The potential energy surface along torsional dihedral angle degrees of freedom is a crucial part of model potentials for computer simulations of bio/organic molecules and polymers, including commonly used molecular mechanics force fields. "Proper" torsion angles (i.e. those involving four consecutively bonded atoms a-b-c-d, and labeled as φ abcd ) can be highly flexible due to the periodic nature and relatively small range of the free energy profile (often less than 5 kcal mol -1 ), which leads to broadly diverse conformations and accessible barrier crossings in ambient temperature experiments and simulations. Because the torsional angle is a principal descriptor of molecular conformation, the torsional potential energy is important for determining the thermodynamic distribution of molecular conformations and kinetics of conformational changes. Therefore, accurate potential parameters are needed to predict properties of interest such as biomolecular structure and function, receptor-ligand binding free energies, and timescales of protein folding. The four-body energy term for proper torsion in most force fields uses a periodic functional form of the dihedral angle φ abcd represented as a truncated Fourier series, i.e.