Transition-state frequencies

In applying the LH model to the above set of kinetic data, the vibrational frequencies associated with the transferring proton in the reactant and product states must be specified to determine Cmpjtr(Q) in Eq. (11). The C—H stretching frequency in the reactant state is set to 2700 cm 1 and the O—H stretching frequency in the product state is set to 3100 cm-1. The numbers were derived from AMI calculations. The transition state frequency o> is set to 2500 cm-1 based on the work of... 

Figure 13, Comparison of phase space and RRKM extrapolation curves by use of parameters for the Ar(benzene) complex. The Eq value was the same for both curves. The RRKM curve was adjusted to give the same rate as PST at 10 s" by variation of transition-state frequencies as described in the text.

Values for transition-state frequencies were assumed following the arguments by Armentrout et al. [143,144] and Squires et al. [145]. For an endothermic dissociation of gas-phase ions, a loose transition state can be assumed. Accordingly, the product frequencies can be used where available. For the five normal modes that correspond, at the asymptotic limit of dissociation, to relative rotations and translations of the departing fragments, further estimates had to be made. Numerical estimates for these five frequencies were taken from computations of analogous oxidative addition, reductive elimination, and a-bond metathesis transition states. The deconvoluted threshold, with the methyl... 

The transition-state frequencies can be obtained by three means. They can be used simply as adjustable parameters in order to fit the data. They can be estimated by schemes such as one developed by Benson (1976) and reviewed by Gilbert and Smith (1990). Finally, they can be calculated by ab initio molecular orbital techniques (see chapter 3). 

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.

A useful additional constraint for adjusting the frequencies is derived from rates obtained for several isotopically substituted molecules or ions (Dutuit et al., 1991 Baer and Kury, 1982 Kuhlewind et al., 1987). With this approach it is possible to determine directly from the experimental rates the values of certain classes of transition state frequencies. In the fitting of the k E) data for various isotopically substituted benzene ions, it was determined that the transition state C—H frequencies are increased, while the C—C vibrations are lowered relative to the molecular ion frequencies (Kuhlewind et al., 1987). 

It is rarely possible to apply the full theoretical expressions such as (160) and (163) to actual reactions, since the required transition-state frequencies are not accessible experimentally, and can be calculated theoretically only for the very simplest systems, such as those involving three hydrogen atoms. However, much valuable information has been obtained by applying these equations to plausible model systems in which force constants and configurations can be varied systematically. Since computer programmes are available for calculating vibration frequencies even in... 

Donahue, N. M. (2001). Revisiting the Hammond postulate the role of reactant and product ionic states in regulating barrier heights, locations, and transition state frequencies. J. 

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