Properties and application of the reduced isotopic product rule for molecular vibration frequencies

The well-known approximate separation of low molecular vibrational frequencies from high frequencies has in the past been combined with the Redlich-Teller isotopic product rule to split the latter into separate rules for the high and for the low frequencies (reduced isotopic product rules). A number of variants and properties of these rules are discussed, along with some modifications applicable when redundant coordinates are involved. A discussion is given of the use of nonbonded distances instead of the related bond angles, and the employment of computer programs which calculate normal frequencies from postulated force constants. A comparison is made of the relative advantages of using these reduced product rules for testing assignments of observed vibration frequencies as opposed to the use of frequencies or frequency product ratios calculated from transferred force constants. Finally benzene, ethylene, methyl isocyanide, and cyclohexane are worked out as examples and some suggestions made of possible remaining uncertainties in the assigned fundamental frequencies.