The Normal Vibrations of Molecules with Internal Torsional Motions

Abstract

The vibrational problem has been treated for molecules consisting of a framework to which are attached any number of symmetrical tops, such as methyl groups. Nitromethane, methyl alcohol, neopentane, etc. are examples. The vibrational problem can be separated from the internal torsional and over‐all rotation if the potential function is restricted so that the vibrational frequencies are independent of the torsion angles. The separation is effected by carrying out the normal coordinate treatment in the usual manner using however the value zero for all force constants involving torsion angles. The frequencies will not depend on the particular equilibrium orientation assumed for the tops. Furthermore the secular equation for the vibrational problem can frequently be factored to a greater extent than is indicated by the symmetry of the rigid molecule. The vibrational selection rules are also discussed and shown to be similar to those for normal molecules.