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Deductive molecular mechanics of carbon allotropes (Review article)

The relative stability of diamond and graphite is readdressed from the new perspective of deductive molecular mechanics. Unlike most theoretical studies that are conducted numerically, this article uses an analytical model to gain insight into the fundamental reasons behind the quasi-degeneracy of these allotropes with very different bonding patterns. The relative energies of the allotropes are derived and several general statements about the structure of these materials are proven. This analysis yields a quasi-degenerate electronic ground state for graphite and diamond at 0 K. Numerical estimates based on this analysis are in astonishingly good agreement with experimental data and recent results of numeric modeling, despite the fact that they were obtained with a drastically smaller numerical effort. An extension of the proposed interpretation to silicon allotropes proves to be very successful as well. The proposed approach is also expanded to four-coordinated carbon allotropes, and the software package Adamas is developed, which is able to calculate allotrope energies and elastic properties (elastic moduli). In the case of diamond and graphene, some general statements could be proven from deductive molecular mechanics parameters. Specifically, it is shown that among the four-coordinated allotropes the cubic diamond structure represents the true minimum. In the cases of allotropes with some C—C bonds that are stronger than those in diamond, the energy gain is compensated by the mandatory presence of weaker bonds in the same allotrope, which leads to the overall increase of the energy relative to the diamond.