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In memory of

To 35th anniversary of the first theoretical calculation of C60 molecule. E.G.Galpern and D.A.Bochvar "On hypothetical systems: carbodecahedron, s-icosahedron and carbo-s-icosahedron". The article was accepted 26.06.1972 at DAN of USSR

Number and fantasy, law and abundance are alive creative
forces of nature. K.Chapek.

C60 molecule - fullerene consists of 60 carbon atoms located at the vertexes of a truncated icosahedron (fig. 1) with 12 pentagons and 20 hexagons.

Fig.1. a) Icosahedron formed by 20 equilateral triangles, b) diagram of "truncation" process, c) truncated icosahedron, d) fragment of the picture (1480) of the famous Italian mathematician and painter, Pietro della Francheska, e) the most stable structure of C60 with double bonds connecting pentagons from single bonds.

The most surprising property is its high symmetry involving 120 operations of rotation about axes and reflections in the symmetry plane This polyhedral shape was known from ancient times as one of Archimedes bodies. Johannes Kepler named this shape truncated isocahedron (1571-1630). In the early twentieth century in Annales de Chemie André-Marie Ampère (1775-1836) attempted to explain chemistry in terms of geometry. He speculated that the main molecules consisted of atoms located at the vertexes of regular polyhedrons, and reactions between molecules were possible where new molecules, polyhedrons with the certain symmetry were formed.
In the last 40 years we have witnessed the embodiment of this outstanding hypothesis. Boranes and carboranes, which were the first predicted in 60th polyhedral molecules, have ushered in chemistry of carcass nano-sized structures. Late in the 60s after the discovery of ferrocene, the investigations of its derivatives were started at Institute of Inorganic Compounds of Academy of Sciences of USSR. The head of the institute, academician A.N.Nesmeyanov, formulated the problem for his collaborators which consisted in finding the ways of synthesis and modeling new compounds in the form of polyhedrons from a carbon cage having one or several atoms of other elements inside. He named these compounds "a bird in the cage". This problem was also discussed in the laboratory of quantum chemistry leaded by Professor D.A.Bochvar. This simingly easy problem of connecting several ferrocene molecules with hydrocarbon bridges turned out to be not so simple. This model had a flaw and gave some dangling bonds. Bochvar suggested to consider C20 dodecahedron.
However the calculations, which were largely performed by E.G.Galpern, showed that the resulting C20 in the ground state had an unclosed electron system and only C20 -2 dication was stable. In addition, very little space remained inside C20 for other atoms. When discussing these results in the laboratory, I.V.Stankevich suggested to consider the larger "cage", locate it on a soccer ball and arrange carbon atoms at 60 vertices of this cage. "This molecule should be very firm because 22 players kick a ball for several hours and nothing happens to it!" - said Ivan Viacheslavovich, an inveterate football player. Everybody liked the idea, but it took one year to write a computing program and make calculations even within the simple Hukkel scheme because such polyatomic systems could not be calculated "by hand". In 1970 based on the obtained results, the paper was finally written and given to A.N.Nesmeyanov to review before publication. Stankevich refused to be among the authors of the paper and agreed only to be mentioned in acknowledgment although he participated in discussing the results and some details of calculations. However Alexandr Nikolaevich was embarrassed by so revolutionary models and said that as it was not his subject-matter, he did not know theory well and could not stake his life on that, everything had to be discussed and considered again. Bochvar was very upset, he had to speak about the unusual models of molecules several times and defend them at seminars and scientific councils. Unusualness of these molecules for chemists and their skepticism concerning the existence of these molecules continued after the publication of the famous paper written by Kroto et al. in 1985 [1] and until the