Diels-Alder reaction of buckybowls

Diels-Alder &fullerene Steven Bachrach 23 May 2016 No Comments

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.



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.


(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: <10.1002/chem.201502248.


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


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

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

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

Benchmarking Platonic solids and related hydrocarbons

QM Method &Schreiner Steven Bachrach 10 May 2016 No Comments

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.







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.


ΔHf (comp)

ΔHf (expt)






142.7 ± 1.2



22.4 ± 1










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.


(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.


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

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

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

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

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

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

Diels-Alder reactions of some arenes

Aromaticity &Diels-Alder &Houk Steven Bachrach 26 Apr 2016 No Comments

Houk has examined the Diels-Alder reaction involving ethene with benzene 1 and all of its aza-substituted isomers having four or fewer nitrogen atoms 2-11.1 The reactions were computed at M06-2X/6-311+G(d,p).

All of the possible Diels-Alder reactions were examined, and they can be classified in terms of whether two new C-C bonds are formed, one new C-C and one new C-N bond are formed, or two new C-N bonds are formed. Representative transition states of these three reaction types are shown in Figure 1, using the reaction of 7 with ethene.

Figure 1. M06-2X/6-311+G(d,p) optimized transition states for the Diels-Alders reactions of 7 with ethene.

A number of interesting trends are revealed. For a given type of reaction (as defined above), as more nitrogens are introduced into the ring, the activation energy decreases. Forming two C-C bonds has a lower barrier than forming a C-C and a C-N, which has a lower barrier than forming two C-N bonds. The activation barriers are linearly related to the aromaticity of the ring defined by either NICS(0) or aromatic stabilization energy, with the barrier decreasing with decreasing aromaticity. The barrier is also linearly related to the exothermicity of the reaction.

The activation barrier is also linearly related to the distortion energy. With increasing nitrogen substitution, the ring becomes less aromatic, and therefore more readily distorted from planarity to adopt the transition state structure.


(1) Yang, Y.-F.; Liang, Y.; Liu, F.; Houk, K. N. "Diels–Alder Reactivities of Benzene, Pyridine, and Di-, Tri-, and Tetrazines: The Roles of Geometrical Distortions and Orbital Interactions," J. Am. Chem. Soc. 2016, 138, 1660-1667, DOI: 10.1021/jacs.5b12054.

Interesting chemistry of biphenalenylidene

Uncategorized Steven Bachrach 19 Apr 2016 No Comments

Uchida and co-workers reported on the preparation of biphenalenylidene 1 and its interesting electrocyclization to dihydroperopyrene 2.1 The experimental barrier they find by experiment for the conversion of 1-Z to 1-E is only 4.3 kcal mol-1. Secondly, the photochemical electrocyclization of 2-anti to 1-Z proceeds rapidly, through an (expected) allowed conrotatory pathway. However, the reverse reaction did not occur photochemically, but rather did occur thermally, even though this is formally forbidden by the Woodward-Hoffman rules.

To address these issues, they performed a number of computations, with geometries optimized at UB3LYP(BS)/6-31G**. First, CASSCF computations indicated considerable singlet diradical character for 1-Z. Both 1-Z and 1-E show significant twisting about the central double bond, consistent with the singlet diradical character. 1-Z is 1.8 kcal mol-1 lower in energy than 1-E, and the barrier for rotation interconverting these isomers is computed to be 7.0 kcal mol-1, in reasonable agreement with the experiment. These geometries are shown in Figure 1.



TS (Z→E)

Figure 1. UB3LYP(BS)/6-31G** optimized geometries of 1-Z and 1- and the transition state to interconvert these two isomers.

The conrotatory electrocyclization that takes 1-Z into 2-anti has a barrier of 26.0 kcal mol-1 and is exothermic by 3.4 kcal mol-1. The disrotatory process has a higher barrier (34.2 kcal mol-1) and is endothermic by 8.4 kcal mol-1. These transition states and products are shown in Figure 2. So, despite being orbital symmetry forbidden, the conrotatory path is preferred, and this agrees with their experiments.

TS (con)

TS (dis)



Figure 2. UB3LYP(BS)/6-31G** optimized geometries of 2-anti and 2-syn and the transition states leading to them.

