Knowledge Bank

The criterion that the sum of the diagonal force constants of a generalized valence force field attain an extremum, consistent with elimination of the arbitrariness inherent in the usual unrestricted formulation of the inverse secular problem of determining $1/2n(n+1)$ vibrational force constants from only n harmonic frequencies and the equilibrium configuration, leads to n*** solutions for the force field. All such solutions are characterized by symmetric GF matrices, and are obtained in terms of the observed vibrational frequencies, the equilibrium configuration, and the scaling chosen for the internal symmetry coordinates. The particular two force fields involving, respectively, the smallest and greatest extrema of the trace of the F matrix correspond to completely reversed assignments of the frequencies. Comparison of the above model with two others also based on kinematically defined normal coordinates, viz., the method of the characteristic set of valence coordinates and the method of progressive rigidity, reveals that the last possesses some advantages. Examples including $H2O,NO2$, and $GeF4$ are discussed.