Chem. Rev. 2001, 101, 1153−1183 1153 Spherical Aromaticity of Fullerenes Michael Bu¨hl*,† and Andreas Hirsch*,‡ Max-Planck-Institut fu¨r Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mu¨lheim an der Ruhr, Germany, and Institut fu¨r Organische Chemie der Universita¨t Erlangen-Nu¨rnberg, Henkestr. 42, D-91054 Erlangen, Germany Received August 21, 2000 Contents of a spherical aromatic molecule”. Later, at about the time when Kra¨tschmer and Huffman reported on the I. Introduction 1153 2 II. Structural Criteria 1154 synthesis of fullerenes in bulk quantities, he pointed out the vision that “it could be that we are entering III. Energetic Criteria 1158 a new age for just as the pre-Columbian assumption 1. MO Resonance Energies of Fullerenes 1158 that the earth was flat made way for a round world- 2. Topological Resonance Energies of 1159 view, it may be that, post buckminsterfullerene, the Fullerenes traditional assumption that polyaromatic organic 3. VB Model of C60 1159 chemistry is essentially a flat field may also make 4. Isodesmic Equations 1159 for a bright, nonplanar future”.3 The question whether 5. Heat of Hydrogenation 1160 fullerenes have to be considered aromatic or not has 6. Summary 1160 been a debate ever since their discovery. This has to IV. Reactivity Criteria 1160 do with initial lack of knowledge of fullerene proper- 1. Reactivity Indices 1160 ties, different interpretations of their newly discov- - 2. Principles of Fullerene Reactivity 1160 ered and unprecedented behavior,4 11 which is diffi- A. Retention of the Structural Type 1160 cult to compare with that of planar aromatics, and B. Chemical Indication of Cyclic Electron 1162 of course also with the fact that the definition of 12-14 Delocalization within C60:cis-1 Reactivity aromaticity itself is controversial and has changed C. Charge and Spin Localization in 1162 many times over the last 175 years. Monoadducts with Nucleophiles and The fullerenes form a unique class of spherical Radicals molecules containing a conjugated π system. Each D. Fullerene Adducts Containing 1163 fullerene represents a closed network of fused hexa- Two-Dimensional Aromatic Substructures gons and pentagons. This building principle is a 3. Summary 1165 consequence of the Euler theorem which states that V. Magnetic Criteria 1165 for the closure of each spherical network of n hexa- 1. Application of Magnetic Criteria to Fullerenes 1166 gons, 12 pentagons are required, with the exception A. “Exohedral” Probes 1167 of n ) 1. The presence of the pentagons allows for B. “Endohedral” Probes 1169 the introduction of the curvature which requires the C. “Theoretical” Probes 1171 C atoms to be pyramidalized. The smallest stable and 2. Application of Magnetic Criteria to Fullerene 1172 at the same time the most abundant fullerene is the Derivatives Ih-symmetrical buckminsterfullerene C60 (Figure 1). A. Anions 1172 The next stable homologue is C70 (Figure 1), followed by higher fullerenes15-17 like C ,C ,C C ,C , B. Adducts 1173 76 78 80, 82 84 etc. In terms of valence bond (VB) theory, there are C. Heterofullerenes 1177 12 500 Kekule´ structures for C60, suggesting, at a first 3. Summary 1177 glance, that it might be very aromatic. The structure VI. Nature of Aromaticity in Fullerenes and Count 1177 of the fullerenes, especially that of the icosahedral Rules representatives such as C , implies that they should − 60 1. Topological Count Rules “Magic Numbers” 1177 be considered as three-dimensional analogues of 2. Spherical Aromaticity in Ih Symmetrical 1178 benzene and other planar aromatics. In contrast to + 2 Fullerenes: The 2(N 1) Rule such classical systems, however, the sp2 networks of VII. Conclusion 1179 the fullerenes have no boundaries which are satu- VIII. Acknowledgment 1179 rated by hydrogen atoms.18 As a consequence, the IX. References 1179 characteristic aromatic substitution reactions retain- ing the conjugated π system are not possible for I. Introduction fullerenes. This is just one example for the general When buckminsterfullerene was discovered in 1985,1 problem to evaluate the aromaticity of fullerenes. Kroto suggested that it could be “the first example What are suitable aromaticity criteria for fullerenes? Against which standards should the aromatic proper- † Max-Planck-Institut fu¨ r Kohlenforschung. Fax: +49-208-3062996. ties of fullerenes be measured? Are there count rules E-mail: [email protected]. similar to the Hu¨ ckel rule for planar monocyclic ‡ Institut fu¨ r Organische Chemie der Universita¨t Erlangen- Nu¨ rnberg. Fax: +49-9131-8522537. E-mail: hirsch@organik. aromatics which express the occurrence of aromatic- uni-erlangen.de. ity with respect to the number of π electrons? 