Potential-Energy Surfaces Sampled in Cremer–Pople Coordinates and Represented by Common Force Field Functionals for Small-cyclic Molecules

The complex conformations of the cyclic moieties impact the physical and chemical properties of the molecules. In this work, we chose 22 molecules of four-, five-, and six-membered rings and performed a thorough conformational sampling using Cremer-Pople coordinates. We sampled hundreds or thousand of conformational structures including all well-known and many less well-known conformers for each molecule. We tried to represent the potential energy surfaces (PESs) by fitting the data to common analytical force field functional forms. Although the general features of PESs can be described by the essential force field functional forms, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R2) values close to 1.0 and mean absolute errors (MAEs) in energy less than 0.3 kcal/mol.