-Shaped Polycyclic Aromatic Hydrocarbons: Relationship to C60," Chem. Eur. J. 2016, 22, 1368-1378, DOI: .

InChIs

1: InChI=1S/C20H10/c1-2-12-5-6-14-9-10-15-8-7-13-4-3-11(1)16-17(12)19(14)20(15)18(13)16/h1-10H
InChIKey=VXRUJZQPKRBJKH-UHFFFAOYSA-N

2: InChIKey=ASIFYFRJNYNQLA-UHFFFAOYSA-N

3: InChI=1S/C26H12/c1-5-13-14-6-2-11-19-20-12-4-8-16-15-7-3-10-18-17(9-1)21(13)25(22(14)19)26(23(15)18)24(16)20/h1-12H
InChIKey=OUWFOTSXASFGQD-UHFFFAOYSA-N

4: InChI=1S/C30H12/c1-2-14-6-10-18-20-12-8-16-4-3-15-7-11-19-17-9-5-13(1)21-22(14)26(18)29(25(17)21)30-27(19)23(15)24(16)28(20)30/h1-12H
InChIKey=JEUCRZPADDQRKU-UHFFFAOYSA-N

5: InChI=1S/C36H12/c1-7-16-17-9-3-14-5-11-20-21-12-6-15-4-10-19-18-8-2-13(1)22-25(16)31-32(26(18)22)34-28(19)24(15)30(21)36(34)35-29(20)23(14)27(17)33(31)35/h1-12H
InChIKey=QMGQDOOJOCPYIA-UHFFFAOYSA-N

Karton, Schreiner, and Martin have benchmarked the heats of formation of some Platonic Solids and related hydrocarbons.¹ The molecules examined are tetrahedrane 1, cubane 2, dodecahedrane 3, trisprismane 4, pentaprismane 5, and octahedrane 6.

The optimized structures (B3LYP-D3BJ/def2-TZVPP) of these compounds are shown in Figure 1.

1	2
3	4
5	6

Figure 1. B3LYP-D3BJ/def2-TZVPP optimized geometries of 1-6.

Using the W1-F12 and W2-F12 composite methods, the estimated the heats of formation of these hydrocarbons are listed in Table 1. Experimental values are available only for 2 and 3; the computed values are off by about 2 kcal mol^-1, which the authors argue is just outside the error bars of the computations. They suggest that the experiments might need to be revisited.

Table 1. Heats of formation (kcal mol^-1) of 1-6.

compound	ΔHf (comp)	ΔHf (expt)
1	128.57
2	144.78	142.7 ± 1.2
3	20.18	22.4 ± 1
4	132.84
5	119.42
6	63.08

They conclude with a comparison of strain energies computed using isogyric, isodesmic, and homodesmotic reactions with a variety of computational methods. Somewhat disappointingly, most DFT methods have appreciable errors compared with the W1-F12 results, and the errors vary depend on the chemical reaction employed. However, the double hybrid method DSD-PBEP86-D3BJ consistently reproduces the W1-F12 results.

References

(1)  Karton, A.; Schreiner, P. R.; Martin, J. M. L. "Heats of formation of platonic hydrocarbon cages by means of high-level thermochemical procedures," J. Comput. Chem. 2016, 37, 49-58, DOI: 10.1002/jcc.23963.

InChIs

1: InChI=1S/C4H4/c1-2-3(1)4(1)2/h1-4H
InChIKey=FJGIHZCEZAZPSP-UHFFFAOYSA-N

2: InChI=1S/C8H8/c1-2-5-3(1)7-4(1)6(2)8(5)7/h1-8H
InChIKey=TXWRERCHRDBNLG-UHFFFAOYSA-N

3: InChI=1S/C20H20/c1-2-5-7-3(1)9-10-4(1)8-6(2)12-11(5)17-13(7)15(9)19-16(10)14(8)18(12)20(17)19/h1-20H
InChIKey=OOHPORRAEMMMCX-UHFFFAOYSA-N

4: InChI=1S/C6H6/c1-2-3(1)6-4(1)5(2)6/h1-6H
InChIKey=RCJOMOPNGOSMJU-UHFFFAOYSA-N

5: InChI=1S/C10H10/c1-2-5-3(1)7-8-4(1)6(2)10(8)9(5)7/h1-10H
InChIKey=TXSUZIHPJIZTJT-UHFFFAOYSA-N

6: InChI=1S/C12H12/c1-2-4-6-5(11-7(1)10(4)11)3(1)9-8(2)12(6)9/h1-12H
InChIKey=DUDCBTWUEJEMGD-UHFFFAOYSA-N