Nonexistence of the decahedral Si20H20 cage: Levinthal's paradox revisited

For C${}₆₀$, the potential energy surface exhibits a driving force toward the ground state that allows it to be found rapidly. However, the potential energy surface of a cluster can also exhibit features that prevent us from finding its global minimum. In the case of decahedral Si${}₂₀$H${}₂₀$, which is a theoretically postulated stable ground state but was never synthesized, there is no driving force towards the global minimum. The system visits a huge number of low energy structures during its evolution without ever falling into the global minimum. This is exactly the scenario described by Levinthal in his famous paradox about protein folding.