Consistent Force Field for Calculations of Conformations, Vibrational Spectra, and Enthalpies of Cycloalkane and n-Alkane Molecules

Abstract

An inductive method for a systematic selection of energy functions of interatomic interactions in large families of molecules is suggested and is applied to the family of cycloalkane and n-alkane molecules. Equilibrium conformations, vibrational frequencies, and excess enthalpies, including strain energies and vibrational enthalpies, are all derived from the same set of energy functions. The energy-function parameters are optimized by a least-squares algorithm to give the best possible agreement with a large amount and variety of observed data. Analytical derivatives of the various calculated quantities with respect to the energy parameters help to facilitate the computational procedures. The resulting agreement with experiment is used as a measure of success of the energy functions with optimized parameters, referred to as “consistent force field” (CFF). Different CFF's are compared and selected according to their relative success. Energy functions commonly used in conformational analysis are examined in preliminary consistent-force-field calculations and are found inadequate. Considerable imporvement is obtained when Coulomb interactions between residual atomic charges are included, and when interactions between atoms bonded to a common atom are represented by a Urey–Bradley-type force field, while Lennard-Jones potentials are used for nonbonded interactions between atoms separated by more than one atom. Vibrational frequencies as well as vibrational molecular enthalpies are derived for all cycloalkanes C5 through C12. The spectroscopic force constants are derived from the CFF as functions of molecular conformations. Agreement with available spectroscopic assignments of frequencies is reasonably good. A few improvements are suggested for cyclopentane assignments. The path and moment of inertia of pseudorotation in cyclopentane are calculated. Cyclodecane frequency assignments, based on the derived conformational C2h symmetry, are suggested for the first time. Calculated excess enthalpies of C5H10 and medium cycloalkanes agree well with observed values. Contributions of vibration–translation–rotation are shown to amount to a significant part of the excess enthalpy.