The authors argue that the large diradical character of 1 leads to both its low Z→E rotational barrier, and the low barrer for electrocyclization. The Woodward-Hoffmann allowed disrotatory barrier is inhibited by its highly strained geometry, making the conrotatory path the favored route.


(1) Uchida, K.; Ito, S.; Nakano, M.; Abe, M.; Kubo, T. "Biphenalenylidene: Isolation and Characterization of the Reactive Intermediate on the Decomposition Pathway of Phenalenyl Radical," J. Am. Chem. Soc. 2016, 138, 2399-2410, DOI: 10.1021/jacs.5b13033.


1-E: InChI=1S/C26H16/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16H/b22-21+

1-Z: InChI=1S/C26H16/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16H/b22-21-

2-anti: InChI=1S/C26H18/c1-3-15-7-11-19-21-13-9-17-5-2-6-18-10-14-22(26(21)24(17)18)20-12-8-16(4-1)23(15)25(19)20/h1-14,19,21,25-26H/t19-,21-,25?,26?/m0/s1

2-syn: InChI=1S/C26H18/c1-3-15-7-11-19-21-13-9-17-5-2-6-18-10-14-22(26(21)24(17)18)20-12-8-16(4-1)23(15)25(19)20/h1-14,19,21,25-26H/t19-,21+,25?,26?

Cyclization reaction of 1,2-cyclohexadiene

cycloadditions &Houk Steven Bachrach 11 Apr 2016 No Comments

1,2-Cyclohexadiene 1 is a very strained and highly reactive species. Houk, Garg and co-workers report on its use as the ene component in a cyclization with a 1,3-dipole, namely nitrones.1 For example, 1 reacts with nitrone 2 to give the cycloadducts 3a and 3b in a ratio of 8.9:1.

To investigate the mechanism of this reaction, they optimized the structures of all compounds at CPCM(acetonitrile)B3LYP/6-31G(d) and single-point energies were obtained using the B3LYP-D3 functional. The structures of some pertinent critical points are shown in Figure 1. They did locate a concerted transition state (TS1) leading to 3a, with a barrier of 14.5 kcal mol-1, but could not find a concerted TS leading to 3b. (Also, the barriers leading to the other regioisomer are much higher than the ones leading to the observed products.) Rather, they identified a stepwise transition state (TS2) with a barrier of nearly the same energy (14.4 kcal mol-1) that leads to the intermediate (INT), which lies 16.5 kcal mol-1 below reactants. They located two transition states from his intermediate, TS3a and TS3b, leading to the two different products. The barrier to 3a is 1.2 kcal mol-1 lower than the barrier leading to 3b, and this corresponds nicely with the observed diastereoselectivity.









Figure 1. CPCM(acetonitrile)B3LYP/6-31G(d) optimized geometries and CPCM(acetonitrile)B3LYP-D3/6-31G(d) free energies.


(1) Barber, J. S.; Styduhar, E. D.; Pham, H. V.; McMahon, T. C.; Houk, K. N.; Garg, N. K.
"Nitrone Cycloadditions of 1,2-Cyclohexadiene," J. Am. Chem. Soc. 2016, 138, 2512-2515, DOI: 10.1021/jacs.5b13304.


1: InChI=1S/C6H8/c1-2-4-6-5-3-1/h1,5H,2,4,6H2

2: InChI=1S/C11H15NO/c1-11(2,3)12(13)9-10-7-5-4-6-8-10/h4-9H,1-3H3/b12-9-

3a: InChI=1S/C17H23NO/c1-17(2,3)18-16(13-9-5-4-6-10-13)14-11-7-8-12-15(14)19-18/h4-6,9-11,15-16H,7-8,12H2,1-3H3/t15-,16-/m0/s1

3b: InChI=1S/C17H23NO/c1-17(2,3)18-16(13-9-5-4-6-10-13)14-11-7-8-12-15(14)19-18/h4-6,9-11,15-16H,7-8,12H2,1-3H3/t15-,16+/m1/s1

A linear acene with 13 rings

Aromaticity Steven Bachrach 04 Apr 2016 No Comments

Bunz and co-workers have synthesized the novel aromatic compound 1 that contains 13 acenes in a row.1

They optimized the geometry of 1 at B3LYP/6-311G*, and its geometry is shown in Figure 1. Even though this compound has quite an extensive π-system, an unrestricted computations collapses to the closed-shell wavefunction.


