Neutral polyenes

In neutral polyenes a clear distinction can be made between essential single bonds (which can be twisted fairly easily) and double bonds (which offer much more resistance to rotation). It has become customary to distinguish stable isomers (classified E/Z with regard to the configuration around the double bonds) and easily interconvertible conform-ers (classified as s-cis, s-trnns or gauche with regard to the substituents on the essential single bonds) in polyenes. 

The above selection rules, therefore, predict that [1, 5] hydrogen shifts in neutral polyenes would be thermally allowed and the reaction would be facile, but thermal [1, 3] and [1, 7] shifts must go by an antarafacial process and they will be difficult to attain because of the geometric strain. This is also confirmed by many experimental observations. Thus concerted uncatalysed [1, 3] hydrogen shifts have not been seen in the diene of the following type, [1, 5] shifts are well known. 

Fig. 4.1 illustrates the first few members of the series of neutral polyenes the equilibria between butadiene 4.1 and cyclobutene 4,2, between hexadiene 4,3 and cyclohexadiene 4.4, and between octatetraene 4.5 and cyclooctatriene 4,6. There are of course heteroatom-containing analogues, with nitrogen or oxygen in the chain of atoms, and the systems can be decked out with substituents and other rings. To appreciate what the fundamental reaction is, it is only necessary to tease out the components—the longer conjugated... 

II. Electronic Structures, Equilibrium Geometries, and Energetics of the Ground States of Polyenyl Cations and Neutral Polyenes... 

Energies. In the case of the polyenyl cations, it is logical to assess the conjugation energies by means of the isodesmic reaction shown as Equation 4 (in analogy to the neutral polyenes). 

An alternative comparison is provided by Reaction 5, where the conjugation energy of the neutral polyene is included on the right-hand side of the equation. 

The Woodward-Hoffmann orbital symmetry rules are not limited in application to the neutral polyene systems that have been discussed up to this point. They also apply to charged systems, just as the Htickel aromaticity rule can be applied to charged ring systems. The conversion of a cyclopropyl cation to an allyl cation is the simplest... 

Electrocyclic reactions are not limited to neutral polyenes. The cyclization of a pentadienyl cation to a cyclopentenyl cation offers a useful entry to five-membered carbocycUc compounds. One such reaction is the Nazarov cyclization of divinyl ketones. Protonation or Lewis acid complexation of the oxygen atom of the carbonyl group of a divinyl ketone generates a pentadienyl cation. This cation undergoes electrocyclization to give an allyl cation within a cyclopentane ring. The allyl cation can lose a proton or be trapped, for example by a nucleophile. Proton loss occurs to give the thermodynamically more stable alkene and subsequent keto-enol tautomerism leads to the typical Nazarov product, a cyclopentenone (3.220). 

The situation is still more complicated for open-shell (radical) conjugated oligomers. In neutral polyene radicals, even the most precise and expensive ab initio correlated methods, such as CCSD(T), can give at best a qualitative prediction of the spin density distributions, and the behavior of common DFT schemes is also mediocre [42]. The problems with exchange and correlation are augmented in this case by the spin-restricted/umestricted ansatz dilemma discussed above. An efficient practical solution is, somewhat unexpectedly, provided by correlated semiempirical methods with a simple Hamiltonian, such as PPP [53]. We therfore also often use semiempirical methods in our studies of conjugated oligomer radical-ions. 

Ma, H.B., et al. 2005. Spin distribution in neutral polyene radicals Pariser-Parr-Pople model studied with the density matrix renormalization group method. 7 Chem Phys 122. 

Faster computers and development of better numerical algorithms have created the possibility to apply RPA in combination with semiempirical Hamiltonian models to large molecular sterns. Sekino and Bartlett - derived the TDHF expressions for frequency-dependent off-resonant optical polarizabilities using a perturbative expansion of the HF equation (eq 2.8) in powers of external field. This approacii was further applied to conjugated polymer (iialns. The equations of motion for the time-dependent density matrix of a polyenic chain were first derived and solved in refs 149 and 150. The TDHF approach based on the PPP Hamiltonian - was subsequently applied to linear and nonlinear optical response of neutral polyenes (up to 40 repeat units) - and PPV (up to 10 repeat units). " The electronic oscillators (We shall refer to eigenmodes of the linearized TDHF eq with eigenfrequencies Qv as electronic oscillators since they represent collective motions of electrons and holes (see Section II))... 

Fig. 1.10 Left. Canonical resonance structures for the l-dimethylamino-l,3,5,7-octatetraen-8-al molecule, DAO. (Top) Neutral polyene limit (middle) cyanine limit (bottom) zwitterionic charge-separated limit. Right Corresponding evolution of bond length alternation BLA (in A) (x) and bond order alternation BOA ( ), as a function of the applied external electric field F.

The second consequence directly involves the geometry of the bridge. Let us consider the case where the bridge is a polyene chain, i.e., the case of push-pull polyenes. The electronic structure of the polyene chain can be described as a linear combination of two canonical structures, namely a neutral polyene structure (a), with alternate single and double bonds. 

In Section 5.3, reactions of polyenes are examined with particular attention to the phase relationships in the highest occupied (HOMO) and lowest unoccupied molecular orbitals (LUMO). Anticipating this, notice that for the neutral polyenes the HOMO is a row of alternating bonding and antibonding relationships whatever the length (shaded 2 up, 2 down, 2 up, etc.), and that the have the opposite phase at the first and last carbons while the phase at the first and last carbons. 

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