Frontier densities

Nevertheless, the puzzling fact to be explained is that the harder ring nitrogen prefers the softer electrophilic center and that this preference is more pronounced than the one observed for the amino nitrogen. Much remains to be done to explain ambident heterocyclic reactivity it was shown recently by comparison between Photoelectrons Spectroscopy and kinetic data that not only the frontier densities but also the relative symmetries of nucleophilic occupied orbitals and electrophilic unoccupied orbitals must be taken into consideration (308). 

Eq. (4.4 a) is satisfied in the position 1 of azulene. Eq. (4.4b) is valid in position 6 of fulvene, position 6 of azulene, position 3 of fluoranthene, and position 5 of acenaphthylene. Even in a few exceptional cases where the previous relations do not hold, a consideration of the coulombic effect of attacking reagents leads to a conclusion favorable to the hypothesis of frontier density growth. An example of such cases is position 3 of... 

The value vr is regarded as a measure of the extent to which the electron in the rth AO takes part in the bond formation with other atoms. In contrast with this, pT is the part of population in the rth AO which is living there and responsible for the interaction with outside. Hence, in view of the role of the frontier orbital in the charge-transfer interaction, it is reasonable to take, as the frontier density, the valence-inactive part 7S>. Namely,... 

We see from Eq. (3) that in addition to its use of approximate orbitals, Fukui s frontier density is a frozen-orbital approximation to the Fukui function, as indicated by the second term on the right-hand side of Eq. (3) [32]. 

Equation (27d) states that the kernel Jf(r,r ) is asymptotically equal to the Hartree-Kohn-Sham static dielectric function. Thus the expression in Eq. (20) for the Fukui function is just a short-range linear mapping of the frontier density, and the expression in Eq. (21) for the local softness is the same mapping of the local DOS. It is the frontier-orbital density which drives the chemical response measured by the Fukui function, and the local DOS which drives that measured by the local softness. 

Table 2. -Electron density, frontier density, and free valence at the exocyclic carbon of CTCX, HCX and TCX ...

The change in the atomic partial charge (Aapc) of key atoms before and after their keto-enol form rearrangement was used to analyze their reactivity. The HOMO density, frontier density, superdelocalizability, LUMO density, and ape (units au) of key elements were calculated. The reaction processes are shown in Figure 11.6 where only the important atoms are numbered. The sensitivity of phenacylalcohol derivatives and steroids and the calculated ape values are summarized in Table 11.2. 

Generally, the electron density of the LUMO is a key property for studying reactivity, but the values did not explain the sensitivity difference, and the electron density of the HOMO was also not useful for explaining the sensitivity, thus, the electron density values of the LUMO and HOMO are not given. The frontier density and the superdelocalizability also should not be used for this purpose, and their values are also not given. 

The HOMO density, frontier density, superdelocalizability, LUMO density, and ape of all elements were calculated using the MOPAC program after optimizing their structures with molecular mechanics. The ape of the keto and enol forms of phenacylalcohol were constructed using the CAChe system and are shown in Figure 11.10. The electron density of the carbonyl carbon was significantly reduced from the keto to the enol form. 

In order to demonstrate the reflection of this polarization in the observed regioselectivity, let us analyze the simple case of substituted Diels-Alder reaction where the diene component bears the donor, and the dienophile component the acceptor substitution. The formation of the preferred reaction product, which is in this case the "ortho" isomer, can be simply rationalized on the basis of a scheme, visualizing the magnitude of the overlap of the HOMO-LUMO orbitals for both alternative possibilities of the attack. It is, namely, possible to demonstrate that from the point of view of the magnitude of the overlap, and consequently also of the ease of the reaction, it is generally more favorable for reaction to proceed along such reaction path where the interaction and the formation of the new bonds takes place by the combination of the atoms vtith the large and the pair of the atoms with the small frontier density, than in the opposite case [43,45]. 

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