Torsional internal coordinates in normal coordinate calculations

Expressions for the s vectors of atoms whose motions constitute a torsional internal coordinate are derived by different methods and the relationships between the various forms appearing in the literature are demonstrated. The expressions for the simple case of a four-atom chain are extended to the general case, as exemplified by the alkanes. Certain errors and ambiguities in the treatment of torsional coordinates are noted. Torsional force constants for ethane, propane, isobutane, and neopentane are presented, being obtained by use of the prescribed methods in normal coordinate calculations.