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The generation of fullerenes.
Gunnar Brinkmann1, Jan Goedgebeur, Brendan D McKay
1Applied Mathematics & Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium.
Journal of Chemical Information and Modeling
|October 2, 2012
Summary
A new, faster algorithm generates fullerenes more efficiently than previous methods. This computational chemistry tool aids in exploring larger molecular structures and verifying mathematical conjectures in graph theory.
Area of Science:
- Computational Chemistry
- Graph Theory
- Materials Science
Background:
- Fullerenes are carbon allotropes with unique properties.
- Generating and analyzing fullerenes is computationally intensive.
- Existing algorithms have limitations in speed and scale.
Purpose of the Study:
- To develop a novel, efficient algorithm for fullerene generation.
- To identify limitations in existing fullerene generation software.
- To tabulate fullerene counts and verify graph theory conjectures.
Main Methods:
- Algorithm development for fullerene structure generation.
- Performance benchmarking against existing software (fullgen).
- Computational verification of mathematical conjectures.
Main Results:
- The new algorithm is over 3.5 times faster than fullgen.
- The algorithm is effective for fullerenes with over 100 vertices.
- A programming error in fullgen was identified.
- Numbers of fullerenes and IPR fullerenes tabulated up to 400 vertices.
- Barnette's conjecture and the spiral conjecture were tested.
Conclusions:
- The developed algorithm offers significant speed and scalability improvements for fullerene generation.
- The findings contribute to the understanding of fullerene structures and their enumeration.
- The study provides computational evidence related to graph theory conjectures.
