Vibrations of Tetrahedral Pentatomic Molecules. Part I. Potential Energy. Part II. Kinetic Energy and Normal Frequencies of Vibration

Part I. It is shown that the most general potential energy function consistent with tetrahedral symmetry involves five force constants, also that with a suitable choice of variables this expression may be written in a quite simple form convenient for the discussion of different types of vibration. Special cases of potential energy such as the "valence" force and the central force cases involving less than five force constants are considered and their connection with the general case discussed.Part II. Expressions for the vibration frequencies of molecules of the type YX₃X* and YX₂X₂* (X* being an isotope of X) are derived in terms of constants in the potential energy function and the masses of the various atoms. These expressions are valid for any value of Δmm where m is the mass of X and m+Δm the mass of X*. Hence the results are applicable to the isotopes of hydrogen. While YX₄ has one single, one double and two triple frequencies, the slight asymmetry introduced by X* in YX₃X* partially removes the degeneracy giving three single and three double frequencies. For YX₂X₂* the degeneracy is completely removed and the molecule has nine single frequencies.