Localization energy values

The reactivities of isomeric thienothiophenes calculated in n -electron approximation by the PPP method, and those calculated considering all valence electrons, show reasonable agreement. It should be noted, however, that the choice of parameters in PPP calculations is somewhat arbitrary, especially for heavy atoms (e.g., sulfur). This may lead to a discrepancy between theoretical (in 7r-electron approximation) and experimental estimation of reactivities. For example, Clark applied the semiempirical method PPP SCF MO to calculate the reactivities of different positions in thienothiophenes 1—3, thiophene, and naphthalene from the localization energy values and found the following order of decreasing reactivity for electrophilic substitution thieno[3,4-b]-thiophene (3) > thieno[2,3-Z>]thiophene (I) > thieno [3,2-b]thiophene... 

Fig. 11. Plot of logiofo against atom localization energy [atom localization energy values taken from S. Sato and R. J. Cvetanovic, J. Am. Chem. Soc., 81, 3223 (1959) TetraME = tetramethylethylene].

Analyses to quantitatively relate the log k values to a combination of molecular interaction energy values, solvent effects, and/or electron localization energy values (calculated as HOMO or LUMO) in reversed-phase liquid chromatography, have been performed. The practical application of this method requires a limited number of standard compounds for column calibration. 

Dewar s treatment of transition state structure, using reactivity numbers, has the logical defect that in the intermediate kinds of transition states for which it provides evidence the electron localisation is only partial. However, in obtaining the values of the reactivity numbers (which are approximate localization energies), the process of localization is considered to be complete thus, values of parameters which strictly are relevant only to the Wheland type of transition state are incorporated into a different model. ... 

Table 1-4 gives some calculated reactivity indices free valence or Wheland atomic localization energies for radical, electrophilic, or nucleophilic substitution. For each set of data the order of decreasing reactivity is indicated. In practice this order is more reliable than the absolute values of the reactivity indices themselves. 

Free-radical reactivity of thiazole has been calculated by semiempirical methods, and results free valence and localization energy) have been compared with experimental data. For mono- and dimethylthiazoles the radical localization energy of the unsubstituted position may be correlated with the logarithm of experimental reactivity (180, 200). The value of the slope shows that a Wheland-type complex is involved in the transition state. 

It is difficult to treat the effect of a heteroatom on the localization energies of aromatic systems, but Brown has derived molecular orbital parameters from which he has shown that the rates of attack of the phenyl radical at the three positions of pyridine relatively to benzene agree within 10% with the experimental results. He and his co-workers have shown that the formation of 1-bromoisoquinoline on free-radical bromination of isoquinoline is in agreement with predictions from localization energies for physically reasonable values of the Coulomb parameters, but the observed orientation of the phcnylation of quinoline cannot be correlated with localization ener-... 

In Figure 27.3, the relationship between the hydrogen bond energy and the product of the local softness values of donor and acceptor atom (A and B) is given for a series of closely related O—H O types of bonds (NR2, N02 family, etc.). 

FIGURE 27.3 (continued) (c) Combined effect of the local softness values of the acceptor and donor atoms on hydrogen bonding energy. (Reprinted from Ozen, A.S., Aviyente, V., De Proft, F., and Geerlings, P., J. Phys. Chem., A110, 5860, 2006. With permission.)... 

Since all localized orbitals have approximately the same spatial extension, it stands to reason that their orbital energies rjn should be of the same order of magnitude. In fact, one finds for the four main types of localized 7r electron orbitals the following orbital energy values ... 

Cf. also the values for the transition states on substitution of aromatic substances, Wheland (1942) and Dewar (1949). Further values for the localization energies are given by Dallinga et al. (1957) Mackor et al. (1958a) Streitwieser (1961). 

The p.K -values of Table 22 are plotted against the localization energies in Fig. 26. The straight line which can to a good approximation be drawn through these points confirms this relationship. Greater deviations occur particularly in the case of the peri-condensed aromatic substances pyrene and perylene. The pX values are lower than one would have expected on the basis of localization energies. 

In contrast to the HMO method, the repulsion forces of the electrons are taken into account when carrying out the SCF method, so that it may be expected that the results of these calculations will give better results for the positive aromatic ions than do the HMO calculations. If the pif -values are plotted against the localization energies obtained by this method, one obtains excellent conformity with the requisite linearity, as shown in Fig. 27. The figures for peri-condensed aromatic... 

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