Vibrational analysis of molecules undergoing large amplitude internal motions
One of tbe primary efforts of investigators of molecular properties has been to determine the forces hindering internal motions in molecules. Molecules are bound by electronic interactions among the atoms and therefore a complete quantum mechanical solution to the problem should determine the force field once the atoms in a particular molecule are specified. However, the complications of this approach have lead to serious difficulties for most molecules. A more empirical method has been quite successful in determining the molecular potential energy along certain vibrational paths and for particular molecular geometries. For many molecules the intramolecular forces binding tbe atomic nuclei are such that the vibrational motions of the nuclei are restricted to small amplitude. The potential energy can then be expanded about the equilibrium configuration in a Taylor series. The potential energy is determined through the quadratic term of the series by adjusting the potential energy so that the frequencies obtained by normal mode analysis agree with experimental values. Anharmonic corrections have been obtained for many molecules by analysis of the deviations from the normal mode approximation.