Vibrational Dynamics of Protons in Solids

1 FORCE-FIELD CALCULATIONS NORMAL VERSUS LOCALIZED MODES 

It is widely accepted that vibrational dynamics of atoms and molecules are reasonably well represented by harmonic force fields. The resolution of the secular equation transforms a set of (say N) coupled oscillators into (N) independent oscillators along orthogonal (normal) coordinates. Eigenvalues of the dynamical matrix are normal frequencies and eigenvectors give atomic displacements for each normal mode [3,4,13]. If band intensities cannot be frilly exploited, as it is normally the case for infrared and Raman spectra, these vectors are unknown and force fields refined with respect to observed frequencies only are largely underdetermined. For complex systems, symmetry consideration or/and isotopic substitutions may remove only partially this under determination. 

With the INS technique, force fields can be refined with respect to the fiiU spectral profiles including both frequencies and intensities [14,15]. This technique is most powerfiil for hydrogenous samples for which intensities are dominated by modes involving large proton displacements. Contributions from other atoms are much weaker and can be easily overlooked. 

2800 cm. Below 200 cm , the lattice density of states forms a quasicontinuum with a maximum at 100 cm .  

As previously for the potassium hydrogen bistrifluoroacetate crystal, INS clearly evidences the decoupling of the proton bending modes from the carbonate entities. This is largely confirmed by a simulation of the spectral profile with valence-bond force-field models of the dimers. With force fields based on infrared and Raman 

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F. Fillaux (1998). Physica D, 113, 172-183. The Pauli principle and the vibrational dynamics of protons in solids, a new spin related symmetry. 

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