Some Mathematical Methods for the Study of Molecular Vibrations

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.