>is it possible to build a ProteinFoldingCoin?

I've thought about it, but don't think it's possible. Basically quantum chemical methods like Hartree-Fock or Coupled Cluster is a question of finding eigenvalues to some very very large matrices and/or solving non-linear equation. Verifying a solution (such as electron correlation energy) can, to my knowledge, only be done by using the result and checking if the equations are still valid, which pretty much is just doing the whole work.