Vibrational spectra thermodynamic function

Infrared Spectrum. The infrared spectrum of gaseous SiF 2 has been recorded from 1050 to 400 cm"1 63 Two absorption bands, centered at 855 and 872 cm 1, were assigned to the symmetric (v j) and antisymmetric (V3) stretching modes, respectively. The assignment was rendered difficult because of the considerable overlap of the two bands. The fundamental bending frequency occurs below the instrumental range of the study, but a value of 345 cm 1 can be determined from the ultraviolet study. The vibrational frequencies were combined with data from a refined microwave study 641 and utilized to calculate force constants and revised thermodynamic functions. 

The gas-phase molecular structures of CF3SF, CF3SCI (332), and of CFsSBr (307) were determined from electron diffraction experiments. Vibrational spectra and harmonic force field calculations were reported for CF3SCI (47). For CFsSBr an improved method of preparation from CF3SCI and HBr was developed, and a full normal coordinate analysis was performed and thermodynamic functions were derived on the basis of a modified assigiunent of the vibrational spectrum (42,307). 

As we saw above, what emerges from our detailed analysis of the vibrational spectrum of a solid can be neatly captured in terms of the vibrational density of states, p(co). The point of this exercise will be seen more clearly shortly as we will observe that the thermodynamic functions such as the Helmholtz free energy can be written as integrals over the various allowed frequencies, appropriately weighted by the vibrational density of states. In chap. 3 it was noted that upon consideration of a single oscillator of natural frequency co, the associated Helmholtz free energy is... 

A knowledge of the vibration spectrum of oscillation of ions and electrons in a crystal at different temperatures and external fields solves, to some extent, the problem of the thermodynamic properties of solids. The value of the internal energy U, the specific heat cy, and other thermodynamic functions is expressed directly in terms of the density of the frequency distribution g(u) and the average energy of the oscillators ... 

Methods to apply quantum corrections for this inadequacy of classical mechanics when applied to crystals, as well as other phases, have been explored (124-127), but there is not yet general agreement on how best to calculate thermodynamic properties for these types of systems. The practical solution of Berens and co-workers (124) entails. . calculating the velocity spectrum S(v) from molecular dynamics and then integrating S(v) over all frequencies with a weighting fimction which is the difference between the quantum and classical harmonic weighting functions for the thermodynamic variable of interest. However, as the statement avers, anharmonic contributions to the vibrational modes will not be captured correctly this relatively minor shortcoming was addressed by Hardy and co-workers (128). 

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