The five in-plane vibrational frequencies of X2CO molecules are used to determine nine independent force constants of a general quadratic force field.
Instead of the usual arbitrary assumptions about the four supernumerary force constants (which four?), yielding simpler force fields, a minimum of very mild constraints was applied to the interaction constants (e.g., assumptions about some signs and the setting of reasonable limiting values). Some of these constraints in turn produced further constraints on the other force constants.
A specially designed analog computer allowed these calculations to be performed in a reasonable time. It was possible to vary continuously any of the force constants and to observe directly the effects on the frequencies and on the other force constants. Thus very quickly some ``feeling'' was developed for the molecule and the interrelation of the force constants.
The result then is not a unique set of force constants (which might be recorded in the literature with several decimals), but rather a nine-dimensional hypersurface of solutions, whereon each of the nine GFF constants occupies a range of values. For example, f(C=O) in Br2CO ranges from 12.9 to 14.2 mdyn/Å, and the C–Br stretch/opposite-angle interaction from −0.25 to −0.34 mdyn.
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