Figure 1. B3LYP/6-311G* optimized geometry of 1. (As always, don’t forget to click on this image to launch JMol and visualize the molecule in 3-D.)

NICS(1)πzz values for the rings are given in Table 1. Interestingly, the aromaticity of the coronene moiety is reduced; in fact the central ring (ring A, with rings labeled sequentially working towards either end from the center) has a very small NICS value of only -3.77.

Table 1. NICS(1)πzz values for the rings of 1.






(1) Endres, A. H.; Schaffroth, M.; Paulus, F.; Reiss, H.; Wadepohl, H.; Rominger, F.; Krämer, R.; Bunz, U. H. F. "Coronene-Containing N-Heteroarenes: 13 Rings in a Row," J. Am. Chem. Soc. 2016, 138, 1792-1795, DOI: 10.1021/jacs.5b12642.


1: InChI=1S/C100H76N8O4Si4/c1-49(2)56-31-24-32-57(50(3)4)75(56)84-95(111)72-47-68-80-78-66(89-91(68)107-99-97(105-89)101-85-58(33-37-113(5,6)7)62-41-52-27-20-22-29-54(52)43-64(62)60(87(85)103-99)35-39-115(11,12)13)45-70-76-71(94(110)74(93(70)109)51-25-18-17-19-26-51)46-67-79(82(76)78)81-69(48-73(96(84)112)77(72)83(80)81)92-90(67)106-98-100(108-92)104-88-61(36-40-116(14,15)16)65-44-55-30-23-21-28-53(55)42-63(65)59(86(88)102-98)34-38-114(8,9)10/h17-32,41-50,74,84H,1-16H3


Uncategorized Steven Bachrach 28 Mar 2016 No Comments

Reid, Rathore and colleagues report on the attempted preparation of the interesting molecule 1,3,5-trifluorenylcyclohexane (TFC) 1.1 They had hoped to prepare it by subjecting the precursor 2 to acid, which might then undergo a Friedel-Crafts reaction to prepare the last fluorenyl group, and subsequent loss of a proton would give 1. Unfortunately, they could not get this step to occur, even at high temperature and for long reaction times. What made it particularly frustrating was that they could get 3 to react under these conditions to give 1,4-difluorenylcyclohexane (14-DFC) 4, and convert 5 into 1,4-difluorenylcyclohexane (13-DFC) 6.

To get at why 1 could not be formed they utilized PCM(CH2Cl2)/M06-2X/6-31G(d) calculations. The lowest energy conformations of 1 and 4 are shown in Figure 1. While 4 is in a chair conformation, 1 is not in a chair conformation since this would bring the three fluorenyl groups into very close contact. Instead, the cyclohexyl ring of 1 adopts a twist-boat conformation, with a much flattened ring. They estimate that 1 is strained by about 17 kcal mol-1, with 10 kcal mol-1 coming from strain in the twist-boat conformation and another 7 kcal mol-1 of strain due to steric crowding of the fluorenyl groups.

They next optimized the structures of the intermediates and transition states on the path taking 2 into 1 and 3 into 4. The transition states of the Friedel-Crafts reaction are the highest points on these paths, and their geometries are shown in Figure 1. The barrier through the TS for the Friedel-Crafts step forming 1 is about 17 kcal mol-1 higher than for the barrier to form 4. This very large increase in activation barrier, due to the strains imposed by that third fluorenyl group, explains the lack of reaction. Furthermore, since the reaction 21 is 2.0 kcal mol-1 endothermic, at high temperature the reaction is likely to be reversible and favors 2.



TS to 1

TS to 4

Figure 1. PCM(CH2Cl2)/M06-2X/6-31G(d) optimized geometries.


(1) Talipov, M. R.; Abdelwahed, S. H.; Thakur, K.; Reid, S. A.; Rathore, R. "From Wires to Cables: Attempted Synthesis of 1,3,5-Trifluorenylcyclohexane as a Platform for Molecular Cables," J. Org. Chem. 2016, DOI: 10.1021/acs.joc.5b02792.


