Relative Stabilities of C92 IPR Fullerenes

Slanina, Zdenêk; Zhao, Xiang; Deota, Pradeep T.; Ōsawa, Eiji

doi:10.1007/pl00010732

Cited by 49 publications

(46 citation statements)

References 13 publications

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“…The smallest fullerene cage that obeys the IPR is C 60 and the C 70 is the second smallest. For C 60 , there is only one isomer that satisfies the IPR. There are 8149 possible isomers of closed cage for C 70 but only one of them obeys IPR [41,42].…”

Section: Isolated Pentagon Rule (Ipr) In Fullerenesmentioning

confidence: 93%

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Remarkable diversity of carbon–carbon bonds: structures and properties of fullerenes, carbon nanotubes, and graphene

2010

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Large scientific community has been passionate in understanding different carbon nanostructures for last two decades. In this review, we present the general description of low-dimensional carbon allotropes such as fullerenes (0D), carbon nanotubes (1D), and graphene (2D). These structures have unique diversity of carbon-carbon bonds. Structures and electronic properties of fullerenes, small closed carbon cages, and giant fullerenes are illustrated. We point out the complexity in the area of fullerene research because of a wide range of structures and number of possible isomers of fullerenes. The concept of isolated pentagon rule in fullerenes is highlighted. We delineate the usefulness of pyramidalization angle in evaluating the curvature of fullerenes. The role of computational chemistry in identifying different isomers of fullerenes and validating the experimental results in ambiguous situations is also briefly mentioned. Properties of different types of carbon nanotubes, particularly singlewalled carbon nanotubes (SWCNTs) and their structural features are summarized. The use of pyramidalization angle (h P ) and p-orbital misalignment angles in predicting the reactivity of different carbon atom sites of SWCNTs is discussed. Finally, we outline the structures and electronic properties of graphene, and discuss the status of experimental investigations of this species.

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Section: Isolated Pentagon Rule (Ipr) In Fullerenesmentioning

confidence: 93%

“…Computational methods have been employed to systematically search and study the low-lying isomeric structures of fullerenes [34,[59][60][61][62][63][64][65]. Such thorough investigations are vital to correctly predict the lowest-energy structure.…”

Section: Isolated Pentagon Rule (Ipr) In Fullerenesmentioning

confidence: 99%

Remarkable diversity of carbon–carbon bonds: structures and properties of fullerenes, carbon nanotubes, and graphene

2010

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“…It has been known for isomeric sets of fullerenes and metallofullerenes (e.g., Refs. [ 12 , 13 , 14 , 15 , 16 ]) that potential energy itself cannot generally decide stability order at high temperatures as the entropic part of the Gibbs energy becomes essential—this feature was also demonstrated for Ca@C

[ 11 ] or La@C

[ 8 ].…”

Section: Introductionmentioning

confidence: 93%

Eu@C72: Computed Comparable Populations of Two Non-IPR Isomers

et al. 2017

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Relative concentrations of six isomeric Eu@C72—one based on the IPR C72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon–pentagon junction (symmetries C2 and C2v), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon–pentagon fusions—are DFT computed using the Gibbs energy in a broad temperature interval. It is shown that the two non-IPR isomers with one pentagon–pentagon junction prevail at any relevant temperature and exhibit comparable populations. The IPR-satisfying structure is disfavored by both energy and entropy.

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“…Moreover, a coexistence of two or more isomers is a rather common feature of higher fullerenes and several mixtures of fullerene isomers have already been studied, for example, C 78 (e.g., 9–12); C 80 (e.g., 13–16); C 82 (e.g., 17–21); C 84 (e.g., 22–26); C 86 (e.g., 2, 27); C 88 (e.g., 2, 28); C 90 (e.g., 2, 29); C 92 (e.g., 3, 6, 30, 31); C 94 (e.g., 32, 33) and even for some still higher members 5, 6, 34, 35. In overall, the computations demonstrated 36 that, from the theoretical point of view, productions of the higher fullerenes cannot be completely interpreted without an inclusion of temperature effects, i.e., without entropy contributions.…”

Section: Introductionmentioning

confidence: 99%

Computing enthalpy–entropy interplay for isomeric fullerenes

Slanina

Zhao

Uhlı́k

et al. 2004

Int J of Quantum Chemistry

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ABSTRACT:Fullerenes represent unique species in many respects, one of them being one of the highest temperature regions ever used for preparation of chemical species. This very factor automatically substantially enhances the importance of the TS part of the Gibbs function. The essential feature of fullerenic systems has consistently been ignored in computational studies of fullerenes, almost always drawing their conclusions from potential energies or heats of formation. This report demonstrates that the simplified treatment cannot really describe all the features of complex mixtures of isomeric fullerenes. General formulas are surveyed and illustrated on C 96 -the biggest set of isomeric fullerenes characterized by 13 C NMR spectra to date. Computations are carried out for the complete set of 187 isolated-pentagon-rule (IPR) isomers of C 96 , using four semiempirical quantum chemical methods (MNDO, AM1, PM3, and SAM1). Entropy terms are also computed and the relative-stability problem is entirely treated in terms of the Gibbs function. In overall, the computed data match the observed data reasonably well, although no method can really reproduce the complete ten-membered observed set. There are however still several aspects to be checked and several possibilities how to improve quality of the computed terms. In principle, such developments are, however, only a question of available computing power. There are, nevertheless, some remaining questions, such as inclusion of anharmonicity effects, contribution from electronic partition function, or even interactions between individual, yet separated motions. This article also discusses a subsequent, more general task of relative stabilities of carbon cages of different dimensions, i.e., relative stabilities of nonisomeric fullerenes. The computational treatment of isomeric mixtures has several interesting features: the results depend on temperature, but not on pressure; only the relative, and not the absolute, values of the heats of formation are needed; and the form of the master equation allows for an ample cancellation of terms in the partition functions. In contrast, for the more general task-relative stabilities of fullerenes of different dimensions-the absolute values of the heats of formation are required, the mentioned cancellations do not operate there, and the scheme is essentially pressure dependent.

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Relative Stabilities of C92 IPR Fullerenes

Cited by 49 publications

References 13 publications

Remarkable diversity of carbon–carbon bonds: structures and properties of fullerenes, carbon nanotubes, and graphene

Remarkable diversity of carbon–carbon bonds: structures and properties of fullerenes, carbon nanotubes, and graphene

Eu@C72: Computed Comparable Populations of Two Non-IPR Isomers

Computing enthalpy–entropy interplay for isomeric fullerenes

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