Phase dislocations

There are two mechanisms by which a phase change on the ground-state surface can take place. One, the orbital overlap mechanism, was extensively discussed by both MO [55] and VB [47] formulations, and involves the creation of a negative overlap between two adjacent atomic orbitals during the reaction (or an odd number of negative overlaps). This case was temied a phase dislocation by other workers [43,45,46]. A reaction in which this happens is... 

In most cases, we can carry out this program completely so that there are no phase dislocations where AOs overlap out of phase with one another this was true in the cases indicated in Figs. 1.36-1.40. As indicated, we can pick the signs (phases) of the AOs so that positive overlaps with positive and... 

No such Mobius strip compound has as yet been synthesized, but the concept underlying it is very important. A system in which there is an inevitable phase dislocation is topologically distinct from one in which all phase dislocations can be avoided. Note that this distinction depends on the topology of overlap of the AOs involved in forming a delocalized system it is quite independent of the MOs that can be constructed from them. 

While neither of these theoretical possibilities has been realized for stable 7i-electron systems, it must be remembered that delocalized systems in chemistry are not all of n type. There is no reason why delocalized systems should be two dimensional or involve exclusively Ti-type overlap of p or d AOs. In a three-dimensional delocalized system involving a- as well as retype overlap, we have much more flexibility and, as we shall see presently, examples of this alternative type of topology become important. Since the MO treatment of n systems was first introduced by Huckel, the normal class of delocalized systems with no required phase dislocations may be described as HUckel systems. The second topological type with one inevitable phase dislocation may then be called anti-Huckel systems. ... 

The PMO treatment of anti-Hiickel systems presents no problems. The distinction between Huckel and anti-Hiickel types applies only to cyclic conjugated systems, since in an open-chain system it is always possible to choose the phases of AOs so that there are no phase dislocations. The only problem then is that of aromaticity under what conditions are the cyclic anti-Hiickel systems more or less stable than the open-chain analogs ... 

It can be seen at once from the argument indicated in Fig. 3.19(c,d), and from equations (3.31) and (3.36) that if we introduce a phase dislocation into an odd AH, we reverse the relative signs of the NBMO coefficients of the terminal AOs. Thus,... 

Assign phases to the AOs, choosing them so as to avoid phase dislocations as far as possible (see again Figs. 5.35-5.37). 

Is there an unavoidable phase dislocation (There cannot be more than one, see p. 106). If not, the transition state is of Hiickel type. If there is, it is of anti-Hiickel type. 

If a 7T cycloaddition takes place by cis addition to the n systems, the transition state is of Hiickel type. If, however, one of them adds trans, the transition state has a phase dislocation and so is anti-Hiickel. This is shown in (158) and... 

The concept of the Mobius strip was explained earlier (see p. 55). The basis of the Zimmerman analysis is an extension of this idea. A cyclic polyene is defined as a Hiickel system if its basis molecular orbital (i.e. the lowest filled TT-level as in the case of benzene, for example) contains zero or an even number of phase dislocations. Mbbius systems possess an odd number of phase dislocations in the basis molecular orbitals. In accordance with the rules predicting aromaticity for these systems, which results from the application of the Hiickel molecular orbital theory, it may be inferred that since cyclic conjugation also arises in the transition states of pericyclic reactions, the foDowing conclusions apply ... 

---