Potential energy curve of the O-H oscillator

The values for Eq have been obtained from the overtones of the O-H stretching mode which occur at approximately twice, thrice, four times etc. the frequency of the O-H fundamental and in part consist of IR + Raman combination bands. Being forbidden by the dipole selection rules their intensities decrease rapidly, by about two orders of magnitude for each increment. As a consequence the higher overtone bands are very 

Despite the experimental difficulties associated with the measurement of such very weak bands, the complete overtone sequence extending from 3 pm in the near IR to 500 nm in the visible region was obtained, using Mg(OH)2 single crystal and powder data . The results are shown graphically in Fig. 9.2. From the first four bands we obtain the Morse potential 

The value of D = 4.70 eV agrees surprisingly well with the dissociation energy of the free OH as derived from thermodynamic data, 4.71 eV, attesting to the fact that, up to the fourth vibrationally excited level. 

An interesting feature of Fig. 9.2 is that the O-H overtone sequence appears to come to an abrupt end above the 05 transition. In fact, the 05 transition appears as an edge, topped by a small band at 16 610 cm or 602 nm. What this means becomes clear when we overlay the OH Morse potentials to give a linear array of OH ions separated by the same distances as in the Mg(OH)2 structure. 

The result, shown in Fig. 9.3. is a series of deep wells where the protons are localized on the 0 level. This defines the valence band (VB). However, the superposition also produces a continuum above the 05 transition, 2.0 eV above the VB. This energy region, hatched in Fig. 9.3, defines a proton conduction band (CB). 

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