Deductive molecular mechanics of carbon allotropes (Review Article)
I.V. Popov1,2, A.L. Chugreev1,2,3, and R. Dronskowski3,4
1Frumkin Institute of Physical Chemistry and Electrochemistry RAS, 31, bld.4, Leninsky prospect, Moscow, 119071 Russia
2Independent University of Moscow, Moscow, Russia
3RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany
4Шэньчжэньский институт передовых технологий Китайской академии наук, Шэньчжэнь, КНР
Received February 21, 2020, published online May 26, 2020
The relative stability of diamond and graphite is readdressed from a new perspective of the deductive molecular mechanics. Unlike most theoretical studies done numerically, we use an analytic model to get an insight into fundamental reasons for quasi-degeneracy of these allotropes with very different bonding patterns. We derive the relative energies of the allotropes and prove several general statements about the structure of materials. Our analysis yields a quasi-degenerate electronic ground state for graphite and diamond at 0 K. Numerical estimates based on it are in an astonishingly good agreement with experimental data and recent results of numeric modeling, although obtained with a drastically smaller numerical effort. An extension of the proposed treatment to the allotropes of silicon proves to be very successful as well. Following similar lines, we extended the proposed treatment to the four-coordinated allotropes of carbon and developed the software package Adamas which is capable to calculate energies of allotropes and their elastic properties (elastic moduli). Similarly, to the case of diamond and graphene, some general statements could be proven within the deductive molecular mechanics setting. Specifically, it is shown that among the four-coordinated allotropes the cubic diamond structure represents the true minimum. In the cases of allotropes that contain some C–C bonds stronger than those in diamond, the energy gain is compensated by the mandatory presence of weaker bonds in the same allotrope finally leading to the overall increase of the energy relative to the diamond.
Key words: diamond, lonsdaleite, graphite, graphene, quantum chemical calculations, hybrid orbitals.