Curvature-induced excess surface energy of fullerenes: Density functional theory and Monte Carlo simulations

Carbon nanostructures are investigated using a multiscale approach based on density functional theory (DFT) and Monte Carlo (MC) simulations. The structure of small fullerenes is calculated using DFT, and simple models are employed to determine classical potential functions which are then used in MC simulations to investigate larger structures. The structural parameters as obtained by DFT and by MC simulations are cross validated for small fullerenes, allowing to understand the effect of the approximations made in MC simulations. It is found that MC overestimates the numerical value of the excess surface energy of carbon nanostructures but the functional dependence, i.e., the decay exponent as a function of the fullerene size, is accurately described. The MC results reveal that bond torsion is the dominant term of the total curvature energy. The combination of DFT and MC allows to get reliable estimates for the excess surface energy of fullerenes as a function of radius for a wide range of fullerene sizes, which may serve as an important input for large-scale finite-element modeling of more complex systems.