Frontier electron densities

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

V-Electron densities, CNDO/2. Total electron densities, CNDO/2. "Total electron densities, CNDO/2 for N(D—H. tr-Electron densities, frontier electron density calculation. "Frontier electron densities. 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

An alternative approach is in terms of frontier electron densities. In electrophilic substitution, the frontier electron density is taken as the electron density in the highest filled MO. In nucleophilic substitution the frontier orbital is taken as the lowest vacant MO the frontier electron density at a carbon atom is then the electron density that would be present in this MO if it were occupied by two electrons. Both electrophilic and nucleophilic substitution thus occur at the carbon atom with the greatest appropriate frontier electron density. 

The significance of frontier electron densities is limited to the orientation of substitution for a given aromatic system, but this approach has been developed to give two more complex reactivity indices termed superdelocalizabilities and Z values, which indicate the relative reactivities of different aromatic systems. 

Polarization and dipole moment studies for alkyl-, aryl-, carbonyl- hydroxy- (keto-) and amino-isoxazoles have been compiled and likewise support the low electron nature of the ring 63AHC(2)365, 62HC(l7)l,p. 177). More recent studies predict the order of electrophilic substitution to be 5>4> 3 on frontier electron density values of 0.7831, 0.3721 and 0.0659, respectively 7lPMH(4)237,pp.245,247). This contrasts with earlier reports of 4>5>3 on density values of —0.09, -t-0.14 and -t-0.18 in that order 63AHC(2 365). 

Soft electrophiles will prefer carbon, and it is found experimentally that most alkyl halides react to give C-alkylation. Because of the n character of the HOMO of the anion, there is a stereoelectronic preference for attack of the electrophile approximately perpendicular to the plane of the enolate. The frontier orbital is ip2, with electron density mainly at O and C-2. The tpi orbital is transformed into the C=0 bond. The transition state for an 8 2 alkylation of an enolate can be represented as below. 

Several calculations of the electronic structure of isoindoles have Ijeen published, and the distribution of charge density around the isoindole nucleus calculated by these methods is summarized in X able I. A common prediction of the calculations, which are based on tlie LCAO-MO method or the frontier electron concept, is the relatively high electron density to bo found at position 1, and the expectation, thei efore, i.s that electrophilic substitution on carbon... 

From Electron Density to Frontier Orbital Amplitude... 

Naphthalene undergoes electrophihc substitutions at the a rather than p position. The Hueckel molecular orbital calculations show that all the carbons have the same jt electron density 1.0. This is not in agreement with the theory of organic reactions based on the Coulombic interaction that electrophilic attack occurs on the most negatively charged atom. Fukui [7] proposed the frontier orbital theory for the discrepancy between the theory and the experimental observation. The importance of... 

Modulation of the electron density on the frontier atomic orbitals centered on the active atom(s) with LUMO and HOMO character... 

The first paper of the frontier-electron theory pointed out that the electrophilic aromatic substitution in aromatic hydrocarbons should take place at the position of the greatest density of electrons in the highest occupied (HO) molecular orbital (MO). The second paper disclosed that the nucleophilic replacement should occur at the carbon atom where the lowest unoccupied (LU) MO exhibited the maximum density of extension. These particular MO s were called "frontier MO s . In homolytic replacements, both HO and LU.were shown to serve as the frontier MO s. In these papers the "partial" density of 2 pn electron, in the HO (or LU) MO, at a certain carbon atom was simply interpreted by the square of the atomic orbital (AO) coefficient in these particular MO s which were represented by a linear combination (LC) of 2 pn AO s in the frame of the Huckel approximation. These partial densities were named frontier-electron densities . 

The frontier-electron density was used for discussing the reactivity within a molecule, while the superdelocalizability was employed in comparing the reactivity of different molecules 44>. Afterwards, the applicability of the frontier-electron theory was extended to saturated compounds 50>. The new theoretical quantity "delocalizability was introduced for discussing the reactivity of saturated molecules 60>. These indices satisfactorily reflected experimental results of various chemical reactions. In addition to this, the conspicuous behavior of HO and LU in determining the steric course of organic reactions was disclosed 44.51). 

Hi) The principle of growing frontier-electron density along the reaction path... 

The importance of the frontier-orbital AO coefficient is evident from Eqs. (3.21) and (3.26). The problem is how this quantity changes along the reaction path. It can be shown by actual calculation that the frontier-electron density generally increases as the reaction proceeds. 

In order to understand qualitatively how the frontier-electron density, (cconjugated hydrocarbons, it is convenient to take account of Stage III. In this stage it is easily proved that... 

The reactivity indices derived from the theory which has been developed in Chap. 3 are the frontier-electron density, the delocalizability, and the superdelocalizability, as has been mentioned in Chap. 2. These indices usually give predictions which are parallel with the general orientation rule mentioned in Chap. 5. The superdelocalizability is conventionally defined for the jr-electron systems on the basis of Eq. (3.21) and Eq. (3.24) as a dimensionless quantity of a positive value by the following equations 49> ... 

The contribution of the frontier orbitals would be maximized in certain special donor-acceptor reactions. The stabilization energy is represented by Eqs. (3.25) and (3.26). Even in a less extreme case, the frontier orbital contribution maybe much more than in the expression of the superdelocalizability. If we adopt the approximation of Eq. (6.3), the intramolecular comparison of reactivity can be made only by the numerator value. In this way, it is understood that the frontier electron density, /r, is qualified to be an intramolecular reactivity index. The finding of the parallelism between fr and the experimental results has thus become the origin of the frontier-electron theory. The definition of fr is hence as follows ... 

The reactivity of hydrogens in norbomane towards abstraction is of interest since the difference between two hydrogen atoms attached to the same carbon atom of position 2 can well be explained. The frontier electron density values 105> are in accord with the reactive exo hydrogen (Fig. 7.20). 

Figure 2. Frontier electron density distribution for the p-toluidinyl radical...

---