Vibratory modes, frequency calculation

Table I summarizes some of the results of the dynamical calculations for adsorbed butane. The calculated surface vibratory mode frequencies are in reasonable agreement with the observed spectrum, lying in the range 50-125 cm"1 with the rocking mode about the chain axis having the highest frequency followed by the closely spaced bouncing and orthogonal rocking modes. Although there is some variation depending on the force-constant model used, the calculated frequencies are within 30 cm of the experimental values.

As we shall discuss below, it is also more straightforward to calculate the relative intensity of vibrational modes observed by inelastic neutron scattering than in electron-energy-loss and optical spectroscopies. The relative intensity of the modes, as well as their frequency, can then be used to identify the atomic displacement pattern or eigenvector of the mode. We shall also see through examples of model calculations how the relative intensity of surface vibratory modes is sensitive to the orientation of the adsorbed molecule and the strength and location of its bond to the surface. 

The appearance of additional peaks in the monolayer spectrum suggests the existence of surface vibratory modes associated with rotations and translations of the free molecule hindered by adsorption. To identify these modes, it is necessary to perform normal mode calculations of the vibrational spectrum of the adsorbed molecule. These calculations are also of interest because of the sensitivity of the frequency and intensity of the surface vibratory modes to the molecular orientation and the location and strength of its bonds to the substrate. 

The empirical potentials can also be used to calculate the frequencies of the surface vibratory modes. Two different methods have been employed (26). In the first case, the molecule-substrate force constants introduced in the model described above are calculated and then used to solve the normal mode problem as before. In the second method, the molecule is treated as a rigid body, since distortions of the molecule induced by adsorption are calculated to be small. The frequencies of the surface vibratory modes are computed from the curvature of the molecule-substrate potential as the rigid molecule is rocked about its two symmetry... 

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