Vibrational frequency phase-space transition states

In the gase phase, the infrared bands are broad (50 cm ), due to the rotational structure, overlapping vibrations, and hot transitions. In the solid state, the rotational motions are quenched, but due to intermolecular (hydrogen bond) and correlation field interactions, the band positions are shifted and the bands are even broader. The infrared absorptions of matrix-isolated molecules are close to the gas-phase frequencies and exhibit a sharp line-like character (half-widths 0.1 to 2 cm ). Hence the spectra of matrix-isolated molecules are less complicated, and, in comparison to gas phase or solid state spectra, the sensitivity and selectivity of detection increase by a factor of about 10 to 100. Closely spaced vibrations attributed to mixtures of similar molecules, such as conformers, rotamers, molecular complexes, or isotopic species, e.g., H C104 and H CI04, are easily distinguished. 

Figure 7.4 Calculated k( ) curves for the bromobenzene ion. The open circles are obtained by lowering the last five vibrational frequencies to 113 cm" in the transition state. The PST (phase space theory) rate constant had the lowest two frequencies replaced by free rotors, while in the other three lines all transition state frequencies were multiplied by the indicated factor. The E and the parent ion vibrational frequencies were the same for all calculations. Note the different slopes.

Not all vibrations that occur in a solid lead to absorption of electromagnetic radiation. There are certain conditions, called selection rules, which must be fulfilled to get an absorption of light energy by molecular vibrations. In addition to the ordinary condition for IR activity (existence of a transition moment, see Krimm and Hummel ), we have lattice vibrations for which no periodicity in space is allowed, which means only frequencies with phase difference Acj) = 0 or infinite wavelength are observable. The quantity that gives the density of vibrational states falling into a certain interval, Ao), called the density of states Z(o)), plays an important role, since it is proportional to (d0)/dk) . Its maxima occur where the 03-k curve has a horizontal tangent. The rule is... 

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