Bollettino dell'Unione Matematica Italiana

, Volume 10, Issue 3, pp 335–354 | Cite as

Stable carbon configurations

  • Ulisse StefanelliEmail author


Molecular Mechanics models molecules as configurations of particles interacting via classical potentials. The specific geometry of covalent bonding in carbon is described by the combination of an attractive-repulsive two-body interaction and a three-body bond-orientation part. We investigate the strict local minimality of specific carbon configurations under general assumptions on the interaction potentials. Carbyne, graphene, some fullerenes, and diamond are proved to be stable.


Configurational energy Carbon Stability 

Mathematics Subject Classification




The support of the Austrian Science Fund (FWF) Projects P 27052 and I 2375 is acknowledged. This work has been Funded by the Vienna Science and Technology Fund (WWTF) through Project MA14-009. Partial support by the Wolfgang Pauli Institute under the thematic project Crystals, Polymers, Materials is also acknowledged. The author is greatefully indebted to the anonymous referee for the careful reading of the manuscript.


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© Unione Matematica Italiana 2016

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” - CNRPaviaItaly

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