appearance of real material from C60 prepared by Kratschmer's group in 1989 [2]. Time passed. In February, 1972 prestigious Journal of American Chemical Society published information about peristilane, the crown from 6 carbon 5-membered cycles, incomplete C20 dodecahedron [3] what convinced A.N.Nesmeyanov in the importance of publishing the work performed by his collaborators. Hence the paper "On hypothetical systems: carbodecahedron, sicosahedron and carbo-s-icosahedron" was sent to Papers of Academy of Sciences of USSR 26, June 1972 and published in 1973 [4]. The most stable C60 structure was found to be the structure with double bonds among pentagons (fig.1e). Although this work represented the results of calculations performed by Hukkel method, which was used for plane unsaturated systems, the general conclusions were confirmed by further calculations by the more precise PMX method [5]. Authors of these two papers learnt about Osawa's prediction of C60, which was published in Japanese in 1970, only in 1987 from paper by Kroto et al. [7]. E.Osawa showed [8] that he had assumed stability of truncated C60 icosahedron only on the basis of symmetry considerations with no calculations.
In 1996 The Nobel Prize in chemistry was awarded to Kroto, Smalley and Kerl for the discovery of fullerenes. Over a period of years these compounds were intensively studied in laboratories of different countries, the scientists attempted to find the conditions of their formation, structure and properties, and possible applications. In particular, the soot produced by arc discharge at graphite electrodes was found to contain a great deal of fullerenes, they had not been observed before. At present the only method of producing fullerenes is their artificial synthesis (for more details, see the excellent books [9, 10]).
Macro-amounts of C60 and C70 fullerenes are synthesized and sold by several enterprises in Russia, such as "Fullerene-Center", Nijniy Novgorod, Russian Scientific Center "Kurchatov Institute". Fullerenes are the basis for new carbon nanomaterials (both C60 crystals - fullerites and their polymeric phases - fullerides (C60Ax, x = 16, A - metal atoms, and others); complexes of C60 with transition metal atoms; heterofullerenes; hydride carbon forms based on C60 fullerenes and nanotubes, and C60-based derivative molecules).
Solar batteries and accumulators can be noted among interesting new applications where in one way or another fullerene additives are used. Also, fullerenes begin to find wide application in the creation of new medicines [11]. The processes of their formation, structure and transformation are under careful study of researchers [12].
The extremely encouraging results of scientists working in this field allow to hope that the designed by E.G.Galpern structure of C60 will become the basis of materials of XXI century.
Author is thankful to E.G.Galpern for a large help in historical reconstruction of prediction of a remarkable C60 molecule.
1. Kroto H.W., Heath J.R., O’Brien S.C., Curl R.F., and Smalley R.E. Nature, 318, 162 (1985). 2. Kratschmer W., Lamb L.D., Fostiropoulos K., Huffman D.R. Nature 347, 354 (1990). 3. Eaton P.E., Mueller R.H. JACS 94, 1014 (1972). 4. Bochvar D.A. and Gal'pern E.G. DAN SSSR 209, 610 (1973): Proc. Acad.Sci. USSR 209, 329 (1973). 5. Stankevich I.V., Nikerov M.V., and Bochvar D.A. Russ. Chem. Rev. 53 , 640 (1984). 6. Osawa E. Kagaku (Kyoto), 25, 854 (1970). In Japanese; Chem. Abstr. 74 (1971). 7. Kroto H.W., Nature 329, 529 (1987). 8. E. Osawa .Philos.Trans.R Soc.London Ser A – Phys.Sci.Eng. 343, 1 (1993). 9. Trefilov V.I., Schur D.V., Tarasov B.P., Shul’ga Yu.M., Chernogorenko A.V., Pishuk V.K., Zaginaichenko S.Yu. Fullerenes - the basis of materials in future. - Kiev: ADEF-Ukraine, 2001. - 148 p. (in Russian). 10. Sidorov L.N. Yurovskaya et al. Fullerenes. – Moscow: Examen, 2005. – 668 p. (in Russian). 11. Piotrovsky L.B., Kiselev O.I. Fullerenes in biology. - St-Petersburg: Rostok, 2006. – 336p. (in Russian). 12. Schur D.V., Matysina Z.A., Zaginaichenko S.Yu. Carbon nanomaterials and phase transformations in these materials.- Dnepropetrovsk: Nauka i obrazovanie.- 2007. - 680p. (in Russian)

Chernozatonskii L.A.
N.M.Emanuel Institute of Biochemical Physics RAS,
October 2007