Classification system for fullerenes

Кустов, Е. Ф.; Nefedov, V. I.; Калинин, А. В.; Chernova, G. S.

doi:10.1134/s0036023608090076

Cited by 6 publications

(12 citation statements)

References 29 publications

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“…They include the groups H 2 , H 3 , and the largest non-crystallographic group H 4 ; the icosahedral group H 3 and its rotational subgroup I are of particular practical importance as H 3 is the largest discrete symmetry group of physical space. Thus, many 3-dimensional systems with high symmetry, such as viruses in biology, [5][6][7][8][9] fullerenes in chemistry, [10][11][12][13] and quasicrystals in physics, [14][15][16][17] can be modeled using Coxeter groups.…”

Section: Introductionmentioning

confidence: 99%

Affine extensions of non-crystallographic Coxeter groups induced by projection

Dechant

Bœhm

Twarock

2013

Journal of Mathematical Physics

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Reidun (2013) 'A ne extensions of non-crystallographic Coxeter groups induced by projection.', Journal of mathematical physics., 54 (9). 093508. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

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Section: Introductionmentioning

confidence: 99%

Affine extensions of non-crystallographic Coxeter groups induced by projection

Dechant

Bœhm

Twarock

2013

Journal of Mathematical Physics

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“…We have derived here the two simplest carbon onions starting with C 60 and C 80 in a simple affine-extension framework in which the affine symmetry relates all shells to each other simultaneously. Carbon onions at higher orders such as ones starting at C 120 and C 140 , which are the next allowed structures in the analysis of Kustov et al (2008) The carbon onion generated from C 80 : (a) C 80 , (b) C 180 and (c) C 320 . All three have pentagons that are oriented edge-to-edge, with each affine translation step inserting an extra hexagon between the pentagons.…”

Section: Discussionmentioning

confidence: 99%

“…that follows a similar pattern C n , where this time n is given by n ¼ 20ðz þ 1Þ 2 for z 2 N (Terrones et al, 2002). We have thus found carbon onions based on the first two allowed icosahedral fullerene structures identified in Kustov et al (2008) within our affine-extension framework, as summarized in Fig. 7.…”

Section: Electronic Reprintmentioning

confidence: 99%

“…Kustov et al (2008) have shown that from a group-theoretical point of view, C n with n ¼ 60z and n ¼ 60z þ 20, for z 2 N, are 'allowable' icosahedral fullerene structures. We therefore extend our classification of affine extensions of the icosahedral group here to include start configurations corresponding to the cases n ¼ 60 and n ¼ 80 with a view to recover these carbon onions in our affine-extension framework; note that the case of n ¼ 20 corresponds to the dodecahedron discussed in the previous section.…”

Section: Application To Fullerenes -Two Families Of Carbon Onionsmentioning

confidence: 99%

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Viruses and fullerenes – symmetry as a common thread?

Dechant¹,

Wardman²,

Keef³

et al. 2014

Acta Cryst Sect A

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Reidun (2014) 'Viruses and fullerenes -symmetry as a common thread ?', Acta crystallographica A., 70 (2). pp. 162-167. Further information on publisher's website:http://dx.doi.org/10.1107/S2053273313034220Publisher's copyright statement:Additional information:Deposited paper was the cover article for the March issue of this journal. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Author(s) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr.For further information see http://journals.iucr.org/services/authorrights.html Acta Crystallographica Section A: Foundations and Advances publishes articles reporting f undamental advances in all areas of crystallography in the broadest sense. This includes metacrystals such as photonic or phononic crystals, i.e. structures on the mesoor macroscale that can be studied with crystallographic methods. The central themes are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements. In the case of metacrystals, the focus is on the methods for their creation and on the structure-property relationships for their interaction with classical waves. The principle of affine symmetry is applied here to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organizational principle in virus structure and assembly. This group-theoretic framework is adapted here to the physical requirements dictated by carbon chemistry, and it is shown that mathematical models for carbon onions can be derived within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.

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“…In general, they are less stable than fullerenes and more difficult to isolate . As a consequence, the study of these systems at the theoretical level has become essential to fully understand their stability and their chemical properties . Quasi‐fullerenes present a very complex and diverse molecular topography and they are particularly interesting since they present a larger diameter compared to their analogous fullerenes.…”

Section: Introductionmentioning

confidence: 99%

Are Small Quasi‐Fullerenes Capable of Encapsulating Trimetallic Nitrides A_3‐xB_xN (A, B =Sc, Y, La,x=0‐3)? A DFT Study

et al. 2018

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The capacity of small quasi‐fullerenes (C48‐q and C60‐q, q stands for quasi) to encapsulate trimetallic nitride clusters; A3‐xBxN (A, B=Sc, Y, La, x=0‐3) was investigated by applying Density Functional Theory (DFT). Optimized geometries and the computation of ΔG formation energies, ΔΕHOMO‐LUMO energy values, chemical potential, chemical hardness and aromaticity were all performed in order to understand chemical reactivity and thermal stability of these novel quasi‐metallofullerenes. Moreover, the donor‐acceptor properties of the quasi‐metallofullerenes systems compared to the bare quasi‐fullerene cages are also analyzed. Finally, to understand the effect of temperature at which quasi‐fullerenes could be subjected to, ab initio molecular dynamics (MD) was also performed. The main conclusion of this report is that small quasi‐fullerenes are capable of encapsulating trimetallic nitride clusters, and that the donor‐acceptor properties are enhanced due to the presence of clusters.

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Classification system for fullerenes

Cited by 6 publications

References 29 publications

Affine extensions of non-crystallographic Coxeter groups induced by projection

Affine extensions of non-crystallographic Coxeter groups induced by projection

Viruses and fullerenes – symmetry as a common thread?

Are Small Quasi‐Fullerenes Capable of Encapsulating Trimetallic Nitrides A_3‐xB_xN (A, B =Sc, Y, La,x=0‐3)? A DFT Study

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Classification system for fullerenes

Cited by 6 publications

References 29 publications

Affine extensions of non-crystallographic Coxeter groups induced by projection

Affine extensions of non-crystallographic Coxeter groups induced by projection

Viruses and fullerenes – symmetry as a common thread?

Are Small Quasi‐Fullerenes Capable of Encapsulating Trimetallic Nitrides A3‐xBxN (A, B =Sc, Y, La,x=0‐3)? A DFT Study

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Are Small Quasi‐Fullerenes Capable of Encapsulating Trimetallic Nitrides A_3‐xB_xN (A, B =Sc, Y, La,x=0‐3)? A DFT Study