Skeletal Rearrangements of the C240 Fullerene: Efficient Topological Descriptors for Monitoring Stone–Wales Transformations

Stone–Wales rearrangements of the fullerene surface are an uncharted field in theoretical chemistry. Here, we study them on the example of the giant icosahedral fullerene C240 to demonstrate the complex chemical mechanisms emerging on its carbon skeleton. The Stone–Wales transformations of C240 can produce the defected isomers containing heptagons, extra pentagons and other unordinary rings. Their formations have been described in terms of (i) quantum-chemically calculated energetic, molecular, and geometric parameters; and (ii) topological indices. We have found the correlations between the quantities from the two sets that point out the role of long-range topological defects in governing the formation and the chemical reactivity of fullerene molecules.

Study on the icosahedral fullerene structure with ultra-light and pressure resistance character

A large-scale helium-filled icosahedral fullerene structure is presented, which could be floatable in the air.

Extension of Caspar-Klug theory to higher order pentagonal polyhedra

Many viral capsids follow an icosahedral fullerene-like structure, creating a caged polyhedral arrangement built entirely from hexagons and pentagons. Viral capsids consist of capsid proteins,which group into clusters of six (hexamers) or five (pentamers). Although the number of hexamers per capsid varies depending on the capsid size, Caspar-Klug Theory dictates there are exactly twelve pentamers needed to form a closed capsid.However, for a significant number of viruses, including viruses of the Papovaviridae family, the theory doesn’t apply. The anomaly of the Caspar-Klug Theory has raised a new question:“For which Caspar and Klug models can each hexamer be replaced with a pentamer while still following icosahedral symmetry?” This paper proposes an answer to this question by examining icosahedral viral capsid-like structures composed only of pentamers, called pentagonal polyhedra. The analysis shows that pentagonal polyhedra fall in a subclass of T, defined by P ≥ 7 and T = 1( mod 3).

Computer models of icosahedral carbon nanostructures (shungite)

A universal algorithm for the generation of three-dimensional models of icosahedral fullerene-like carbon nanostructures has been developed. Coordinates of atoms on their surface are calculated and three-dimensional models of fulleroids – nested icosahedra – are built. A flat model consisting of five graphite layers of varying diameters is computed in an attempt to explain the nature of the diffraction maximum (d≃ 6.81 Å, 2θ ≃ 13°) in shungite carbon by the existence of edge effects, carbon atoms or small fragments of layers in the interlayer space, or dislocation rings.