There is a very fundamental difference in the use of torsional potential functions as compared to bond length and angle potentials. Only a small subset of the full potential energy domain, around the minumum, is realized in the parabolic-like bond length and angle potentials. Therefore the emphasis in fitting these potentials is to reproduce potential near the minimum, with not so much concern about the functional form, or parameterization, or large excursions from equilibrium because they are energetically disallowed.
On the other hand, torsional potentials are evaluated over the full 360° of rotation around a bond. Therefore, the torsional parameters must be valid for full torsional rotation. Thus, the precision of fit about individual torsional minima is partially sacrificed for overall fit. The goal, then becomes to reproduce all extrema with less concern about the well shapre about minima.
The Rotational Profiler attempts to facilitate the task of performing this overall fit. The functional torsional form used in the code is
where is the force constant is the multiplicity is the phase shift or offset and is the torsional angle between the i, j, k, l particles.
The input files are two columns ASCII files. The first column contains the torsional angles in degrees and the second column the torsional energy values. The value of the torsional angles of both files must match. During the fitting procedure, the energy values of both profiles are shifted such that the lowest energy values are set to zero.
Example files can be downloaded here.