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

Abstract

The complex conformations of the cyclic moieties impact the physical and chemical properties of 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. With consideration of symmetries, we obtained a total of 1504 conformational structures for fourmembered, 5576 for five-membered, and 13509 for six-membered rings. All well-known and many less well-known conformers for each molecule were identified. We represented the potential energy surfaces (PESs) by fitting the data to common analytical force field (FF) functional forms. We found that the general features of PESs can be described by the essential FF functional forms; however, the accuracy of representation can be improved remarkably by including the torsion-bond and torsion-angle coupling terms. The best fit yields R-squared (R 2 ) values close to 1.0 and mean absolute errors in energy less than 0.3 kcal/mol.