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Fullerene Stability by Geometrical Thermodynamics
Author(s) -
Parker Michael C.,
Jeynes Chris
Publication year - 2020
Publication title -
chemistryselect
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.437
H-Index - 34
ISSN - 2365-6549
DOI - 10.1002/slct.201903633
Subject(s) - fullerene , formalism (music) , thermodynamics , entropy (arrow of time) , statistical physics , physics , theoretical physics , stability (learning theory) , chemistry , materials science , mathematical physics , mathematics , quantum mechanics , computer science , machine learning , art , musical , visual arts
This work proves that stability of C 60 is a geometrical property of the thermodynamics of the system: a significant methodological advance since a detailed treatment of the energetics may be avoidable. This approach may be fruitful, not only for fullerenes but also for general problems of molecular stability and in other applications of conformational chemistry. For the non‐chiral C 60 , C 384 , and the weakly‐chiral C 28 , C 76 and C 380 (of these, C 380 and C 384 are classed as “unspirallable”), Schlegel projections are used to show that these fullerenes can all be represented by pairs of spirals counter‐propagating in anti‐parallel (C2) symmetry. For C 60 , the high symmetry is used to construct an analytical approximation for the spherical double‐spirals, shown mathematically to be Maximum Entropy ( MaxEnt ) using the formalism of Quantitative Geometrical Thermodynamics ( QGT ). Therefore C 60 is necessarily stable. This MaxEnt stability criterion is general, depending only on the geometry and not the kinematics of the system. The sense and degree of chirality for C 76 and C 380 is also quantified using a Shannon entropy‐based fragmentation metric.