Abstract
The infra-red spectra of KH2PO4, NH4H2PO4, NaH2PO4, KH2AsO4, NH2H2AsO4, Ag2H3IO6 and (NH4)2H3IO6 and of their deuterated analogues have been recorded at room temperature and some of them also at low temperature in the ferroelectric phase. The interpretation of the particularly interesting spectral region between 3000 and 1500 cm−1, containing several OH bands, has been made in terms of the tunnelling of the protons between two minima of potential energy. These were taken to be of equal depth in the non-ferroelectric phase and unsymmetrical in the ferroelectric form. A quantum-mechanical treatment of the vibrational problem of the latter type has been carried out and is presented in the Appendix. Good agreement has been found between the theoretically predicted energy levels and the experimental data.

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