A semi-classical model of proton tunnelling in hydrogen-bonded compounds

• Main Author: Lawrence, Michael Colin
• Other Authors: Robertson, G N
• Format: Doctoral Thesis
• Language: English
• Published: University of Cape Town 2016
• Subjects: Physics
• Online Access: http://hdl.handle.net/11427/17663

Bibliography: pages 233-238. === Two back-to-back Morse potentials are used to model the protonic potential in a hydrogen bond. A mathematical method is developed to obtain semi-classical solutions for the eigenvalues and eigenfunctions of the potential. Particular care is taken over the form of approximation used in the vicinity of the barrier top. The double Morse potential is then used as the fundamental element in the analysis of the proton dynamics in a number of hydrogen-bonded species: a) Chromous acid. A consistent, quantitative explanation is found for the νs(OH)/vs(OD) bands in the mid-infrared spectra of CrOOH/CrOOD. The 226 cm⁻¹ band in the far infrared and neutron scattering spectra of CrOOH is shown to be caused by the protonic tunnelling mode. b) Carboxylic and Dicarboxylic acids. The 140 cm⁻¹ protonic upper state splitting in dimeric formic acid proposed by Excoffon and Marechal (1972) is shown to be supported by the double Morse potential analysis. The analysis suggest's however that the two hydrogen-bonded protons in (HCOOH)₂ tunnel independently. The anomalous vs(OH)/vs(OD) intensity ratios observed in the infrared spectra of both adipic acid and dimeric formic acid could not be explained in terms of mechanical anharmonicity alone. The protonic tunnelling frequency in crystalline formic acid is shown to be about 23 cm⁻¹ , which supports the order-disorder interpretation of the observed phase transition in this crystal. c) Potassium Dihydrogen Phosphate (KDP). The crystallographic and infrared spectroscopic data for KDP and DKDP are interpreted consistently using the double Norse potential. The bare single-particle tunnelling frequency Ω is estimated to be 320 ± 10 cm⁻¹ and the overtone band at 4600 cm⁻¹ in the infrared spectrum of KDP is shown to be a :0 →:3> single particle transition. The model is capable of predicting the temperature and pressure dependence of both the protonic tunnelling frequency and the protonic inter-site separation δ. The soft-mode Raman data of Peercy (1975) is re-analysed allowing for the temperature dependence of Ω.