1 (TFC): InChI=1S/C42H30/c1-7-19-34-28(13-1)29-14-2-8-20-35(29)40(34)25-41(36-21-9-3-15-30(36)31-16-4-10-22-37(31)41)27-42(26-40)38-23-11-5-17-32(38)33-18-6-12-24-39(33)42/h1-24H,25-27H2

4 (14-DFC): InChI=1S/C30H24/c1-5-13-25-21(9-1)22-10-2-6-14-26(22)29(25)17-19-30(20-18-29)27-15-7-3-11-23(27)24-12-4-8-16-28(24)30/h1-16H,17-20H2

6 (13-DFC):InChI=1S/C30H24/c1-2-11-22(12-3-1)24-14-4-5-15-25(24)23-13-10-20-30(21-23)28-18-8-6-16-26(28)27-17-7-9-19-29(27)30/h1-9,11-19H,10,20-21H2

FEP study

FEP Steven Bachrach 21 Mar 2016 No Comments

The ACS National Meeting this week in San Diego had computers in chemistry as its theme. A number of sessions featured computer-aided drug design, and the paper that garnered a lot of attention in many of these sessions was one I missed from last year. The work, done by the Schrödinger company, presents the application of some improved techniques for performing free energy perturbation (FEP) computations.1 FEP involves changing a small number of atoms from one type to another and determining the free energy change with this perturbation. Since so much of the system is left unaffected, the idea is that errors in the non-perturbed parts of the system will cancel, allowing for accurate determination of the free energy change due to the perturbation.

This study features a number of new technologies that have enabled much more accurate predictions. First, they have employed a new force field, OPLS2.1, which appears to provide much improved energies. Second, they have improved sampling of configuration space using the Desmond program and replica exchange with solute tempering (REST). Third, these have been implemented on GPUs that results in dramatically improved throughput. And fourth, they developed a workflow to automate the selection of ligands, created by the perturbations with the protein of interest. They examined up to 10 atom perturbations within the initial ligand.

In a validation study of 8 proteins involving 330 ligands, the RMS error in the free energy of binding was about 1 kcal mol-1. Case studies of different types of perturbations leading to gain or loss of hydrophobic or electrostatic interactions, loss of a binding water and exposure to solvent are detailed. Lastly, in a study of two new proteins, they report a high success in predicting both strong binders and weak binders, with very few false positives.


(1) Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M. K.; Greenwood, J.; Romero, D. L.; Masse, C.; Knight, J. L.; Steinbrecher, T.; Beuming, T.; Damm, W.; Harder, E.; Sherman, W.; Brewer, M.; Wester, R.; Murcko, M.; Frye, L.; Farid, R.; Lin, T.; Mobley, D. L.; Jorgensen, W. L.; Berne, B. J.; Friesner, R. A.; Abel, R. "Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field," J. Am. Chem. Soc. 2015, 137, 2695-2703, DOI: 10.1021/ja512751q.

Mechanism of organocatalysis by Cinchona alkaloids

Houk &Michael addition &stereoinduction Steven Bachrach 03 Mar 2016 No Comments

Cinchona alkaloids cat catalyze reactions, such as shown in Reaction 1. Wynberg1 proposed a model to explain the reaction, shown in Scheme 1, based on NMR. Grayson and Houk have now used DFT computations to show that the mechanism actually reverses the arrangements of the substrates.2

Reaction 1

Scheme 1.

Wynberg Model

Grayson and Houk Model

M06-2X/def2-TZVPP−IEFPCM(benzene)//M06-2X/6-31G(d)−IEFPCM(benzene) computations show that the precomplex of catalyst 3 with nucleophile 1 and Michael acceptor 2 is consistent with Wynberg’s model. The alternate precomplex is 5.6 kcal mol-1 higher in energy. These precomplexes are shown in Figure 1.

Wynberg precomplex

Grayson/Houk precomplex

Figure 1. Precomplexes structures

However, the lowest energy transition state takes the Grayson/Houk pathway and leads to the major isomer observed in the reaction. The Grayson/Houk TS that leads to the minor product has a barrier that is 3 kcal mol-1 higher in energy. The lowest energy TS following the Wynberg path leads to the minor product, and is 2.2 kcal mol-1 higher than the Grayson/Houk path. These transition states are shown in Figure 2. The upshot is that complex formation is not necessarily indicative of the transition state structure.

Wynberg TS (major)
Rel ΔG = 5.3

Wynberg TS (minor)
Rel ΔG = 2.2

Grayson/Houk TS (major)
Rel ΔG = 0.0

Grayson/Houk TS (minor)
Rel ΔG = 3.0

Figure 2. TS structures and relative free energies (kcal mol-1).


