The vibrations and the molecular structure of urea and guanidonium

The vibrations of urea and guanidonium have been calculated for a field containing valence and angle forces. The assumption is made that urea has the symmtery C$_{2v}$ and guanidonium C$_{3h}$. It is shown that it is possible to assign every observed frequency of these two substances to definite modes of vibration under these assumptions. The force constants have been evaluated and have been found to be f$_{\text{C} \chembond{1,0} \text{N}}$ = 7$\cdot $1 $\times $ 10$^{5}$ dynes/cm. for guanidonium, and f$_{\text{C} \chembond{1,0} \text{N}}$ = 6$\cdot $6 $\times $ 10$^{5}$ dynes/cm. and f$_{\text{C} \chembond{2,0} \text{O}}$ = 9$\cdot $7 $\times $ 10$^{5}$ dynes/cm. for urea. These values are compatible with the hypothesis that quantum mechanical resonance occurs in both molecules, with the result that the C$\chembond{1,0}$N bond in urea has approximately 28% double-bond character and the C$\chembond{2,0}$O linkage a corresponding single-bond character. The guanidonium ion shows complete resonance; each C$\chembond{1,0}$N bond has $\frac{1}{3}$ double-bond character. Curves have been drawn to illustrate the relation between the valence force constants and the bond character.