The Kernel energy method: Application to graphene and extended aromatics

The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of π‐electrons, Clar sextets, and the approximate overall aromaticity. Sivaramakrishnan et al. J Phys Chem A, 2005, 109, 1621] define similar “ring conserved isodesmic reactions (RCIR).” The principal innovation of this article is the suggestion that kernels may be mathematically extracted from an extended aromatic molecule such as graphene by a fissioning of aromatic bonds. Hartree Fock (HF) and Møller‐Plesset (MP2) chemical models using a Gaussian basis of 3‐21G orbitals are used to calculate the total energy of a graphene flake. This demonstration calculation is performed on a graphene flake in which dangling bonds are saturated with hydrogens (C₇₈H₂₆) composed of a total of 104 atoms arranged in 27 benzenoid rings. The KEM with both types of chemical model are shown to be accurate to nearly 1 kcal/mol, of a total energy, which is nearly 3000 atomic units, that is, with an absolute error within “chemical accuracy” and a relative error of the order of 5 × 10⁵% of the total energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011