Potential functions and conformations in cycloalkanes

Energy functions of bending of the C-C-C angle and of twisting of the CH₂-CH₂ torsional angle have been examined through their effect on calculations of stable conformations and excess enthalpies of all the cycloalkane molecules from C₆H₁₂ to C₁₂H₂₄. The total strain energy was expressed as a function of the internal coordinates-bond lengths, bond angles and torsional angles. H-H distances were derived by matrix algebra, and the method of steepest descent was applied. Energy parameters like the bending force constant, the zero-strain value of bond angles, torsional potential barrier, were varied one at a time, and their effect on conformation and strain energy examined. Results have been compared with calorimetric measurements and with Xray and electron diffractions. Enthalpy of translation-rotation-vibration was also considered and found to be significant. Best agreement between calculations and experiment was obtained when the energy parameters were derived from n-alkanes. Thus, the n-alkane bond angle value of 112·7° is preferable to the tetrahedral angle as the zero-strain value; the torsional potential barrier of propane, 3·4 kcal/mole, is preferable to the corresponding value for ethane, 2·8 kcal/mole.