The Secular Equation for Molecular Vibrations

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6. If it is required in addition that these coordinates have the proper symmetry properties to factor the secular equation, they become the “symmetry coordinates” of Howard and Wilson, (J. Chem. Phys. 2, 630 (1934)). These coordinates have been criticized as unsuitable for use in connection with the isotope effect because they involve the atomic masses. We cannot understand this criticism because the secular equation will always contain the atomic masses in any event, and to change from one isotopic molecule to another of the same symmetry requires the same operations no matter what coordinates are used, whereas if the introduction of the isotopic atom lowers the symmetry, a new secular equation is necessary anyway. We have found these coordinates very useful. Google ScholarScitation

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