GF Method

The GF method, sometimes referred to as FG method, is a classical mechanical method introduced by E. Bright Wilson to obtain certain internal coordinates for a vibrating semi-rigid molecule, the so-called normal coordinates Q_k. Normal coordinates decouple the classical vibrational motions of the molecule and thus give an easy route to obtaining vibrational amplitudes of the atoms as a function of time. In Wilson's GF method it is assumed that the molecular kinetic energy consists only of harmonic vibrations of the atoms, i.e., overall rotational and translational energy is ignored. Normal coordinates appear also in a quantum mechanical description of the vibrational motions of the molecule and the Coriolis coupling between rotations and vibrations.

It follows from application of the Eckart conditions that the matrix G−1 gives the kinetic energy in terms of arbitrary linear internal coordinates, while F represents the (harmonic) potential energy in terms of these coordinates. The GF method gives the linear transformation from general internal coordinates to the special set of normal coordinates.