Principle of the GF Matrix Method

To calculate the vibrational frequencies, it is necessary first to express both the potential and the kinetic energies in terms of some common coordinates (Sec. 1.4). Internal coordinates (Sec. 1.9) are more suitable for this purpose than rectangular coordinates, since (1) force constants expressed in terms of internal coordinates have clearer physical meanings than those expressed in terms of rectangular coordinates, and (2) a set of internal coordinates does not involve translational and rotational motion of the molecule as a whole. 

Using the internal coordinates / , we write the potential energy as 

For a bent Y1XY2 molecule such as that in Fig. 1.20b, R is a column matrix of the form 

The kinetic energy is not easily expressed in terms of the same internal coordinates. Wilson [78] has shown, however, that the kinetic energy can be written as 

E is the unit matrix, and X is related to the wavenumber v by the relation X = 4ti c v. The order of the equation is equal to the number of internal coordinates used. 

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SPECTRA OF INORGANIC AND COORDINATION COMPOUNDS 1-H. PRINCIPLE OF THE GF MATRIX METHOD ... 

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