Some Mathematical Methods for the Study of Molecular Vibrations
E. Bright Wilson
Source abstract
Developments which reduce the labor of calculating the vibration frequencies of complex molecules are described. In particular a vectorial scheme is given for obtaining the reciprocal of the matrix of the kinetic energy in terms of valence-type coordinates. A general rule for writing down the coefficients of the transformation to symmetry coordinates is derived together with a method of obtaining the kinetic energy reciprocal matrix (G) in terms of symmetry coordinates with a minimum of algebra. A treatment of redundant coordinates is developed. In addition, reduction of the secular equation by the splitting out of high frequencies, a new type of isotope product rule, and the determination of normal coordinates are discussed. The molecule CH3Cl is worked out as an illustration.
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