Readers should note the cautionary statements concerning the Marquardt-Levenberg algorithm in Tables 12.7 and 12.8. We have discussed the reasons for poor convergence of the ECE model with this algorithm in Section 4.A.2. Actually, the partial correlation of parameters in the models causes long convergence times even when using programs based on steepest descent or simplex algorithms, although the errors in the final parameters are negligible.
Figure 12.13 Influence of dielectric constant of the medium (s) on k2 for compounds 2 (O) and its 1-deuterio derivative (•). (Reprinted with permission from , copyright by the American Chemical Society.)
Orthogonalization of the ECE model can be used to achieve better convergence properties when k is the main parameter of interest. The orthogonalization procedure and the ECE model is discussed in detail in Section 4.A.3. The orthogonalized model for the ECE pathway was used to analyze chronocoulometric data to obtain lifetimes as tm = 1 Ik for the spontaneous decomposition of aryl halide radicals .
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