Torsional Coordinates in Vibrational Anharmonicity; Application to Ethylene

Abstract

Formulas for the first through third derivatives of torsional coordinates with respect to difference Cartesian coordinates are given. These formulas may also be used for out‐of‐plane bending coordinates. A sample calculation of an anharmonic potential function involving these coordinates has been made for ethylene and ethylene‐d 4. The procedure of anharmonicity calculation for polyatomic molecules is formulated by the use of matrix direct product notation and is discussed.