Protein folding has very little to do with free energy minimum, as most of the previous posts would like you to believe. Less than 20% of eukaryotic proteins would ever fold on its own. Besides, a deep energy minimum is equivalent to lack of change or death in biological language. People are still very attached to the Anfinsen principle from the 60s for which he got a Nobel prize. This view has been proven highly outdated and very approximate (see issue 324 of Science Apr 2009). Unfortunately, change of a paradigm is a painfully arduous process.
Proteins are mixtures of locally minimal "solid state" domains and locally flexible "liquid state" contributions. If someone can talk abut a conditional stability of the solid domains (conditional because prions and many other proteins have multiple stable conformers depending on the surrounding condition) than there is no real sense talking about a minimum energy for the "liquid like" domains. (Proc Natl Acad Sci U S A. 2009 Jun 30;106(26):10505-10) In essence only around 30% proteins have dominating 3D structure, ~30% some structure, and around 30% almost never any dominant structure. The distribution is completely smooth form very solid-like proteins to liquid-like proteins.
Despite all these caveats spelled out above there is a natural folding energy scale. An average folded protein has a stability of around 30 kcal/mol (which by the way is only around 10 hydrogen bonds), signaling events cannot change the energy by more than ~10 kcal/mol and the stability of individual conformational change that is controlled by small molecule binding would be around 3 kcal/mol (which is around a single hydrogen bond). Life indeed lives dangerously unstable.
Therefore, protein folding is a complex question from a domain of self organized systems. Some proteins use thermodynamics, some proteins use kinetics some protein use conditional partners and excretion and some proteins never acquire any shape that we could call a folded state. The state of our knowledge is so weak and incomplete that we have difficulties in even predicting which sequence would form what protein. I do not even mention the pretentious folding sites which success rate is in low percentages but their authors are highly regarded as solvers of protein folding. Only recently some web service established crystallization probabilities that actually try to answer this question heuristically (XtalPred). Protein folding by definition does not have any unique solution because it cannot have one.
Therefore, you have to reevaluate your question and we all need to rethink how to adapt to a new paradigm.