Aromaticity Hiickel theory

In terms of simple Hiickel theory the change from polyenic to aromatic the system experiences on passing from (1) and (2) to (3) was attributed primarily to the lower LVMO energy of the latter (B-73MI52000). A more detailed Hiickel calculation (72T3657) utilizing properly selected models in conjunction with thermochemical data also correctly accounts for the differences in tt-electron makeup between 1/Z-azonine (3a) and oxonin (1), which... 

The most common procedure is that of semiempirical theory, which treats Hi as a parameter assumed reasonably constant for a given series of compounds. For example, in the case of aromatic hydrocarbons, each carbon atom is in a similar state and contributes one orbital (a 2orbital with its nodal plane corresponding to the molecular plane) to the above linear combination. Hiickel theory applied to these compounds assumes... 

A recent Hflckel calculation based on the proper choice of models correctly accounts for the observed differences in w-electronic makeup between lff-azonine (26a) and oxonin (24a) which were calculated to possess resonance energies of 0.139 and 0.0010, respectively [B. A. Hess, L- J. Schaad, and C. W. Holyoke, Tetrahedron 28, 3657 (1972)]. In terms of simple Hiickel theory the differences between 26a and 24a were attributed chiefly to the lower LVMO energy of the latter (A. G. Anastassiou, in Topics in Nonbenzenoid Aromatic Chemistry (T. Nozoe, R. Breslow, K. Hafner, S. Ito, and I. Murata, eds.), Vol. I, pp. 1-27. Hirokawa Publ., Tokyo, 1973). 

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... 

Anti-aromaticity was predicted by the Hiickel approach for conjugated cyclic planar structures with 4n 7i electrons due to the presence of two electrons in antibonding orbitals, such as in the cydopropenyl anion, cydobutadiene, and the cydopentadienyl cation (n = 1), and in the cydoheptatrienyl anion and cydooctatetraene (n = 2). It has been argued that a simple definition of an anti-aromatic molecule is one for which the 1H NMR shifts reveal a paramagnetic ring current, but the subject is controversial. The power of the Hiickel theory indeed resides not only in the aromatic stabilization of cydic 4n + 2 electron systems, but also in the destabilization of those with An electrons [22, 27, 42]. 

London orbitals were introduced by Fritz London, who in 1937 used Hiickel theory to calculate the contribution to the magnetizability from the ring currents in the 7r-orbital backbone of some aromatic molecules [13]. The great virtue of London s approach is that each individual AO—the building blocks of molecular wave functions—has been harnessed to respond correctly (to first order at least) to the application of an external magnetic field, irrespective of the choice of the external gauge origin. Moreover, since, in London s approach, only the atomic orbitals are modified, this method is fully transparent to the treatment of the electronic structure otherwise. 

Aromatic systems provide the most significant applications of Hiickel theory. For benzene, we find the secular equation... 

The theoretical reason is that the maximum Hiickel theory resonance energies per atom of the fullerenes increase more or less monotonically from C20 to the graphite limit, reflecting the increased aromaticity associated with a larger proportion of six-membered rings. Clearly, then, thermodynamic equilibrium between the fullerenes will never account for any ion... 

The other polarizabilities, and S e obtained in a similar way, and the third order term in (105) is also easily obtained (Diercksen and McWeeny, 1965). Again it should be noted that it is framework parameters, to, and ]8 , which occur most naturally in the perturbation theory. Numerical values of the indices are now in course of calculation, for both aromatic hydrocarbons and heteroaromatic systems, and it will be of great interest to make a more detailed and systematic comparison with Hiickel theory. 

There are, of course, certain circumstances in which the SCF equations can easily be shown to reduce to Hiickel-type equations. Thus in the standard excited-state equations of Hall for 7r-electron aromatic hydrocarbons, it can be shown that the LCAO coefficients are often precisely the same as in the Hiickel scheme. However, this particular state is not of direct value for our purposes. Further, Pople has shown that if the Pariser-Parr approximation of zero differential overlap is accepted, then, apart from some (usually) small terms in inverse internuclear distances, the total w-electron energy is given by an expression identical in form to that of Hiickel theory. Both writers adopt the approximation of neglecting all overlap integrals. This is particularly serious with overlap integral may be as large as... 

Milun et al [94] reported the calculation of aromatic stabilities, using the standard form of Hiickel theory, in which the acyclic polyenelike reference structure was represented by a two-bond parameter scheme (k = 2 in eq. (81)),... 

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