Quantum Monte Carlo study on the structures and energetics of cyclic and linear carbon clusters Cn ( n = 1,...,10)

Abstract

Using fixed-node diffusion quantum Monte Carlo (DMC) simulation we investigate the structural properties and energetics of the linear and cyclic carbon clusters ${\mathrm{C}}_{n}$ for $n\ensuremath{\le}10$. We calculate the binding energy, the electron correlation energy, the dissociation energy, and the second difference in energy. We also present an analysis of the structural properties of the clusters. It is found that the bond lengths, binding energies, and dissociation energies obtained from the DMC calculations are in excellent agreement with the available experimental results. The electron-correlation contribution to the binding energy indicates that in the case of the linear isomers, the clusters of odd-number size are relatively more favored than their neighbors of even-number size, whereas for the cyclic isomers, we do not observe the oscillation pattern. In the range of cluster size under investigation, we find that the electron-correlation impact in the binding energy of the cyclic clusters is larger than that of the corresponding linear ones, varying from $30%$ to $40%$ of the binding energy values. The electron correlation is also essential to the stability of the clusters enhancing by up to $52%$ their dissociation energy. A comparative analysis of the dissociation energy and second difference in energy indicates that the linear isomers ${\mathrm{C}}_{3}$ and ${\mathrm{C}}_{5}$ are the most stable ones.