Structure and Stability of Molecular Carbon: Importance of Electron Correlation

The electronic structure of medium-size molecular carbon is determined by a variety of methods, including density functional, quantum chemistry, and quantum Monte Carlo approaches. We demonstrate (i) significant differences between the mean-field methods in determining the minimum energy structure of a set of ${\mathrm{C}}_{10}$ and ${\mathrm{C}}_{20}$ isomers, and (ii) the crucial importance of an accurate account of electron correlation which enables us to predict, e.g., that of the available geometries for ${\mathrm{C}}_{20}$ the relaxed graphite fragment (bowl) is lower in energy than either the ring or fullerene isomers.