Modelling free energy of a rigid protein in solid water: Comparison between rigid-body motions and harmonic oscillators

We test two methods to estimate a partition function of a system consisting of multi-atom molecules with intermolecular interaction. Our test case is a protein in water. The first method is based on rigid-body motions. The space in which the protein (bovine pancreatic trypsin inhibitor) would be moving is limited, so by making a correction to a partition function of a rigid body, we can obtain the function. The function depends on temperature and space. The second method is based on harmonic oscillators. Under the potential field produced by surrounding water molecules, a protein behaves like a set of harmonic oscillators. We obtain the partition function for the oscillators within a harmonic approximation. The function also depends on temperature and the strength of potential energy between the protein and waters. Comparison of the two methods indicates that the second method is better for estimating a partition function for a protein in water.