Sign inversion

Note that both the 2 + 2 and 2 + 4 transition states are Hiickel systems no matter what basis sets we chose. For example. Figure 15.8 shows other basis sets we might have chosen. In every case there will be zero or an even number of sign inversions. 

As expected, the Mobius-Hiickel method leads to the same predictions. Here we look at the basis set of orbitals shown in G and H for [1,3] and [1,5] rearrangements, respectively, A [1,3] shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1070) with one or an odd number of sign inversions. As can be seen in G, only an antarafacial migration can achieve this. A [1,5] shift, with six electrons, is allowed thermally only when it is a Hiickel system with zero or an even number of sign inversions hence it requires a suprafacial migration. 

Figure 9.17. (a) Conrotatory, Mobius system, one sign inversion, (b) Disrotatory, Hiickel system, no sign inversions. 

In the most common LB films with the Y-type structure, the center of inversion exists, and hence they are not suitable for pyroelectric usages. On the other hand, since LB films with X- or Z-type structure have no center of symmetry, it is possible to construct the polar pyroelectric film with permanent dipoles pointing toward one direction. Similar structures can also be formed in hetero LB films with two different amphiphiles stacked altematingly. The first report on the pyroelectric LB film with X-or Z-type structure appeared in 1982 by Blinov et al. [12], It was followed by those of the alternate LB films by Smith et al. [13] and Christie et al. [14]. The polarized structure of the fabricated LB film can be checked by the surface potential measurements using the Kelvin probe [15], the Stark effect measurements [12], or the sign inversion of the induced current between heating and cooling processes. 

The transition state in suprafacial attack is designated as of Huckel type in which no sign inversion of the cycle has taken place. The other type of migration involves one sign inversion. This is called mobius type inversion. The Huckel type of inversion occurs when the total number of electrons is 2, 6,. .., (4n + 2). This is also called aromatic transition state. In mobius type the participating electrons is 4, 8,. .. i.e. An. 

Brown PO.. and N.R. Cozzarelli "A Sign Inversion Mechanism for Enzymatic Supercoiling of DNA." Science. 206. IIX - 1083 < t979]... 

Another feature of the resonance mixing, already alluded to, is the sign inversion which is caused by the different nature of the matrix elements that mix the Kekule structures for aromatics and antiaromatics. Thus, in the case of benzene (part a), the ground state is the positive combination of the two Kekule structures, while in cyclobutadiene (part b), the ground state is the negative combination.15116158210 214 Consequently, the twin excited states are the negative and positive linear combin-tions, respectively, for aromatics and antiaromatics.13-15-115-209 212 This relationship of the ground and excited states to the fundamental Kekule structures has been derived early on by the pioneers of VB theory.211-214... 

The Mobius-Huckel concept was introduced by Zimmerman in 1966 35). It was suggested that each cyclic array of orbitals in a reacting system may be categorized as a Hiickel type or a Mobius type , depending on the number of plus-minus overlaps between adjacent orbitals. With zero or an even number of such sign inversions, the system is a Hiickel variety array while with one or some other odd number the system is a Mobius system. 

As we saw on p. 1210, in this method we choose a basis set of p orbitals and look for sign inversions in the transition state. Figure 18.4 shows a basis set for a 1,3-diene. It is seen that disrotatory ring closing (Fig. 18.4a) results in overlap of plus lobes only, while in conrotatory closing (Fig. 18.4h) there is one overlap of a plus... 

Fig. 18.4. The 1,3-diene-cyclobutene interconversion. The orbitals shown are not molecular orbitals, but a basis set of p-atomic orbitals, (a) Disrotatory ring closure gives zero sign inversion, (b) Conrotatory ring closure gives one sign inversion. We could have chosen to show any other basis set (e.g., another basis set would have two plus lobes above the plane and two below, etc.). This would change the number of sign inversion, but the disrotatory mode would stiU have an even number of sign inversions, and the conrotatory mode an odd number, whichever basis set was chosen.

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