A Method of Obtaining the Expanded Secular Equation for the Vibration Frequencies of a Molecule

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Abstract
A method is described for obtaining the secular equation for the vibration frequencies of a molecule directly in expanded form, i.e. as an algebraic rather than a determinantal equation. The force constants occur literally and the masses may occur either literally or numerically, as desired. The symmetry may be employed as usual to factor the secular equation. Several methods of obtaining approximate roots are described for which the expanded form is particularly suitable. Finally, an example, the nonlinear general triatomic molecule, is worked out algebraically.

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