Anharmonic state counting

RRKM theory has been used widely to interpret measurements of unimolecular rate constants. However, harmonic state counting procedures are usually used in the RRKM calculations. This is not because enharmonic effects are thought to be unimportant, but because they are difficult to account for. The only comprehensive attempt to include the effect of anharmonicity has involved treating the vibrational degrees of freedom as separable Morse oscillators. However, since this correction is an obvious oversimplification it has not been widely used. The importance of anharmonicity is illustrated by comparing the trajectory unimolecular rate constant for C2H5 H + C2Hi dissociation at 100 kcal/mol (Fig. 4b), which is about 4.7 X 10 with that predicted by harmonic classical RRKM... 

The importance of enharmonic state counting in computing unimolecular rate constants must also be determined. In prior work it has been neglected and gross errors may be present in previous interpretations of unimolecular rate constants. If anharmonicity is important, statistical models could still be used to fit unimolecular rate constants by decreasing the number of effective vibrational modes in... 

The BSSR Direct Count of Anharmonic Density of States... 

Thus, at very low energies, the direct count method is recommended. At higher energies, the faster steepest descent approach is preferred, especially when the densities or sums of states are required at a high resolution. It must be recalled that both of these approaches are only approximate because they do not include anharmonicities. 

The IVR rates in the aniline(Ar)i case are rather sensitive to the densities of states. In this case, the values of pi (=N(E used in the construction of the IVR transition probability matrix are calculated with a direct count method, Vibrational frequencies of 45 cm l (stretch), and IS cm l (both bends) and anharmonicities of 3% (i.e., Avi, i+i /Avi-i,i =. 97) are assumed. 

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