A Constructive Enumeration of Fullerenes

Brinkmann, Gunnar; Dress, Andreas

doi:10.1006/jagm.1996.0806

Cited by 132 publications

(123 citation statements)

References 3 publications

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“…Calculations implementing the rules embodied in Tables I and II were carried out for various sets of graphs. Generators geng (part of the nauty software written by B. D. McKay and available at http://cs.anu.edu.au/~bdm/), plantri, 35 CaGe, 36 fullgen, 37 and our own ad hoc programs were used to construct general families of graphs.…”

Section: A Statistics Of Conduction Of Molecular Graphsmentioning

confidence: 99%

Omni-conducting and omni-insulating molecules

Fowler

Pickup

Todorova

et al. 2014

The Journal of Chemical Physics

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The source and sink potential model is used to predict the existence of omni-conductors (and omniinsulators): molecular conjugated π systems that respectively support ballistic conduction or show insulation at the Fermi level, irrespective of the centres chosen as connections. Distinct, ipso, and strong omni-conductors/omni-insulators show Fermi-level conduction/insulation for all distinct pairs of connections, for all connections via a single centre, and for both, respectively. The class of conduction behaviour depends critically on the number of non-bonding orbitals (NBO) of the molecular system (corresponding to the nullity of the graph). Distinct omni-conductors have at most one NBO; distinct omni-insulators have at least two NBO; strong omni-insulators do not exist for any number of NBO. Distinct omni-conductors with a single NBO are all also strong and correspond exactly to the class of graphs known as nut graphs. Families of conjugated hydrocarbons corresponding to chemical graphs with predicted omni-conducting/insulating behaviour are identified. For example, most fullerenes are predicted to be strong omni-conductors. © 2014 AIP Publishing LLC.

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Section: A Statistics Of Conduction Of Molecular Graphsmentioning

confidence: 99%

Omni-conducting and omni-insulating molecules

Fowler

Pickup

Todorova

et al. 2014

The Journal of Chemical Physics

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“…Polyhedra in general can be built from successive additions of polygons in spiral patterns [7,16] and this spiral algorithm was implemented in the program bspiral. Not all sequences of polygons Figure 2.…”

Section: Spiral Algorithmmentioning

confidence: 99%

“…Considerable effort has gone into investigating the geometry of fullerene shells in the context of carbon chemistry [7,16]. Acknowledging the basic differences between C atoms and CA subunits, this work provides a platform for considering retroviral capsid geometry.…”

Section: Diversity Of Closed Polyhedramentioning

confidence: 99%

Irregular and Semi‐Regular Polyhedral Models for Rous Sarcoma Virus Cores

Heymann

Butan

Winkler

et al. 2000

Computational and Mathematical Methods in Medicine

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Whereas many viruses have capsids of uniquely defined sizes that observe icosahedral symmetry, retrovirus capsids are highly polymorphic. Nevertheless, they may also be described as polyhedral foldings of a fullerene lattice on which the capsid protein (CA) is arrayed. Lacking the high order of symmetry that facilitates the reconstruction of icosahedral capsids from cryo-electron micrographs, the 3D structures of individual retrovirus capsids may be determined by cryoelectron tomography, albeit at lower resolution. Here, we describe computational and graphical methods used to construct polyhedral models that match in size and shape, capsids of Rous sarcoma virus (RSV) observed within intact virions. The capsids fall into several shape classes, including tubes, 'lozenges' and 'coffins'. The extent to which a capsid departs from icosahedral symmetry reflects the irregularity of the distribution of pentamers, which are always 12 in number for a closed polyhedral capsid. The number of geometrically distinct polyhedra grows rapidly with increasing quotas of hexamers, and ranks in the millions for particles in the size range of RSV capsids, which typically have 150-300 hexamers. Unlike the CAs of icosahedral viruses that assume a minimal number of quasi-equivalent conformations equal to the triangulation number (T), retroviral CAs exhibit a near-continuum of quasi-equivalent conformations -a property that may be attributed to the flexible hinge linking the N-and C-terminal domains.

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“…[6]) that a top-down Divide&Conquer strategy allows to design an algorithm for fullerene enumeration which is absolutely reliable -that is, it guarantees complete lists -and simultaneously amazingly efficient: On an HP9000/735, a complete enumeration of e.g. all 0 60 -structures (of which there are 1812) needs about 12 seconds: 6.5 seconds for the generation of sufficiently many such structures and 5.5 seconds for testing structural isomorphism.…”

Section: Fullerene Structure Enumerationmentioning

confidence: 99%