Nuclear Magnetic Resonance Spectrum for Isosceles Triangular Configurations of Nuclei

The nuclear magnetic resonance spectrum is calculated for an assembly of isotropically oriented systems of three identical nuclei of spin number ½ situated at the corners of an isosceles triangle. The theoretical spectra for triangles departing in various degrees from equilateral shape are compared with those recorded by Richards and Smith for the monohydrates of nitric and perchloric acids in polycrystalline form. It is concluded that if the oxonium ion in these acid hydrates is not equilateral, it does not depart from that shape by more than 10%. Interionic broadening is examined and it is concluded that for the acid hydrates a Gaussian function gives a good description of this broadening.