(1) Hiemstra, H.; Wynberg, H. "Addition of aromatic thiols to conjugated cycloalkenones, catalyzed by chiral .beta.-hydroxy amines. A mechanistic study of homogeneous catalytic asymmetric synthesis," J. Am. Chem. Soc. 1981, 103, 417-430, DOI: 10.1021/ja00392a029.

(2) Grayson, M. N.; Houk, K. N. "Cinchona Alkaloid-Catalyzed Asymmetric Conjugate Additions: The Bifunctional Brønsted Acid–Hydrogen Bonding Model," J. Am. Chem. Soc. 2016, 138, 1170-1173, DOI: 10.1021/jacs.5b13275.


1: InChI=1S/C10H14S/c1-10(2,3)8-4-6-9(11)7-5-8/h4-7,11H,1-3H3

2: InChI=1S/C8H12O/c1-8(2)5-3-4-7(9)6-8/h3-4H,5-6H2,1-2H3

3: InChI=1S/C18H22N2O/c1-12-11-20-9-7-13(12)10-17(20)18(21)15-6-8-19-16-5-3-2-4-14(15)16/h2-6,8,12-13,17-18,21H,7,9-11H2,1H3/t12?,13?,17?,18-/m1/s1

4: InChI=1S/C18H26OS/c1-17(2,3)13-6-8-15(9-7-13)20-16-10-14(19)11-18(4,5)12-16/h6-9,16H,10-12H2,1-5H3/t16-/m0/s1

Calculating large fullerenes

fullerene Steven Bachrach 22 Feb 2016 4 Comments

What is the size of a molecule that will stretch computational resources today? Chan and co-workers have examined some very large fullerenes1 to both answer that question, and also to explore how large a fullerene must be to approach graphene-like properties.

They are interested in predicting the heat of formation of large fullerenes. So, they benchmark the heats of formation of C60 using four different isodesmic reactions (Reaction 1-4), comparing the energies obtained using a variety of different methods and basis sets to those obtained at W1h. The methods include traditional functionals like B3LYP, B3PW91, CAM-B3LYP, PBE1PBE, TPSSh, B98, ωB97X, M06-2X3, and MN12-SX, and supplement them with the D3 dispersion correction. Additionally a number of doubly hybrid methods are tested (again with and without dispersion corrections), such as B2-PLYP, B2GPPLYP, B2K-PLYP, PWP-B95, DSD-PBEPBE, and DSD-B-P86. The cc-pVTZ and cc-pVQZ basis sets were used. Geometries were optimized at B3LYP/6-31G(2df,p).

C60 + 10 benzene → 6 corannulene

Reaction 1

C60 + 10 naphthalene → 8 corannulene

Reaction 2

C60 + 10 phenanthrene → 10 corannulene

Reaction 3

C60 + 10 triphenylene → 12 corannulene

Reaction 4

Excellent results were obtained with DSD-PBEPBE-D3/cc-pVQZ (an error of only 1.8 kJ/mol), though even a method like BMK-D3/cc-pVTZ had an error of only 9.2 kJ/mol. They next set out to examine large fullerenes, including such behemoths as C180, C240, and C320, whose geometries are shown in Figure 1. Heats of formation were obtained using isodesmic reactions that compare back to smaller fullerenes, such as in Reaction 5-8.

C70 + 5 styrene → C60 + 5 naphthalene

Reaction 5

C180 → 3 C60

Reaction 6

C320 + 2/3 C60 → 2 C180

Reaction 7




Figure 1. B3LYP/6-31G(2df,p) optimized geometries of C180, C240, and C320. (Don’t forget that clicking on these images will launch Jmol and allow you to manipulate the molecules in real-time.)

Next, taking the heat of formation per C for these fullerenes, using a power law relationship, they were able to extrapolate out the heat of formation per C for truly huge fullerenes, and find the truly massive fullerenes, like C9680, still have heats of formation per carbon 1 kJ/mol greater than for graphene itself.


(1) Chan, B.; Kawashima, Y.; Katouda, M.; Nakajima, T.; Hirao, K. "From C60 to Infinity: Large-Scale Quantum Chemistry Calculations of the Heats of Formation of Higher Fullerenes," J. Am. Chem. Soc. 2016, 138, 1420-1429, DOI: 10.1021/jacs.5b12518.

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