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

## TL;DR

This paper introduces a new stability descriptor for small carbon clusters that better correlates with experimental mass spectra by focusing on atom-evaporation energies, enhancing understanding of cluster stability.

## Contribution

The paper proposes a novel stability index based on atom-evaporation energies, improving correlation with experimental data over traditional total energy comparisons.

## Key findings

- The new stability descriptor shows a substantially better correlation with mass spectrum features.
- Atom-evaporation energies directly relate to cluster abundance in mass spectra.
- The improved descriptor enhances understanding of cluster stability in gas-phase carbon clusters.

## Abstract

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.