Annulene Hiickel theory

The Hiickel theory [21, 22], which has become the standard description of annulene aromaticity, is one of the cornerstones of physical organic chemistry. Unfortunately, in its qualitative version, from which the famous Hiickel rules are derived, the theory does... 

We will now engage in a more elaborate application of Hiickel theory, which demonstrates the power of this simple model. The purpose is to determine the energy shifts of the eigenvalues when an annulene is brought into a uniform magnetic field, B. This field is independent of position and time. It can be defined as the curl (or rotation) of a vector potential A, and, in terms of a position vector r from a given... 

Quantum mechanics, even in the crudest approximation as formulated in Hiickel theory [23], is suitable for explaining the n aromaticity. Application of this theory clarifies the planarity and stability of benzene and leads to the well-known (4n + 2)n electron rule for annulenes. The delocalized n electrons affect not only the structure (planarity and high symmetry) and enhanced stability of aromatic systems they also... 

Annulenes have been utilized in the investigation of the effect of adding (or removing) electrons to Ti-conjugated systems [lb]. Annulenes can be used in demonstrating the validity of the Hiickel theory and the experimental criteria of aromaticity [57], because the molecular frame can hold different numbers of electrons. 

In this section we describe the reduction of some classical annulenes , [8]-annulene 3, [12]annulene 4, [16]annulene 5 and [18]annulene 6. In all of these systems the reduction is accompanied by changes in the molecular frame. We shall concentrate on the NMR spectra of the diamagnetic anions and the EPR spectra of the [4n- -l]-radical anions, both of which serve as probes for the delocalization and planarity of these r-systems. The Hiickel theory [58], which only considers the 71-energy, neglecting the c-frame, can only describe planar, strain-free r-perimeters therefore, it is important to analyze the structure of the annulenes and their anions. 

The major importance of the Hiickel rule is that its predictions can be experimentally checked and hence the predictive power of the Hiickel MO theory (i. e. topological MO theory) can be critically evaluated. The efforts made to prove or disprove the Hiickel rule strongly influenced the development of annulene chemistry 141.142),... 

The annulenes are that series of monocyclic polyolefins (C H ) containing a complete system of contiguous double bonds. While benzene (the best known member of this class of compounds) has been in evidence for some time it is only of late that interest in the higher members has become apparent. This interest has its origins in the LCAO-MO theory of re-elec-tron systems as formulated by E. Hiickel (in particular the "Hiickel rule relating aromatic stability to structure). Although the non-classical chemistry of the benzenoid hydrocarbons had previously been the subject of some conjecture, Httckel s theoretical studies provided the first satisfactory explanation of the peculiar stability of this class of compounds and, incidently, the elusiveness of cyclobutadiene. 

This non-mobile spectrum shows [18]annulene to be aromatic, a fact which follows from Hiickel s theory, together with the finding i ) that this molecule is almost planar, displacement of the carbon atoms from the mean plane being less than 0.1 A. Further X-ray crystallographic analysis shows that there is no bond alternation in this molecule, (but not all bonds are exactly the same length). 

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. 

According to standard perturbation theory applied to the Hiickel solutions for the [4m] annulene problem, the first-order correction to the MO of angular momentum A2 arising from the mixing with an MO of angular momentum Ai caused by addition of new bonds between positions 4r - 3 and 4r, is proportional to the matrix element... 

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