Annulene, perimeter model

SJAnnulene dianion, frontier orbitals. 90 [l4)Annulene perimeter. 87, 174 Annulene, perimeter model, 78. 85 aniiaromatic. 167.205,445 bridged. 70... 

Alternatively, the porphyrin ring can be constructed starting from [16]annulene. In the first step, two electrons are added to form the corresponding [16]annulene dianion, which is transformed into porphyrin Cl") by adding bridges and heteroatoms. Unlike the structure derived from [18]annulene, the dianion-based model has a fourfold symmetry, and was considered suitable for the description of metal complexes [23] (see Sect. 2.3.2). In yet another approach [24], based on the so-called perimeter model, the porphyrin macrocycle is derived from the [20]annulene dication (I "). Both the [16]- and [20]annulene models were employed to describe electronic absorption spectra and magnetic circular dichroism of porphyrinoids [24, 25],... 

Biphenylene and trisdehydro[12]annulene are representatives of conjugated hydrocarbons with a 4 -membered ring. The pattern of their absorption spectra is completely different from that of benzenoid aromatics. Their HOMO and LUMO are derived from the two NBMOs of an ideal perimeter and both the lowest excited singlet and triplet state can be described by the configuration A ho lu- The transition is symmetry forbidden in molecules of D2h symmetry or higher. Nonradiative decay usually dominates their photophysical properties. Quantum yields of fluorescence and intersystem crossing are low.307 The LCAO version of Platt s perimeter model has been extended to treat conjugated systems with AN jt-electrons derived from [ ]annulenes.308,309... 

Figure 2.11. The perimeter model of an (4N+2)-electron [/i]annulene, geometry on the left, energies of the MOs t on the right. The angular momentum quantum number is given for each MO. The sense and magnitude of electron circulation and the resulting orbital magnetic moment are shown schematically in a perspective view. Orbital occupancy in the ground configuration and the four one-electron HOMO->LUMO excitations are indicated (by permission from Michl, 1978).

ReUance on simple classical electron coimting rules corresponds to an approximate description of the clamped cycle in terms of its annulene perimeter, and this is clearly insufficient. We can propose three perturbed perimeter models, whereby the simple perimeter annulene analogy is considered as the zeroth-order solution (Model 0) in a perturbative treatment. Model I includes the non-perimeter bonds perturbatively. Model II includes the perimeter heteroatoms perturbatively. Model III includes both (see Scheme 5). By means of these pictorial perturbative models (I, II and III) it is shown below that, when first-order corrections to the angular momentum character and orbital energies of the perimeter annulene (Model 0) are taken into account, it is possible, within the ipsocentric model, to give a unified rationalisation for the survival of the original ring current in XHXH clamped monocycles, and its extinction in HC = CH-clamped monocycles, even at the simple Hiickel level of theory. 

Michl, J., Magnetic circular dichroism of cyclic. pi.-electron systems. 1. Algebraic solution of the perimeter model for the A and B terms of high-symmetry systems with a (4N -I- 2)-electron [n]annulene perimeter, J. Am. Chem. Soc., 100, 6801 (1978). 

Various substituted l,6-methano-[10]annulenes have been prepared and characterized, and in particular the n.m.r. of such compounds reflects their delocalized nature 17,120,124-127) (a 71-complex formed from reaction of l,6-methano-[10]annulene with hexacarbonylchromium has also been characterized 128>). The X-ray crystallographic analysis 129> of the 2-carboxylic acid derivative 24 shows the bridge angle to be 99.6 °, and thus that the Cio perimeter is even flatter than expected from molecular models. Furthermore, the ten perimeter bonds have lengths which vary over the narrow range 1.38 to 1.42 A, the values being typical of benzenoid aromatic bonds. This lack of appreciable... 

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