The fitting and functional analysis of a double rotor potential energy surface for the R and S enantiomers of 1-chloro-3-fluoro-isobutane

A model compound was chosen to see whether it mimics a backbone of an amino acid residue in a peptide structure so that a model Ramachandran potential energy surface could be fitted by a mathematical function. A Fourier series of two independent variables (ϕ and ψ) has been used to fit a set of grid points representing the surface. To determine the accuracy of the fitted equation vs. the generated data points three grids were examined, 242=576 points (15° intervals), 122=144 points (30° intervals), and 62=36 points (60° intervals). The grid points were generated for the S enantiomer and a Fourier expansion was fitted to the grid points along with a functional analysis of each fitted expansion. A series of functions were found for 15, 30, and 60° increments in order to see the lowest limit of resolution of the grid needed for a relatively accurate fit. Ab initio calculations were also carried out for the R and S enantiomer to fit a 31 term Fourier expansion where a functional analysis determined the location of the critical points from the expansions. Geometry optimizations were preformed to locate more precisely the minima. The optimized minima were then included in a new surface that was fit.