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Non-IPR fullerenes with properly closed shells

Fullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and... Full description

Journal Title: Physical Chemistry Chemical Physics 2010, Vol.12(44), pp.14822-14826
Main Author: Fowler, Patrick W.
Other Authors: Myrvold, Wendy
Format: Electronic Article Electronic Article
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ID: ISSN: 1463-9076 ; E-ISSN: 1463-9084 ; DOI: 10.1039/c0cp01513j
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title: Non-IPR fullerenes with properly closed shells
format: Article
creator:
  • Fowler, Patrick W.
  • Myrvold, Wendy
ispartof: Physical Chemistry Chemical Physics, 2010, Vol.12(44), pp.14822-14826
description: Fullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR (‘ super - sporadic ’ fullerenes). All have negative LUMO eigenvalues of small magnitude. Exhaustive search finds four examples with 160 or fewer vertices: one isomer of C 120 , two of C 156 and one of C 160 . The first three contain single pentagon pairs and the fourth, a linear triple of fused pentagons. Larger examples can be found. A capping construction gives a series of properly closed shell fullerenes of C 3 / C 3v symmetry, each with a single fully fused triple of pentagons and ≥632 vertices. Tubular extension of the C 120 example leads a series of C 1 / C s isomer pairs with ≥168 vertices, retaining the single pentagon adjacency and approaching isospectrality with increasing size. Both constructions are conjectured to lead to an infinite number of super-sporadic fullerenes.
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identifier: ISSN: 1463-9076 ; E-ISSN: 1463-9084 ; DOI: 10.1039/c0cp01513j
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  • 1463-9076
  • 1463-9084
  • 14639084
  • 14639076
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descriptionFullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR (‘ super - sporadic ’ fullerenes). All have negative LUMO eigenvalues of small magnitude. Exhaustive search finds four examples with 160 or fewer vertices: one isomer of C 120 , two of C 156 and one of C 160 . The first three contain single pentagon pairs and the fourth, a linear triple of fused pentagons. Larger examples can be found. A capping construction gives a series of properly closed shell fullerenes of C 3 / C 3v symmetry, each with a single fully fused triple of pentagons and ≥632 vertices. Tubular extension of the C 120 example leads a series of C 1 / C s isomer pairs with ≥168 vertices, retaining the single pentagon adjacency and approaching isospectrality with increasing size. Both constructions are conjectured to lead to an infinite number of super-sporadic fullerenes.
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abstractFullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR (‘ super - sporadic ’ fullerenes). All have negative LUMO eigenvalues of small magnitude. Exhaustive search finds four examples with 160 or fewer vertices: one isomer of C 120 , two of C 156 and one of C 160 . The first three contain single pentagon pairs and the fourth, a linear triple of fused pentagons. Larger examples can be found. A capping construction gives a series of properly closed shell fullerenes of C 3 / C 3v symmetry, each with a single fully fused triple of pentagons and ≥632 vertices. Tubular extension of the C 120 example leads a series of C 1 / C s isomer pairs with ≥168 vertices, retaining the single pentagon adjacency and approaching isospectrality with increasing size. Both constructions are conjectured to lead to an infinite number of super-sporadic fullerenes.
doi10.1039/c0cp01513j
pages14822-14826
date2010-11-03