Knowledge Bank

Using the Green's function, we have generated the cartesian force constants for the in-plane vibrations of planar $XY3$ molecules. These force constants are linear combinations of internal coordinate symmetry force constants, and the transformation may be easily obtained. The result is four explicit expressions for the independent force constants which determine the zero-order vibrational frequencies Heretofore, three of the force constants have appeared as unknown parameters in a set of two simultaneous non-linear equations, limiting the accuracy conveniently attainable. For $XY3$ planar molecules, it is possible to determine the six valence force constants of the complete quadratic potential function. Comparison of our results with those of previous calculations indicates that we have obtained greater accuracy with significantly less effort. Variations in the force constants with small changes in frequencies indicate the desirability of utilizing the Green's function approach, and bypassing the force constant model, wherever possible.