On relative stability reasoning for clusters of different dimensions: an illustration with the C60-C70 system

Slanina, Zdenêk; Rudziński, Jerzy M.; Togasi, M.; Ōsawa, E

doi:10.1016/0040-6031(89)87287-9

Cited by 21 publications

(8 citation statements)

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“…A subsequent, more general (and more important) task, relative stabilities of carbon cages of different dimensions, i.e., non‐isomeric fullerenes, is discussed only very rarely 51–55. Interestingly enough, the problem was, probably for the first time, touched by Schultz 1.…”

Section: Treatment Of Non‐isomeric Clustersmentioning

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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Section: Treatment Of Non‐isomeric Clustersmentioning

confidence: 99%

Computing enthalpy–entropy interplay for isomeric fullerenes

Slanina

Zhao

Uhlı́k

et al. 2004

Int J of Quantum Chemistry

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“…An agreement can be reached by a proper computational evaluation of the mole fractions in the saturated vapour over graphite (Table 4, AM1 description [14] of C60/C7o ). The vapour was simulated by seven species C,(g) (n = 1-5, 60, 70) for which input information was available [14,15]. However, the saturated-vapour condition is rather strong requirement; it can be reduced by applying mere C6o/Cvo inter-cluster equilibrium.…”

mentioning

confidence: 72%

“…From the point of view of the stability evaluations the species could be treated in a unified way. However, with respect to technical demands the area of the small species (e.g., C4 [2-8], Cs [9, 10], or C 6 [11, t2]) is naturally understood in a more complete way than the larger species [13][14][15]. Several recent computational studies demonstrated isomerism for some of the small clusters.…”

mentioning

confidence: 99%

“…Temperature evolutions of the mole fractions w i of the 3Z~-linear (the curves lying highest in the high-temperature limit), D3h cyclic (the lowest curves in the limit), and 3Z 5 linear structures of C6(g) for two evaluations [11] of their potential energy; the difference AE between the first two structures: 85 (top, 6-31G*/MP4) and 46 k J/tool (bottom, "the best" values) Table 4. Relative stability" of the C6o(9) and C70(9) species under conditions of the saturated vapour b or estimated conditions of observation [17] T Based on the AM1 data [14] and the saturatedvapour b pressure [15] b The saturated vapour simulated by the equilibrium mixture of C,(9) (n = 1-5, 60, 70) over graphite c Index of the C, cluster possessing the highest mole fraction in the saturated vapour b d The ratio of the C60 and C70 in the saturated vapour b…”

mentioning

confidence: 99%

“…The maximum sublimation-cell temperature [17] I The pressure of the C6o/C7o mixture (not saturated vapour) yielding, within the AM1 computational scheme, the observed ratio g " An observed C~o/C¢o ratio [t7] observation disagreement [13,14] with the C6o/C7o relative stability. An agreement can be reached by a proper computational evaluation of the mole fractions in the saturated vapour over graphite (Table 4, AM1 description [14] of C60/C7o ).…”

mentioning

confidence: 99%

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C n carbon clusters (n=4−6, 60, 70): interesting cases of computation/observation comparisons

Slanina

Rudziński

Ōsawa

1991

Z Phys D - Atoms, Molecules and Clusters

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Abstract. Recent theoretical studies proved some of the small carbon clusters C, (n ~ 1 -10) are represented by several isomeric structures. Evaluation of the isomer relative stabilities is necessary for comparison of theoretical data with observation, this being exemplified by the C4 and C6 cases. For the former cluster a new energy estimation has been suggested based on the isomerism reasoning. Relative-stability evaluation for clusters of different dimensions is discussed on the C6o/C7o system, pointing out a strong pressure-dependency of the picture. The scheme is matched to the recent observations of Bethune and Meijer. The vigorous interest in larger carbon species of the C6o type is connected with continuing studies in small carbon clusters C, (n ~ 1 -10)-for review, [1]. From the point of view of the stability evaluations the species could be treated in a unified way. However, with respect to technical demands the area of the small species (e.g., C4 [2-8], Cs [9, 10], or C 6 [11, t2]) is naturally understood in a more complete way than the larger species [13][14][15]. Several recent computational studies demonstrated isomerism for some of the small clusters. It requires a more complex scheme (cf. Table 1, exemplifying the C4 case) for comparison of theoretical data with observation than the isomerism-free situation (cf. Table 2 with the C 5 system). Another instructive example is represented by the C 6 species, which was predicted [11] to possess the D3h cyclic structure in its ground state, however, followed by linear triplet structure and other two species. However, a consistent thermodynamic treatment [16] shows that at the observational temperature (T = 2500 K) the actual stability order is substantially different from that found at 0 K: more than 95% of the mixture is formed by the linear structure (Table 3)! Systems with cluster isomerism can be classified according to the presence of the isomeric relative-stability interchange. Three evaluations of the energy differences AE between the linear and Dzh rhombic C 4 isomers are considered in Fig. t. In addition to the previous evaluations [5,6], we derived the third value from an isomeric

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Computations in Treating Fullerenes and Carbon Aggregates

Slanina

Lee

1996

Reviews in Computational Chemistry

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On relative stability reasoning for clusters of different dimensions: an illustration with the C60-C70 system

Cited by 21 publications

References 44 publications

Computing enthalpy–entropy interplay for isomeric fullerenes

Computing enthalpy–entropy interplay for isomeric fullerenes

C n carbon clusters (n=4−6, 60, 70): interesting cases of computation/observation comparisons

Computations in Treating Fullerenes and Carbon Aggregates

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