Polyene energies

Difference in SCF-MO total energy (in kcal mol) for heterocycle and sum of localized polyene energies (benzene = 20 kcal/mol). ... 

We can follow the formation of the polyene energy-band gap in four consecutive steps, as shown in Figure 5.8. The uppermost curve is obtained at the HF level using the fixed geometry obtained for the minimal basis (a). In this case, the extension of the atomic basis does not influence the value of d (HF) significantly. On the other hand, the value is reduced by about 4 eV if the bond alternation is optimized (at the HF level) with each basis set (second curve from the top). An approximately 0.7 eV further reduction is obtained if the structural optimization is performed with the correlated total energy (third curve from the top). The lowest curve shows the energy-band gap values after polaron forma-... 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

The An + 2) tt electron standard follows from the pattern of orbital energies m monocyclic completely conjugated polyenes The tt energy levels were shown for ben zene earlier m Figure 114 and are repeated m Figure Figure 11 13a and 11 13c... 

A modified definition of resonance energy has been introduced by Dewar (66T(S8)75, 69JA6321) in which the reference point is the corresponding open-chain polyene. In principle this overcomes the difficulties inherent in comparing observed stability with that of an idealized molecule with pure single and double bonds, as thermochemical data for the reference acyclic polyenes are capable of direct experimental determination. In practice, as the required data were not available, recourse was made to theoretical calculations using a semiempirical SCF-MO method. The pertinent Dewar Resonance Energies are listed in Table 30. 

The most easily obtained information from such calculations is the relative orderings of the eneigy levels and the atomic coefficients. Solutions are readily available for a number of frequently encountered delocalized systems, which we will illustrate by referring to some typical examples. Consider, first, linear polyenes of formula C H 2 such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such compounds are given by the expression... 

Although the Hiickel method has now been supplanted by more complete treatments for theoretical analysis of organic reactions, the pictures of the n orbitals of both linear and cyclic conjugated polyene systems that it provides are correct as to symmetry and the relative energy of the orbitals. In many reactions where the n system is the primary site of reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the reader should develop a familiarity with the qualitative description of the n orbitals of typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the basis for further discussion in Chapters 9 and 11. 

Both thermochemical and MO approaches agree that benzene is an especially stable molecule and are reasonably consistent with one another in the stabilization energy which is assigned. It is very significant that MO calculations also show a destabilization of certain conjugated cyclic polyenes, cyclobutadiene in particular. The instability of cyclobutadiene has precluded any thermochemical evaluation of the extent of destabilization. Compounds that are destabilized relative to conjugated noncydic polyene models are called antiaro-maticf ... 

The rectangular structure is calculated to be strongly destabilized (antiaromatic) with respect to a polyene model. With 6-3IG calculations, for example, cyclobutadiene is found to have a negative resonance energy of—54.7 kcal/mol, relative to 1,3-butadiene. In addition, 30.7 kcal of strain is found, giving a total destabilization of 85.4 kcal/mol. G2 and MP4/G-31(d,p) calculations arrive at an antiaromatic destabilization energy of about 42kcal/mol. ... 

The energy parameters used for the reference polyene by Hess and Schaad were developed on a strictly empirical basis. Subsequendy, Moyano and Paniagua developed an alternative set of reference bond energies on a theoretical basis. These values are shown... 

The predictions of relative stability obtained by the various approaches diverge more widely when nonbenzenoid systems are considered. The simple Hiickel method using total n delocalization energies relative to an isolated double-bond reference energy (a + fi) fails. This approach predicts stabilization of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for much more stable aromatics. The HMO, RE, and SCF-MO methods, which use polyene reference energies, do much better. All show drastically reduced stabilization for such systems and, in fact, indicate destabilization of systems such as butalene and pentalene (Scheme 9.2). 

Ultraviolet-visible (UV-VIS) spectroscopy (Section 13.21) Analytical method based on transitions between electronic energy states in molecules. Useful in studying conjugated systems such as polyenes. 

How can we predict whether conrotatory or disrotatory motion will occur in a given case According to frontier orbital theory, the stereochemistry of an electro-cyclic reaction is determined by the symmetry of the polyene HOMO. The electrons in the HOMO are the highest-energy, most loosely held electrons, and are therefore most easily moved during reaction. For thermal reactions, the ground-state... 

Considering their potential antiaromatic character, thiepins are also of theoretical interest. HMO calculations of -resonance energies, using reference data from 27 acyclic polyenes containing sulfur, predict antiaromatic character for thiepin and 2-benzothiepin, whereas 1- and... 

In the following we shall consider the effect of polyconjugation and configuration of the polyene chain on the equilibrium dissociation of polyconjugated polyelectrolytes40, 41 45 264, such as PPA. The comparison of pAa and Z(energy of... 

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