Do Levinthals arguments lead to a paradox for Si₂₀H₂₀?

Levinthal argued that the folding of a protein should require a time longer than the age
of the universe. However, since
it is experimentally well established that proteins do fold on a quite short time scale, these
arguments are known as the Levinthal paradox. The paradox is resolved by folding funnel
hyphothesis. Here we will present a system whose global
minimum is not embedded in a large funnel. The global minimum is virtually
not accessible on a reasonable time scale.
The potential energy surface of Si₂₀H₂₀ is considered for this study. The dodecahedron
cage of Si₂₀H₂₀ is the theoretically established ground state. However it has never been
observed experimentally. Based on an extensive exploration of possible reaction pathways
of Si₂₀H₂₀ we show that there exists a huge number of intermediate structures that consist
mainly of collapsed cages. Among all these reaction pathways that lead into the ground
state, the system has to go through energetically flat regions before it reaches the Si₂₀H₂₀
ground state. This implies that there is no clear driving force towards this ground state
that would give rise to a short directional reaction pathway that would lead rapidly into the
ground state.