The effect of ionization on the global minima of small and medium sized silicon and magnesium clusters

We re-examine the question of whether the geometrical ground state of neutral and ionized clusters are identical. Using a well defined criterion for being “identical” together, the extensive sampling methods on a potential energy surface calculated by density functional theory, we show that the ground states are in general different. This behavior is to be expected whenever there are metastable configurations which are close in energy to the ground state, but it disagrees with previous studies.

💡 Research Summary

This paper presents a comprehensive re-examination of a long-standing assumption in cluster science: whether the geometric ground-state (global minimum) structures of neutral clusters and their positively charged (cation) counterparts are identical. Focusing on small to medium-sized silicon (Si_n, n=3-19, 32) and magnesium (Mg_n, n=6-30, 56) clusters, the study employs extensive, unbiased global geometry optimization using Density Functional Theory (DFT) with the LDA functional, coupled with the Minima Hopping algorithm and the BigDFT wavelet-based code.

The core of the work lies in its rigorous definition of structural “relatedness” or identity. Moving beyond simple geometric similarity measured by configurational distance, the authors define two structures (one neutral, one cation) as “related” if and only if a reversible mapping exists between them upon instantaneous addition or removal of an electron. Specifically: (1) the cation’s minimum structure i must relax to the neutral’s minimum j when an electron is added, and (2) the neutral’s minimum j must relax back to the cation’s minimum i when an electron is removed. This criterion is designed to reflect the actual timescales of experimental ionization processes.

Contrary to numerous previous studies that often concluded the structures were “more or less identical,” the results demonstrate that for the majority of cluster sizes investigated, the global minimum structures of the neutral and cation are not related according to this strict definition. For silicon clusters with more than 7 atoms, only Si_9 and Si_18 exceptions were found. For magnesium clusters in the studied range, related ground states were found in only 12 out of 33 cases.

The physical rationale for this prevalent discrepancy is analyzed in depth. The energy differences between the global minimum and low-lying metastable isomers are typically very small (on the order of a few kT at room temperature). In contrast, ionization energies and electron affinities are orders of magnitude larger (several eV). Crucially, these ionization energies/affinities are configuration-dependent. Therefore, the perturbation caused by adding or removing a single electron can easily alter the delicate energetic ordering of competing isomers, promoting a different structure to the global minimum on the cation’s potential energy surface.

The paper provides detailed “mapping charts” for representative clusters like Si_10 and Mg_16. These charts visually trace the relaxation pathways between multiple low-energy minima of the neutral and cation systems, revealing both reversible and irreversible mappings. A key insight is that structures can have very small configurational distances (e.g., 0.03 Å) yet reside in different catchment basins on the potential energy surface, leading to irreversible mappings upon ionization. This subtlety may have led earlier researchers to overlook actual changes in the global minimum.

The study concludes that the non-identity of neutral and cation ground states is a general behavior to be expected whenever a landscape possesses many metastable configurations close in energy to the global minimum. This finding holds significant implications for interpreting experimental data (often on ions) and for theoretical modeling (often on neutrals), urging caution in directly transferring structural information between the two charge states. The observation that both covalent/semiconductor-like (Si) and more metallic (Mg) clusters exhibit this behavior suggests it is a universal feature of complex energy landscapes rather than a material-specific phenomenon.