The Determination of the Constants of Harmonic Vibrations

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Abstract
A general method is developed to find the relations between constants of the potential energy and the frequencies of point systems for harmonic vibrations. Useful formulas are derived (Eqs. (16) and (23)); and matrices required frequently for the solution of problems are tabulated. Relations are also found between the force constants of a molecule with a number of equivalent atoms and the vibration frequencies of an isotopic molecule of a lower degree of symmetry. This also gives the relations between the frequencies of isotopic molecules of different degrees of symmetry.