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C60 Related Clusters

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Multi-shell Polyhedral Clusters

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 10))

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Abstract

A hyper-structure is a (molecular) construction, of formula MY(mS; p) . n: M is the parent molecule in the Y “hyper”-building while m is the number of substructures S, joined by the type p facets; the total number n of atoms suffixes the name of the hyper-structure. Point-centered clusters and “cell-in-cell” clusters, used as seeds for map operations or even stellated “monomers” contributed to hyper-structure building, all based on the topology of M = C60(I h ). Examples are given starting from C750 = C60Y(60C20).750, transformed by dual, medial and truncation operations, to obtain hyper-structures of the type C60Y(60S; p).n.

Vertex equivalence classes found by topological descriptors were confirmed by permutations performed on the adjacency matrix associated to such complex graphs (by using Mathematica software). An atlas section illustrates the discussed multi-shell polyhedral clusters.

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References

  • Bergman G, Waugh JLT, Pauling L (1952) Crystal structure of the intermetallic compound Mg32(Al, Zn)49 and related phases. Nature 169:1057–1058

    Article  CAS  Google Scholar 

  • Bhattacharya D, Klein DJ, Ortiz Y (2016) The astounding buckyball buckyball. Chem Phys Lett 647:185–188

    Article  CAS  Google Scholar 

  • Diudea MV (2013) Quasicrystals, between spongy and full space filling. In: Diudea MV, Nagy CL (eds) Diamond and related nanostructures. Springer, Dordrecht, pp 333–383

    Chapter  Google Scholar 

  • Diudea MV, Rosenfeld VR (2017) The truncation of a cage graph. J Math Chem 55:1014–1020

    Article  CAS  Google Scholar 

  • Euler L (1752–1753) Elementa doctrinae solidorum-Demonstratio nonnullarum insignium proprietatum, quibus solida hedris planis inclusa sunt praedita. Novi Comment Acad Sc Imp Petropol 4:109–160

    Google Scholar 

  • Nagy CL (2016) Symmetry computation by Mathematica (to be published)

    Google Scholar 

  • Nagy CL, Diudea MV (2009) Nano studio software. Babes–Bolyai University, Cluj

    Google Scholar 

  • Stefu M, Parvan-Moldovan A, Kooperazan-Moftakhar F, Diudea MV (2015) Topological symmetry of C60-related multi-shell clusters. MATCH Commun Math Comput Chem 74:273–284

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, Cluj-Napoca, Romania

    Mircea Vasile Diudea

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  1. Mircea Vasile Diudea
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Chapter 9 Atlas: C60 Related Structures

Chapter 9 Atlas: C60 Related Structures

figure a

C60

dC60.32

12(35).20(36)

P^32@dC60.33

figure e

C60

m(C60).90

mC60@C60.150

figure i

dC60.32

mC60.90

P^32@dC60.33

figure m

m(P32@dC60.33).122

C60@(12mP5;20mP6).330_5

C60@(12mP5;20mP6;60C).390_5

d(C122).390

figure q

CO.12

mC60.90

C122

figure u

Rh12 =dmC.14

C122

m(C122).450

figure y

mmC.24

C122

m(C122).450

figure ac

tO.24=TO.24

l(C60).180

C 122

figure ag

TT.12

dC60.32= st(D).32

P^32@dC60.33

figure ak

dC60.32

P32@dC60.33

stC60.92

figure ao

C84=t(IP).84

C100=t(P@st(A6)).100

C540(I h )

figure as

TT.12

P32@dC60.33

l(C60).180

figure aw

dC60.32

P32@dC60.33

P32@dC60@C60.93

figure ba

A5.10

mA6.24

C92=C60@dC60.92

figure be

d(C60).32

O@3O.15

m(C60).90

figure bi

CO@3CO.39

m(C92).360

C60@dC60.92

figure bm

TO@3TO.78

m(C92).360

C92=C60@dC60.92

figure bq

TT@3TT.30

l(C60).180

C92=C60@dC60.92

figure bu

TT.12

C60

dC60@C60.92

figure by

dC60.32

P32@dC60.33

dC60@C60.92

figure cc

d(C60).32

m(P32@dC60.33).122

m(C60@d(C60)).360

figure cg

C450

C1260

P32@dC60@C60.93

figure ck

C60

dC60.32

st(dC60).92

figure co

C60

dC60.32

st(dC60).92

figure cs

mC60.90

dC60.32

st(dC60).92

figure cw

C180 = l(C60).180

dC60.32

st(dC60).92

figure da

st(ID).50

6(st(ID).50).210

5(st(ID).50).175

figure de

C1650_2

C1650_3

C1650_5

figure di

(12HC20;20HC24).330

t sel (p 4(C60)).330

(H=half)

s 2(C60).420

C60P.61

P@tI.61

P60@C60.61

figure dm

C60

s 2(C60).420

C810

figure dq

d(C750).630sp_2

d(C750).630sp_3

d(C750).630_5

figure du

C60P60.61_2

C60P60.61_3

C60Y(60D).750

figure dy

d(C750).630_5

C3600_3

C3600/C5040_5

figure ec

C60Y(60C60; hh[2+2]).3600_2

C60Y(60C60; hh[2+2]).3600_5

C60Y(60C60; ph[2+2]).3600_3

figure eg

t(C60).180

m(C20).30=ID.30

C24

figure ek

dmD.32= Rh30.32

C750

C1350

figure eo

t(C750).2700_2

t(C750).2700_3

t(C20).60 = TD

figure es

l(C750).3150_2

l(C750).3150_3

C750_5

figure ew

C9900_2

C9900_3

t(C60).180

figure fa

C60

C24

C60@C330.390

figure fe

C20

C24

(12HC20;20HC24).330

t sel (p 4(C60)).330

figure fi

C1500_2

C1500_3

C1350_5

figure fm

t(C810).3000_2

t(C810).3000_3

t(C60).180

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Diudea, M.V. (2018). C60 Related Clusters. In: Multi-shell Polyhedral Clusters. Carbon Materials: Chemistry and Physics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-64123-2_9

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