Systematic description of molecular deformations with Cremer-Pople puckering and deformation coordinates utilizing analytic derivatives: Applied to cycloheptane, cyclooctane, and cyclo[18]carbon.

The conformational properties of ring compounds such as cycloalkanes determine to a large extent their stability and reactivity. Therefore, the investigation of conformational processes such as ring inversion and/or ring pseudorotation has attracted a lot of attention over the past decades. An in-depth conformational analysis of ring compounds requires mapping the relevant parts of the conformational energy surface at stationary and also at non-stationary points. However, the latter is not feasible by a description of the ring with Cartesian or internal coordinates. We provide in this work, a solution to this problem by introducing a new coordinate system based on the Cremer-Pople puckering and deformation coordinates. Furthermore, analytic first- and second-order derivatives of puckering and deformation coordinates, i.e., B-matrices and D-tensors, were developed simplifying geometry optimization and frequency calculations. The new coordinate system is applied to map the potential energy surfaces and reaction paths of cycloheptane (C7H14), cyclooctane (C8H16), and cyclo[18]carbon (C18) at the quantum chemical level and to determine for the first time all stationary points of these ring compounds in a systematic way.