An Improved Descriptor of Cluster Stability. Application to Small Carbon Clusters

The mass spectra of gas-phase clusters in cluster beams have a rich structure where the relative heights of the peaks compared to peaks corresponding to clusters of neighbor sizes reveal the stability of the clusters as a function of the size $N$. In an analysis of the published mass spectrum of carbon clusters cations $C_N^{+}$ with $N\leq$16 we have employed the most common descriptor of cluster stability, which is based on comparing the total energy of the cluster of size $N$ with the averaged energies of clusters with sizes $N$+1 and $N$-1. Those energies have been obtained from density functional calculations. The comparison between the stability function and the mass spectrum leaves some experimental features unexplained; in particular, the correlation with the detailed variation of the height of the mass peaks as a function of size $N$ is not satisfactory. We then propose a novel stability descriptor which improves matters substantially, in particular the correlation with the detailed variation of the height of the mass peaks. The new stability index is based on comparing the atom-evaporation energy of the cluster of size $N$ with the averaged atom-evaporation energies of clusters with sizes $N$+1 and $N$-1. The substantial improvement achieved is attributed to the fact that evaporation energies are quantities directly connected with the processes controllig the cluster abundances in the beam.