Huckel topology

Huckel aromatics The benzene molecule has the suprafacial topology this means that the TT - electron density in benzene is continuous along the top or bottom face of the molecule. If the transition state for the pericyclic reaction has the same topology, it is said to resemble Huckel topology (Fig. 8.17). 

A thermally activated pericyclic reaction will proceed via a Huckel topology containing only suprafacial components if the cyclically conjugated ir-electrons equal [4n - - 2] (n = 0, 1,2,...). 

A. A Huckel topology with no nodes, or an even number of nodes. B. A Mobius topology. The twist in the system alters the topology,. such that the top" of one i orbital must interact with the "bottom" of the other. Such a system must have at least one node (dotted line), and will always have an odd number of nodes. 

Now, we may consider the TS structure for a Diels-Alder cycloaddition reaction. The Huckel TS structure of zero node is aromatic in nature. Thus, the reaction takes place in suprafacial mode following the Huckel topology, whereas in Mobius... 

Chair- like TS, 6e process Huckel topology aromatic... 

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. 

To cast some light on the relative importance of steric effects on the positional reactivities of benzenoid hydrocarbons, correlations of experimental a values of phenanthrene (4), tetrahelicene (5), pentahelicene (<5), and hexahelicene (7) with purely topological reactivity indices (Huckel cation localization energy, Dewar reactivity number and Herndon structure count ratio) have been studied [59],... 

Transition state aromaticity (Huckel and Mobius topologies)... 

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. 

One point which it is important to remember concerning the approach described in these pages is that it is based upon the ideas of simple Huckel theory. The type of problem therefore which may be viewed in terms of moments is therefore at present restricted to those for which such a topologically based theory is applicable. We have already disqual-... 

The antiaromatic geometry found along the concerted path of ground-state-forbidden pericyclic reactions, which is topologically equivalent to an antiaromatic HUckel [4/t]annulene or Mdbius [An 4- 2]annulene, is a particularly interesting type of biradicaloid geometry. (Cf. Section 4.4.) Other biradicaloid geometries and combinations of those mentioned are equally possible. 

EARLY COMPUTATIONAL RESULTS TOPOLOGICAL-HUCKEL TREATMENTS... 

We have considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbital, orbital correlation diagrams, and transition state aromaticity. All arrive at the same conclusions about the stereochemistry of electrocyclic reactions. Reactions involving 4n + 2 electrons are disrotatory and involve a HUckel-type transition structure, whereas those involving 4n electrons are conrotatory and the orbital array are of the Mobius type. These general principles serve to explain and correlate many specific experimental observations. The chart that follows summarizes the relationship between transition stmcture topology, the number of electrons, and the feasibility of the reaction. 

The last decade has produced a number of results which indicate that the successful longevity of Huckel theory is based on the fact that this theory contains intrinsic Information about the internal connectivity in the conjugated structures, i.e. it reflects the nrighbourhood of the atoms in the conjugated systems [5,16]. Here we will be concerned with the rdationship between Huckel theory and the topology of the molecular x-network. 

Fig. 12. Histogram representing the projected DOS on the Pb cluster (6p and 6py components). This topology gives within the frame of the simple Huckel theory (one MO per atom) 3 non bonding levels mainly localized on the A atoms.

In the PMO method, we analyze an electrocyclic reaction through the following steps (1) Define a basis set of 2p-atomic orbitals for all atoms involved (li for hydrogen atoms). (2) Then connect the orbital lobes that interact in the starting materials. (3) Now let the reaction start and then we identify the new interactions that are occurring at the transition state. (4) Depending upon the number of electrons in the cyclic array of orbitals and whether the orbital interaction topology corresponds to a Huckel-type system or Mobius-type system, we conclude about the feasibility of the reaction under thermal and photochemical conditions. 

Here, with six electrons involved, it is in the disrotatory mode (Huckel system) that the transition state is stabilized. The chart that follows gives a general summary of the relationship between transition state topology, the number of electrons, and the stability of the transition state. 

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