Knowledge Bank

This study was designed to investigate the effect of various potential-constant assumptions on the remaining constants of a general force field. Symmetric carbonyl halides yield five observable in-plane stretching and deformation frequencies, but need nine potential constants to describe a general quadratic force field. This is a problem of five equations in nine unknowns, whose infinite possible solutions lie on a nine-dimensional hypersurface. Instead of selecting one point on this surface by arbitrarily assigning some values to four of the constants, we merely restricted the area of this hypersurface through the application of mild constraints on the interaction constants (restricting them to reasonable values, relating their signs, etc.). An analog computer is particularly suited for determining the boundary of such a hypersurface. By visually and directly observing the effect produced when one or more constants are varied (simply by twisting some potentiometer dials). we quickly developed a ``feeling'' for our molecule and then systematically explored the limits of our hypersurface, much as a skilled blind man taps his way along a curb. The resulting ranges of the force-constant values clearly reveal just how sensitive these are to the chosen assumptions. On the other hand, it is interesting to note how even very mild constraints can produce a quite limited range of solutions.