Frontier orbitals coefficients

Fig. 8.2 Frontier-orbital coefficients and energies (eV) for acrolein and protonated acrolein [2 ...

The observed regioselectivity can be explained by taking into account the frontier orbital coefficients of the reactants. 

The differences in stabilization energies for the formation of the various regioisomers are mainly determined by the differences in the largest term of equation 15. Formation of that regioisomer is favored for which the largest term consists of the largest frontier orbital coefficients from both diene and dienophile. 

FIGURE 8. Relative frontier orbital coefficients of fulvene... 

The reactions of 521 with 1,3-dienes were found to proceed exclusively in an [8 + 2] addition mode. The reactions were completely site and regioselective, as exemplified by the reaction between 521 and 2-methyl-l,3-pentadiene (525) which gave 526 after loss of CO2 (equation 152). The regiochemistry observed was in agreement with the frontier orbital coefficients calculated with semi-empirical methods. 

Figure 5 Calculated (AMI) heats of formation AHf), dipole moments (/r), and frontier orbital coefficient and energies (e) for methyl esters 31a and 8a.

Frontier molecular orbital (FMO) theory has been successful in rationalizing the reactivity, electroselectivity, and regioselectivity of many heterocycles, including mesomeric betaines. To apply FMO theory, some knowledge of the frontier orbital coefficients and energies is necessary, and it is useful to draw some general conclusions about the frontier orbitals in mesomeric betaines. 

In comparison to other aromatic hydrocarbons, t-1 forms a more stable charge-transfer complex with tetracyanoethylene than would be expected on the basis of its ionization potential (79). That is, when EgT for a series of hydrocarbon donors is plotted against IPj), the point for t-1 falls well below the line (Fig. 3). The unusual stability of t-1 complexes may be related to their large frontier orbital coefficients which allow effective interaction with a small acceptor such as tetracyanoethylene. 

Fig. 5. Calculations for 10,9-borazarophenanthrene. (a) PMO localization energies (x /S-1 ) (b) -electron densities (c) frontier orbital coefficients.

In these Hiickel calculations,273 the intramolecular distance is presumed to be the same for each transition state. Therefore, the atomic overlaps are identical and the V- values are proportional to the frontier orbital coefficients. 

Condition (2) is only properly satisfied if the two sites under comparison involve the same chemical element. If the elements are different, their orbitals are not of the same size and their interactions with the incoming reagent will depend on overlaps in addition to on frontier orbital coefficients. FO analysis is then much more complicated. Great care must be taken if the two elements are from different rows of the periodic table, C and S, for example. 

Indole and benzofuran combine two problems they are nonalternant and they contain heteroatoms. The indole frontier orbital coefficients in the 8- and 9-positions78 are very similar, 0.491 and 0.493, respectively. The subjacent orbital lies only 0.256/1 below the HOMO, but it has very small coefficients in these positions. The overriding factor seems to be the net charge (—0.12 at position 9, essentially neutral at position 8), which strongly favors attack at position 9. The case of benzofuran is still more complicated. There is a difference between the frontier orbital coefficients at position 8 (0.54) and 9 (0.47), but charge control still prefers the 9-position (—0.10 versus —0.03 units for the 8-position). The experimental results show that the frontier orbital terms dominate. 

Fig. 15.26. Frontier orbital coefficients and energy difference of the H0M0-LUM0 gaps in orientation-selective Diels— Alder reactions (cf. Figure 15.25, X = H).

Here we are mostly interested in the transition states of one-step cycloadditions between two unsaturated molecules I and II. In this special case, the frontier orbitals will be 7r-type orbitals, and overlaps at two ends of each orbital fragment contribute to each frontier orbital interaction overlap at the termini Cl /C1 n and another overlap involving the termini Goi/Goh. (Substrate I reacts at its C atom 1 with C atom 1 of substrate II and at its C atom oj with C atom o> of substrate II. Substrate I possesses the frontier orbital coefficients Cihomoj and cgLUMOj at its reactive center Cl and the coefficients C ,f iomo, and c, UMO at Ca>. In analogy, the frontier orbital coefficients of substrate II are c homo, and c i umo, at its reactive center Cl and c , HOMOn and cm>mMon at reactive center Go. The stabilization A TS of the transition state of such a one-step cycloaddition can be expressed in terms of the frontier orbitals as Equation 12.2. 

The familiar explanation for this example of site selectivity is that reaction at the 9,10-position creates two isolated benzene rings, whereas reaction at the 1,4-position would create a naphthalene nucleus, which is a less stable arrangement of two benzene rings. This explanation relies on the influence of product-like character in the transition structure, but we may also note that the same product is accounted for by looking at the frontier orbital coefficients of the starting materials the largest coefficients in the HOMO of 6.287 are at the 9,10-positions (see p. 174). 

For example, heptatriene 6.290 and 1-cyanobutadiene 6.294 react with maleic anhydride and isoprene 6.293 to give mainly the lower-energy adducts 6.291 and 6.295, respectively, rather than the alternatives 6.292 and 6.296.837 These reactions are similarly governed both by the formation of the thermodynamically favoured products and by the initial overlap with the larger frontier orbital coefficient in each component leading to the unsymmetrical transition structure. 

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