A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C60

Kekulé count is not as useful in predicting the thermodynamic stability of fullerenes as it is for benzenoid hydrocarbons. For example, the Kekulé count of the icosahedral C60, the most stable fullerene molecule, is surpassed by its 20 fullerene isomers (Austin et al. in Chem Phys Lett 228:478–484, 1994). This article investigates the role of Clar number in predicting the stability of fullerenes from Clar’s ideas in benzenoids. We find that the experimentally characterized fullerenes attain the maximum Clar numbers among their fullerene isomers. Our computations show that among the 18 fullerene isomers of C60 achieving the maximum Clar number (8), the icosahedral C60 has the largest Kekulé count. Hence, for fullerene isomers of C60, a combination of Clar number and Kekulé count predicts the most stable isomer.

[1]  S. C. O'brien,et al.  C60: Buckminsterfullerene , 1985, Nature.

[2]  Isao Ikemoto,et al.  NMR characterization of isomers of C78, C82 and C84 fullerenes , 1992, Nature.

[3]  S El-Basil.  Clar sextet theory of buckminsterfullerene (C 60 ) , 2000 .

[4]  Douglas J. Klein,et al.  Favorable structures for higher fullerenes , 1992 .

[5]  Pierre Hansen,et al.  Fullerene isomers of C60. Kekulé counts versus stability , 1994 .

[6]  Craig E. Larson,et al.  Graph-Theoretic Independence as a Predictor of Fullerene Stability , 2003 .

[7]  E. Clar.  The aromatic sextet , 1972 .

[8]  Douglas J. Klein,et al.  Elemental carbon cages , 1988 .

[9]  P. W. Kasteleyn.  Dimer Statistics and Phase Transitions , 1963 .

[10]  Douglas J. Klein,et al.  Resonance in C60, buckminsterfullerene , 1986 .

[11]  P. Fowler,et al.  Molecular graphs, point groups, and fullerenes , 1992 .

[12]  H. Abeledo,et al.  Unimodularity of the Clar number problem , 2007 .

[13]  Heping Zhang,et al.  Extremal fullerene graphs with the maximum Clar number , 2009, Discret. Appl. Math..

[14]  W. C. Herndon.  Resonance energies of aromatic hydrocarbons. Quantitative test of resonance theory , 1973 .

[15]  M. Randic.  Aromaticity of polycyclic conjugated hydrocarbons. , 2003, Chemical reviews.

[16]  Douglas J. Klein,et al.  Sixty‐atom carbon cages , 1991 .

[17]  D. Klein,et al.  VARIATIONAL RESONANCE VALENCE BOND STUDY ON THE GROUND STATE OF C60 USING THE HEISENBERG MODEL , 1998 .

[18]  H. W. Kroto,et al.  The stability of the fullerenes Cn, with n = 24, 28, 32, 36, 50, 60 and 70 , 1987, Nature.

[19]  Douglas J. Klein,et al.  Many‐body conjugated‐circuit computations , 1991 .

[20]  Douglas J. Klein,et al.  Preferable Fullerenes and Clar-Sextet Cages , 1994 .

[21]  D. Klein,et al.  C60 carbon cages , 1986 .

[22]  M. Randic.  Conjugated circuits and resonance energies of benzenoid hydrocarbons , 1976 .

[23]  Pierre Hansen,et al.  The Clar number of a benzenoid hydrocarbon and linear programming , 1994 .

[24]  Clar theory for molecular benzenoids. , 2009, The journal of physical chemistry. A.

[25]  R. Whetten,et al.  Isolation of C76, a chiral (D 2) allotrope of carbon , 1991, Nature.

[26]  Patrick W. Fowler,et al.  Independence number and fullerene stability , 2007 .

[27]  Douglas J. Klein,et al.  An extended Heisenberg model for conjugated hydrocarbons. II. Kekulé basis , 2003 .

[28]  T. Došlić.  Bipartivity of fullerene graphs and fullerene stability , 2005 .

[29]  Y. Rubin,et al.  Characterization of the soluble all-carbon molecules C60 and C70 , 1990 .

[30]  Heping Zhang,et al.  Clar and sextet polynomials of buckminsterfullerene , 2003 .

[31]  Harold W. Kroto,et al.  Isolation, separation and characterisation of the fullerenes C60 and C70 : the third form of carbon , 1990 .

[32]  W. Krätschmer,et al.  Solid C60: a new form of carbon , 1990, Nature.

[33]  Heping Zhang,et al.  An Upper Bound for the Clar Number of Fullerene Graphs , 2007 .

[34]  On the Number of Aromatic Sextets in a Benzenoid Hydrocarbon , 1976 .

[35]  Patrick W. Fowler,et al.  Faraday communications. An end to the search for the ground state of C84 , 1992 .