The Normal Frequencies of Vibration of Symmetrical Pyramidal Molecules AB3 with Application to the Raman Spectra of Trihalides

The symmetrical pyramidal molecule AB3 is treated by a general normal-coordinate method, six force constants being required. The convenience of the use of ``symmetry coordinates'' is illustrated in obtaining the formulas for the normal frequencies for several types of potential functions. It is found that with two constants the central force treatment and valence force treatments fit the data equally well. The four constants K, H, K′ and H′ of the potential function 2V=KΣiΔRi2+12HR02Σij′Δαij2+K′Σij′ΔRiΔRj +2H′R02(Δα12Δα23+Δα23Δα31+Δα31Δα12)for certain trihalides are obtained from Raman data. The interatomic distances calculated using these values of K in the empirical relation found by Badger for diatomic molecules agree with the distances obtained by other methods to within about 0.1A.