Method for Calculation of the Conformation of Minimum Potential-Energy and Thermodynamic Functions of Molecules from Empirical Valence-Force Potentials—Application to the Cyclophanes

Abstract

A method for determining the conformation of minimum potential energy of molecules from empirical valence-force potentials is presented. The energy is written in terms of valence coordinates, expanded through quadratic terms about an assumed geometry, and transformed to Cartesian coordinates. It differs from steepest-descent methods in that the linear equations resulting from differentiation to find the minimum are solved directly to find a set of displacements. These displacements are used to calculate a new geometry, and the process repeated. It is found to converge rapidly in practice. In addition, the final coefficient matrix of the linear equations is used to calculate the vibrational frequencies of the molecule, and, along with moments of inertia from the final geometry, the gas-phase thermodynamic functions are calculated. The method is illustrated by calculations of the structures, strain energies, and thermodynamic functions of four cyclophanes.