From small fullerenes to the graphene limit: A harmonic force‐field method for fullerenes and a comparison to density functional calculations for Goldberg–Coxeter fullerenes up to C₉₈₀

Abstract

We introduce a simple but computationally very efficient harmonic force field, which works for all fullerene structures and includes bond stretching, bending, and torsional motions as implemented into our open-source code Fullerene. This gives accurate geometries and reasonably accurate vibrational frequencies with root mean square deviations of up to 0.05 Å for bond distances and 45.5 cm(-1) for vibrational frequencies compared with more elaborate density functional calculations. The structures obtained were used for density functional calculations of Goldberg-Coxeter fullerenes up to C980. This gives a rather large range of fullerenes making it possible to extrapolate to the graphene limit. Periodic boundary condition calculations using density functional theory (DFT) within the projector augmented wave method gave an energy difference between -8.6 and -8.8 kcal/mol at various levels of DFT for the reaction C60 →graphene (per carbon atom) in excellent agreement with the linear extrapolation to the graphene limit (-8.6 kcal/mol at the Perdew-Burke-Ernzerhof level of theory).

Atomistic potential for graphene and other sp2 carbon systems

“…As one can see, the energy of the isomers rise linearly with the number N p of their pentagon adjacencies in accordance with the results of Ref. 42 Using our potential we found that the energy of the icosahedral C 60 fullerene with respect to the energy of graphene is ∆U (C 60 ) = 23.4 eV or ∆U (C 60 )/N = 0.39 eV/atom, which is consistent with the corre- sponding experimentally obtained energy value 0.41 ± 0.02 eV/atom 43,44 , and the theoretically obtained value 0.38 eV/atom using the DFT method at the GGA/PBE level 45 . The corresponding energy found from the optimum C 40 isomer (isomer 40:38 of Ref.…”

“…41, with N p = 10) is 0.64 eV/atom, in accordance with the value 14.6 kcal/mole (0.63 eV/atom), that can be obtained from Ref. 45. In that work, the energies of both the optimum C 40 isomer and graphene are given with respect to that of the icosahedral C 60 obtained with the DFT/PBE method.…”

Hollow Gold Cages and Their Topological Relationship to Dual Fullerenes

“…This is indeed the case and is depicted in Figure using a N −1 scaling law analogue to the one used for fullerenes (for details see ref. )…”

“…Program FULLERENE was used to construct initial structures of all isomers of the golden dual fullerenes from Au 12 to Au 20 using a recently developed force‐field for fullerenes (as already mentioned the golden dual fullerene Au 13 does not exist). The following isomers need to be considered according to the isomer list for the fullerenes (number in parenthesis gives the number of different isomers of same symmetry): I h ‐Au 12 , D 6 d ‐Au 14 , D 3 h ‐Au 15 , D 2 ‐Au 16 , T d ‐Au 16 , D 5 h ‐Au 17 , C 2 v ‐Au 17 (2), D 3 h ‐Au 18 , D 3 d ‐Au 18 , D 3 ‐Au 18 , D 2 ‐Au 18 , C 3 ‐Au 18 (2), C 3 v ‐Au 19 , C 2 ‐Au 19 (3), C s ‐Au 19 (2), D 6 h ‐Au 20 , D 3 h ‐Au 20 , D 2 d ‐Au 20 (2), C 2 v ‐Au 20 , D 2 ‐Au 20 (2), C 2 ‐Au 20 (3), C 2 ‐Au 20 (2), C 1 ‐Au 20 (2) and I h ‐Au 32 .…”

Theoretical investigation of the interactions between the π‐systems of molecular organic semiconductors and an analysis of the contributions of repulsion and electrostatics

“…Molecular mechanics (MM) plays a very important role in modern computational material sciences as the force fields provide a very efficient route to quickly calculate energies and geometries . To analyze their applicability and to gain insight, we compared the energy decompositions of different force fields for intermolecular potentials with their quantum‐mechanical counterparts like SAPT(DFT) or LMO‐EDA.…”