Computing the Permanent of the Adjacency Matrix for Fullerenes
نویسندگان
چکیده
Motivation. Novel carbon allotropes, with finite molecular structure, including spherical fullerenes are nowadays currently produced and investigated. These compounds have beautiful architectures and show unusual properties that are very promising for the development of nanotechnologies. The Kekulé structure count and permanent of the adjacency matrix are computed for these molecules. Method. A method for computation of the permanent of the adjacency matrix is herein optimized for fullerenes. The method finds exact values for permanents of adjacency matrices up to 60u60. Results. The results provide linear and non–linear correlations between different structural parameters involving the presence of contiguous pentagons, ln[per(A)]/ln K, ln K and ln[per(A)]. Conclusions. A method for computing the permanent of the adjacency matrix is optimized for fullerenes. As ln[per(A)]/ln K can be related with thermodynamic stability, this aspect of chemistry could be useful for designing or predicting unknown fullerenes and their structure. The non–linear correlation for ln[per(A)]/ln K is improved. The variance decreases 49% and the risk of co–linearity diminishes. Availability. The software programs are available on request from the author ([email protected]) and are free for academics.
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