Triatomic molecules anharmonic force fields

Linear Unsymmetric Triatomic Molecules.—Reducing the symmetry from Daoh to Coot, as in NaO, OCS, and HCN, increases the number of parameters in the general quartic force field to 2re + 4/2 + 6f3 + 9/i Table 7 shows their relationship to the primary spectroscopic observables. It is clear that problems of insufficient data to determine the general force field are already on the horizon for example, data from at least two different isotopic species must be combined in order to determine frrr, frrit, fruit, and fium from the observed values of a and a . In practice, of course, substitutions like 14N for 15N tend to change the spectroscopic constants by only a small fraction, and conversely the observed data on the constants of such isotopic species tend to give nearly parallel information on the force field to that obtained from the parent species. For these reasons the anharmonic force field of molecules like N20 is much less well determined than that of C02. These effects are apparent in the uncertainties obtained on the force constants in the refinement calculations referred to in Table 4. 

Table 13 Anharmonic force fields of some bent triatomic molecules in curvilinear internal co-ordinates, up to cubic terms only ...

Force fields up to quartic anharmonic terms are now known with reasonably high accuracy for several triatomic molecules and the results shown in Table 3 for H2O are typical. However, even for these there has had to be an assumption that some of the quartic interaction terms are zero in order that the equations from which the constants are derived shall have unique solutions. It can be seen moreover that some of the cubic and quartic terms have uncertainties which are larger than the values of the constants themselves. 

Bent Triatomic Molecules.—Calculations have been reported for many bent triatomic molecules (see Table 4). The general force field contains 2re + 4/ + 6/3 + 9A parameters, the relation to the primary spectroscopic constants being shown in Table 9. The fact that these are asymmetric top molecules, for which otj, a , and a can all be determined (generally from the microwave spectrum for the heavier molecules), means that 9 a values are available from each isotopic species to determine the 6 cubic force constants, so that the cubic force field is generally well determined. For the quartic force field the situation is much less satisfactory the experimental data on the anharmonic constants xrs are generally incomplete, and are in any case insufficient to fix all the quartic constants without good isotopic data. 

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