Utilizing finger prints to construct the disconnectivity graph.

Theoretical studies have identified the dodecahedron of Si₂₀ H₂₀ as the lowest energy structure
among many competing configurations several years ago. However this ground state structure has
never been observed experimentally. The characteristics of an energy landscape are ultimately the
key to understand the existence of a particular configuration. We employ a fingerprint distance (FP)-
based exploration of the Potential Energy Surface, to establish relationships between the minima
and their connecting transition states (saddle points of the PES). We apply this in a comparative
investigation of Si₂₀H₂₀ with two existing structures, namely the C₆₀ and C₂₀H₂₀ fullerenes. The
striking differences between the PES of these three systems are used to understand why the global
minimum is experimentally observed only for C₆₀ and C₂₀H₂₀. We show that the complex pathways
between different metastable configurations and the ground state of the Si₂₀H₂₀ cluster explain the
lack of observation of the global minima configuration in experiment.