Effect of DFT-functional on the energy and electronic characteristics of carbon compounds with the unconventional geometry of the framework

We report how strongly the energy and electronic properties of carbon nanostructures with the unconventional framework calculated by means of density functional theory (DFT) depend on the choice of DFT-functional on the example of carbon [n,5]prismanes. For comparative analysis we used such characteristics of molecular system as the values of binding energy and energy difference between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO gap). We obtained the binding energies and HOMO-LUMO gaps using seven different functionals B3LYP, X3LYP, M11, B3PW91, PBE0, PW, PBE, which belong to generalized gradient approximation and hybrid functionals, and standard 6-31G(d) electronic basis set. We show that the binding energies obtained for the long [n,5]prismanes with the efficient length of ~150 Å within the various DFT-functionals can differ by a factor of 1.1, and corresponding HOMO-LUMO gaps can differ by a factor of 23. Additional precision calculations at CCSD(T) level of theory of [2,5]prismane allow us to conclude that for determining the binding energies of carbon nanostructures with the unconventional framework, the hybrid functionals B3LYP, X3LYP, and M11 are the best choice, whereas for the HOMO-LUMO gap estimation M11 gives the closest to CCSD(T) result. The reported study is of methodological interest for carrying out the correct DFT-calculations with respect to novel nanomaterials with unconventional carbon framework such as hypercubane system, fullerene composites or pillared graphene.