Huckel Reference Structure

Figure 7. Hiickel delocalization energies per electron in units of p for the conjugated monocyclic hydrocarbons using the Huckel reference structure and the Hiickel computational method.

It was never a surprise that the Huckel computational method together with the Huckel reference structure of isolated double bonds gave imperfect predictions of aromaticity as seen in column 1 of Figure 6. The computational method, after all, contained many approximations. With these obvious deficiencies in the computational method, it was natural that more Investigations aimed at improving it rather than studying the reference structures used. 

The terms aromatic and antiaromatic have been extended to describe the stabilization or destabilization of TRANSITION STATES of PERICYCLIC REACTIONS. The hypothetical reference structure is here less clearly defined, and use of the term is based on application of the Huckel (4n+2) rule and on consideration of the topology of orbital overlap in the transition state. Reactions of molecules in the ground state involving antiaromatic transition states proceed, if at all, much less easily than those involving aromatic transition states. 

It might be expected that the relative stabilities of 4n -E 2) and 4n systems suggested by the Huckel rule would be reflected in the 7r-electron energies of the compounds. As a reference compound, a hypothetical structure is chosen in which the double bonds are localized. Thus, the resonance energy (RE) is assumed to be equal to the total 7r-electron energy ( ) minus the total TT-electron energy of the reference structure... 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

Removal of two electrons from the formal cyclic Sir-electron structures serves to produce potential Huckel 4n +2 aromatic systems. The loss of one electron to form a radical cation was referred to in Section 2.26.2.1, and removal of a second electron by electrochemical oxidation, leading to dicationic structures, has also been achieved for a wide range of unsaturated compounds with heteroatoms in the 1,4 positions (70ZC147, 73JA2375). The oxidations are discussed further in Section 2.26.3.1.5, where tabulated data are presented. An interesting feature is the stability of certain salts of the dications, some of which have been isolated. 

In 1967, Sauer said, referring primarily to regioselectivity, that the relative amounts of structurally isomeric adducts... cannot yet be explained . In fact stereoselectivity was by then understood qualitatively on the basis of frontier orbital theory and site selectivity quantitatively in terms of Brown s para-localization energy, but no explanation of regioselectivity and periselectivity was available. Within the year, however, Feuer, Herndon, and HalF were able to explain stereoselectivity and regioselectivity quantitatively in terms of a perturbation method based on HUckel or extended HUckel theory and including only the frontier orbital term, and now all these properties, together with the relative reaction rates, are satisfactorily understood " purely on the basis of frontier orbital theory. 

The problem is, however, more complex than the above Huckel s rule for aromaticity suggests. In fact, there are many examples of molecules that possess the structural features required by Huckel s rules but are not aromatic (see ref. 122 and references therein). 

Extended Huckel molecular orbital calculations were used to obtain an initial, qualitative picture of the electronic structure changes involved in two-electron transfer. EHMO calculations were carried out in D2h symmetry on H2P" bridged analogs of the [M2(p-PR2)2(CO)8] complexes using the CACAO program (50). Structural information and computational details are provided in reference 18. 

M(C0)4 fragment can be referred to a square antiprism with four outpointing hybrids, four bonding hybrids and a d 2 non-bonding orbital. Extended Huckel c eulations [8a] on M(CO)4 fragments predict 4, pyramidal structures for d (Q = 117.5°) and d Q = 122.5°). The nodal cone of d a occurs at 0 = 125.27°. 

Band structure for a cubic lattice in which each has only three p atomic orbitals. The energies were evaluated (Reference [23]) using only nearest-neighbor a and it interactions within the Huckel framework—see equation 13.44. 

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