Estimating the proton potential in kdp from infrared and crystallographic data

Abstract

Abstract We show that the double minimum potential governing the proton motion in KDP, and its dependence on the oxygen-oxygen separation 2R, can be well represented by two back-to-back Morse functions. The overtone infrared absorption band at 4600 cm−1 observed by Viswanath and Miller is assigned as a |0> - |2> transition, and the fundamental absorption band between 2000 cm−1 and 3000 cm−1 as a broadened |1> - |2> transition. The splitting between the lowest symmetrical and antisymmetrical proton levels is estimated to be 320 cm−1. Values of 2.94 eV, 4.68 Å−1 and 1.000 Å are obtained for the Morse function parameters D, α and r o respectively. We calculate the variation of the proton inter-site separation Δ with temperature and pressure in terms of the TP dependence of the oxygen-oxygen separation. The results are in fair agreement with the values of ΔH determined crystallographically by Nelmes. Using the Morse function parameters D, α and r 0 obtained for KDP, but substituting the oxygen-oxygen separation 2R appropriate for DKDP, we calculate the intersite separation Δo in DKDP and its temperature dependence. These results are also in agreement with Nelmes'. The model potential thus gives a consistent account of all available infrared and crystallographic data. Reasons are advanced for the lack of temperature dependence of the |1> → |2> infrared absorption band intensity. The broadening of the absorption bands can be partly, but not wholly, understood in terms of the modulation of the proton potential by the oxygen thermal motion.