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Comment on “Favourable structures for higher fullerenes”
Volume 192, number 2,3
CHEMICAL PHYSICS LETTERS
1 May 1992
Comment Comment on “Favourable structures for higher fullerenes” David E. Manolopoulos Department of Chemistry,
University OfNottingham,
Nottingham,
NG7 2RD, UK
Received 5 February 1992
A corrected version of the ring spiral computer code finds 18 12 spectrally distinct fullerene isomers of &a, 22 more isomers than are found by the independent computer enumeration method of Liu, Schmalz and Klein.
In the title Letter [ 11, Liu, Schmalz and Klein note that their method for the systematic generation of all fullerenes with a given number of vertices produces 1790 isomers for CeO,whereas our ring spiral algorithm produces only 1760 [ 21. They conclude that the ring spiral algorithm produces only a lower bound on the correct fullerene isomer count. The purpose of this Comment is to stress, with apologies to the authors of ref. [ 11, that a programming error has been found in the ring spiral computer code since ref. [ 21 was published. In fact, the total number of spectrally distinct C6,,fullerene isomers found by the corrected code is 18 12 [ 3 1. The corrected ring spiral code has been tested extensively for internal consistency with respect to both the leapfrog construction [ 41, and the pyracylene transformation [ 5 1, neither of which are enforced by the algorithm per se. [ 21. (Indeed the error in the original code was detected precisely by applying the first of these tests to the C40++C12,-, leapfrog pair.) The computer enumeration of fullerene isomers will nevertheless remain a hazardous occupation until a
330
rigorous analytical solution has been found, and to state unequivocally that Cbo has only 1812 isomers might well be an overture to disaster. The spectrally distinct isomer counts found by the corrected ring spiral code are listed in ref. [ 3 ] for all general fullerenes C, in the range n = 20-60, and for all isolated-pentagon fullerenes C, in the range n= 70-100. Happily, in view of their greater experimental relevance, these latter isolated-pentagon fullerene isomer counts agree perfectly with those in table 1 of Liu, Schmalz and Klein’s Letter [ 11. References [ 1] X. Liu, T.G. Schmalz and D.J. Klein, Chem. Phys. Letters 188 (1992) 550. [2] D.E. Manolopoulos, J.C. May and S.E. Down, Chem. Phys. Letters 181 (1991) 105. [3] D.E. Manolopoulos and P.W. Fowler, Molecular Graphs, Point Groups, and Fullerenes, J. Chem. Phys., in press. [ 41 P.W. Fowler and J.I. Steer, J. Chem. Sot. Chem. Commun. (1987) 1403. [5] A.J. Stone and D.J. Wales, Chem. Phys. Letters 128 (1986) 501.
0009-2614/92/$ OS.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
CHEMICAL PHYSICS LETTERS
1 May 1992
Comment Comment on “Favourable structures for higher fullerenes” David E. Manolopoulos Department of Chemistry,
University OfNottingham,
Nottingham,
NG7 2RD, UK
Received 5 February 1992
A corrected version of the ring spiral computer code finds 18 12 spectrally distinct fullerene isomers of &a, 22 more isomers than are found by the independent computer enumeration method of Liu, Schmalz and Klein.
In the title Letter [ 11, Liu, Schmalz and Klein note that their method for the systematic generation of all fullerenes with a given number of vertices produces 1790 isomers for CeO,whereas our ring spiral algorithm produces only 1760 [ 21. They conclude that the ring spiral algorithm produces only a lower bound on the correct fullerene isomer count. The purpose of this Comment is to stress, with apologies to the authors of ref. [ 11, that a programming error has been found in the ring spiral computer code since ref. [ 21 was published. In fact, the total number of spectrally distinct C6,,fullerene isomers found by the corrected code is 18 12 [ 3 1. The corrected ring spiral code has been tested extensively for internal consistency with respect to both the leapfrog construction [ 41, and the pyracylene transformation [ 5 1, neither of which are enforced by the algorithm per se. [ 21. (Indeed the error in the original code was detected precisely by applying the first of these tests to the C40++C12,-, leapfrog pair.) The computer enumeration of fullerene isomers will nevertheless remain a hazardous occupation until a
330
rigorous analytical solution has been found, and to state unequivocally that Cbo has only 1812 isomers might well be an overture to disaster. The spectrally distinct isomer counts found by the corrected ring spiral code are listed in ref. [ 3 ] for all general fullerenes C, in the range n = 20-60, and for all isolated-pentagon fullerenes C, in the range n= 70-100. Happily, in view of their greater experimental relevance, these latter isolated-pentagon fullerene isomer counts agree perfectly with those in table 1 of Liu, Schmalz and Klein’s Letter [ 11. References [ 1] X. Liu, T.G. Schmalz and D.J. Klein, Chem. Phys. Letters 188 (1992) 550. [2] D.E. Manolopoulos, J.C. May and S.E. Down, Chem. Phys. Letters 181 (1991) 105. [3] D.E. Manolopoulos and P.W. Fowler, Molecular Graphs, Point Groups, and Fullerenes, J. Chem. Phys., in press. [ 41 P.W. Fowler and J.I. Steer, J. Chem. Sot. Chem. Commun. (1987) 1403. [5] A.J. Stone and D.J. Wales, Chem. Phys. Letters 128 (1986) 501.
0009-2614/92/$ OS.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.