Valence force field-based Monte Carlo bond-rotation method for the determination of sp²-bonded carbon structures

We present a valence force field (VFF)-based Monte Carlo (MC) bond-rotation method capable of identifying stable sp²-bonded carbon configurations. The VFF contains four parameters that are adjusted to fit density functional theory (DFT) calculations for both planar and non-planar model structures; the simple VFF model is shown to reliably reproduce the DFT energetics of disordered sp²-bonded carbon with various topologies and sizes. The MC bond-rotation method combined with the VFF is demonstrated to be effective in determining minimum-energy sp²-bonded carbon structures, such as topological defects and fullerenes with different sizes. The computational approach is also applied to investigate possible configurations of multi-vacancy defects (V_2n, 2 n 8) and their relative stability.