Information Entropy of Fullerenes

Abstract

The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (<1% of the studied structures) lie between the values of C60 and C70, the two most abundant fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.

Coarse-Grained Simulations Using a Multipolar Force Field Model

“…However, for more flexible polymers, those effects can be significant, such as those in rubber elasticity. This effect is currently under study in our group, which can provide extensions of the CGRB model [30,31]. …”

Activation energies and information entropies of helium penetration through fullerene walls. Insights into the formation of endofullerenes nX@C60/70(n = 1 and 2) from the information entropy approach

“…The application of the information theory approach [55][56][57][58][59][60][61] to endofullerenes was performed by distinguishing the inequivalent atoms in their structures, as in our previous studies. 62,63 Accordingly, the probability, p i , of nding an atom of i type equals N i /N where N i is the number of i atoms and N ¼ SN i is the total number of atoms in the molecule. Then, the information entropy (in bits) of the structure under consideration equals:…”

“…The V 1 values are the values of the inner cavities of C 60 and C 70 taken from the study of Adams et al 65 and Previously, the proposition has been made that the stochastic processes (which are not dened by the energetic factor) in fullerene-containing systems may be described in terms of information entropy. 62,63 This is a structural index that shows the diversity of the molecular system deduced from the number of inequivalent atoms. 56,57 Within such approach, the molecule is considered a message and its atoms symbols.…”

“…68 Indeed, the use of this quantity allows us to discriminate 14 experimentally achievable fullerenes (including C 60 and C 70 ) from 2079 possible fullerene structures. 62 Later, the information-entropy approach was extrapolated to oxygen allotropes. 63 This encouraged us to analyze the complexity of the title endofullerenes and their analogs with other llings.…”

Quantum mechanical study of GaxAsx fullerene type Micro-Clusters for X=10, 13, 15, 18, 20, 25 and 30 atoms

“…III -V group semiconductor materials have been the focus of numerous experiments [8][9]. Due to high electron mobility of III -V compounds such as GaAs, these have the capability of replacing Si in the electronics industry.…”