  The fundamental law for protein folding is the Thermodynamic Principle: the
amino acid sequence of a protein determines its native structure and the native
structure has the minimum Gibbs free energy. If all chemical problems can be
answered by quantum mechanics, there should be a quantum mechanics derivation
of Gibbs free energy formula G(X) for every possible conformation X of the
protein. We apply quantum statistics to derive such a formula. For simplicity,
only monomeric self folding globular proteins are covered. We point out some
immediate applications of the formula. We show that the formula explains the
observed phenomena very well. It gives a unified explanation to both folding
and denaturation; it explains why hydrophobic effect is the driving force of
protein folding and clarifies the role played by hydrogen bonding; it explains
the successes and deficients of various surface area models. The formula also
gives a clear kinetic force of the folding: Fi(X) = - \nablaxi G(X). This also
gives a natural way to perform the ab initio prediction of protein structure,
minimizing G(X) by Newton's fastest desciending method.
