8.4 Methodology

The range of isomers studied, $\mathrm {C}_{24}$ to $\mathrm {C}_{32}$, was selected to cover the range of masses from where the fullerene is clearly predicted to be unstable to where a fullerene is clearly observed. This enables the prediction of the smallest energetically stable fullerene.

To determine the lowest energy isomers a hierarchy of methods of increasing accuracy and computational cost is commonly used. The first stage is to select candidate structural isomers via empirical methods such as bond counting and geometric rules such as ``minimize the number of adjacent pentagons''. [153] Quantum mechanical calculations such as tight-binding and density functional theory (DFT) based methods are then used to refine the selection. In order to finally establish the energetic ordering of different isomers, very accurate calculations must be performed. Although it would be desirable to perform coupled cluster calculations as well as QMC calculations, these are severely limited by the size of basis set that is computationally affordable for systems of the size of interest.

In this study, isomer selection was based on several previous density functional and quantum chemical studies. Geometries were then optimised within DFT, using the B3LYP hybrid functional. [154]