10.1021/cr990332q CCC: $36.00 © 2001 American Chemical Society Published on Web 03/21/2001 1154 Chemical Reviews, 2001, Vol. 101, No. 5 Bu¨hl and Hirsch Michael Bu¨hl was born in Wu¨rzburg, Germany, in 1962. He studied chemistry at the University of Erlangen, Germany, where he obtained his Ph.D. degree in 1992 under the supervision of Paul Schleyer. After a postdoctoral stay at the University of Georgia in Athens, GA, with Henry F. Schaefer III, he moved to the University of Zurich (Switzerland), where he finished his Habilitation in 1998. Since 1999 he has been Group Leader in the Theoretical Department of the Max-Planck-Institut fu¨r Kohlenfors- chung in Mu¨lheim/Ruhr (Germany). His main research interests are rooted in the application of modern quantum-chemical tools to study structures and reactivities of organic and transition-metal compounds, with emphasis on the computation of NMR properties. His main areas of application are fullerenes, computational support of experimentally determined structures, Figure 1. Schematic representation of C60 and C70. and homogeneous catalysis with transition-metal complexes. gated π system, is to a large extent driven by the reduction of strain.18 Analysis of the reactivity and regiochemistry of addition reactions reveals a behav- ior reminiscent of electron-deficient olefins. However, especially the magnetic properties of fullerenes clearly reflect delocalized character of the conjugated π system, which, depending on the number of π elec- trons, can cause the occurrence of diamagnetic or paramagnetic ring currents within the loops of the hexagons and pentagons (see section V). Neutral C60, for example, containing diatropic hexagons and para- tropic pentagons was labeled “ambiguously aro- matic”.18 Whereas in the early fullerene days the debate about the presence or absence of aromaticity Andreas Hirsch was born in Esslingen, Germany, in 1960. He studied in fullerenes was controversial, the accumulating chemistry at the University of Tu¨bingen, Germany, where he obtained his Ph.D. degree in 1990 under Michael Hanack. He has conducted amount of experimental and theoretical research postdoctoral research at the Institute for Polymers and Organic Solids in within the last years provided a much clearer inter- Santa Barbara, CA, with Fred Wudl. In 1991 he subsequently returned to pretation of this term with respect to this new class Tuebingen as Research Associate at the Institute of Organic Chemistry. of compounds. It is the aim of this review to sum- After his Habilitation in 1994, he joined the faculty of the Department of marize the research of fullerene aromaticity. The Chemistry at the University of Karlsruhe as Professor. Since October 1995, he has been Full Professor of Organic Chemistry at the Friedrich- evaluation of fullerene aromaticity is based on the Alexander-Universita¨t Erlangen-Nu¨rnberg. Andreas Hirsch’s main research classical aromaticity criteria, namely, structure, en- activities have been focused on the development of methodologies of ergy, reactivity, and magnetism, which are covered efficient syntheses of exohedral derivatives of fullerenes and the use of in this sequence in the following sections. Finally, the such compounds as structural templates and building blocks for supra- nature of fullerene aromaticity considering count molecular architectures and nanomaterials. Other research interests are in the area of synthesis of dendrimers, calixarene conjugates, new alkynes, rules involving the whole π-electron system and the new types of synthetic lipids and amphiphiles, model compounds for presence of two-dimensional Hu¨ ckel-aromatic sub- photoinduced charge separation, chemical derivatization, and solubilization structures will be discussed. of carbon nanotubes, including investigation of their synthetic potential and properties as new materials. II. Structural Criteria Compared to benzene, being the archetype of a two- dimensional aromatic molecule,19 the discussion of Icosahedral buckminsterfullerene is the only C60 aromaticity in fullerenes must take into account the isomer and the smallest possible fullerene that obeys strain provided by the pyramidalization of the C the ‘isolated pentagon rule’ (IPR).28,29 The IPR pre- atoms.18 The rich exohedral chemistry of fuller- dicts that those fullerene isomers with all pentagons enes,8,20-26 which is basically addition to the conju- isolated by hexagons will be stabilized against struc- Spherical Aromaticity of Fullerenes Chemical Reviews, 2001, Vol. 101, No. 5 1155 Table 1. Calculated and Measured Bond Distances in Table 2. Calculated and Experimental Structure of C60 [Å] C70 method [5,6]-bonds [6,6]-bonds ref bond length (Å) HF(STO-3G) 1.465 1.376 51 experiment theory HF(7s3p/4s2p) 1.453 1.369 52 bond type ab(dzp/SCF)60 LDF(11s6p) 1.43 1.39 53 HF 1.448 1.370 54 a 1.462 1.462 1.475 MP2 1.446 1.406 55 b 1.423 1.414 1.407 NMR 1.45 1.40 56 c 1.441 1.426 1.415 neutron diffraction 1.444 1.391 57 d 1.432 1.447 1.457 electron diffraction 1.458 1.401 58 e 1.372 1.378 1.361 X-ray 1.467 1.355 59 f 1.453 1.445 1.446 g 1.381 1.387 1.375 h 1.463 1.453 1.451 tures with adjacent pentagons.