Hiickel array

In the case of butadiene to cyclobutene interconversion (4n 7u-electron system), a disrotatory mode of ring closure leads to a Hiickel array, which is antiaromatic with 4n 7c-electrons (Figure 2.9). Therefore, the disrotatory mode... 

Similarly, we can analyze the hexatriene-cyclohexadiene system having (4n + 2) 7T-electrons (Figure 2.10). In this case, a disrotatory mode of ring closure leads to a Hiickel array, which is aromatic with (4n + 2) rr-electrons. Therefore, the disrotatory mode of reaction now becomes thermally allowed. However, a conrotatory mode of ring closure uses a Mobius array, which is antiaromatic with (4n + 2) 7r-electrons. Therefore, the reaction is thermally forbidden in this mode. 

Hiickel orbital aray Mdbius orbital array... 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

Porphyrin systems therefore obey Hiickel s rule in having An + 2 n = A) TT-electrons in a planar, cyclic, conjugated array. Both major tautomeric forms have delocalization pathways with opposite N-Hs (trails tautomers), as shown in 71a 71b. It is already known (76AHCS1) that tautomers with inner hydrogens adjacent (cis tautomers) are much less stable, playing an important role only in the mechanism of proton transfer in porphyrins and phthalocyanines. 

Similar considerations apply to the thiirene oxide system (18), since in this case too the sulfur s 3d-orbitals have the potential of interacting with the 2p-orbitals of both the adjacent carbon and oxygen atoms. Such an interaction should facilitate some kind of conjugation of the carbon-carbon double-bond -electrons with the formally unoccupied 3d-orbitals, which in turn would give rise to Hiickel-type stabilization associated with cyclic array of 4n + 2 (n = 0) 7t-electrons. 

Valence electron rules have been theoretically proposed for three- and four-membered atomic rings [7], The p, p and p orbital arrays are of the Hiickel or Mobius conjugation (Scheme 2) [9, 10], The splitting patterns of the energy levels are well known... 

The i-orbital array of three and four-membered rings is of the Hiickel conjugation. (Scheme 2). The splitting patterns of the orbital energy levels (Scheme 3) show that the total number of valence electrons for the closed-shell structures is 4Af + 2 for the three- N= 0) and four-membered rings (N= 0, 1). 

Conjugation of the 7t-electrons of the carbon-carbon double bond with the LUMO sulfur 3d-orbitals would be expected to stabilize the Hiickel 4n -I- 2 (n = 0) array of n-electrons in the thiirene dioxide system. No wonder, therefore, that the successful synthesis of the first member in this series (e.g. 19b) has initiated and stimulated several studies , the main objective of which was to determine whether or not thiirene dioxides should be considered to be aromatic (or pseudo-aromatic ) and/or to what extent conjugation effects, which require some sort of n-d bonding in the conjugatively unsaturated sulfones, are operative within these systems. The fact that the sulfur-oxygen bond lengths in thiirene dioxides were found to be similar to those of other 802-containing compounds, does not corroborate a Hiickel-type jr-delocalization... 

The l,5-dibora-2,5-cyclohexadiene system (7) is of unusual interest because such a planar array of atoms is predicted to be a Hiickel antiaromatic system, similar to boroles themselves. Indeed, when 103 is generated at low temperatures, it readily rearrange into the nWo-2,3,4,5-tetracarba-hexaboranes6 (8)" (Eq. 33). 

The factors that control if and how these cyclization and rearrangement reactions occur in a concerted manner can be understood from the aromaticity or lack of aromaticity achieved in their cyclic transition states. For a concerted pericyclic reaction to be thermally favorable, the transition state must involve An + 2 participating electrons if it is a Hiickel orbital system, or 4 electrons if it is a Mobius orbital system. A Hiickel transition state is one in which the cyclic array of participating orbitals has no nodes (or an even number) and a Mobius transition state has an odd number of nodes. 

Day21 has given a careful account of the relationship between the Woodward-Hoffmann rules and Mobius/Hiickel aromaticity, and has defined the terms supra-facial and antarafacial in terms of the nodal structure of the atomic basis functions. His approach makes quite explicit the assumption that the transition state involves a cyclic array of basis functions. Thus the interconversion of prismane (10) and benzene, apparently an allowed (n2s+ 2S+ 2S) process, is in fact forbidden because there are additional unfavourable overlaps across the ring.2... 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Fig. 4.4 The simple Hiickel method is used mainly for planar arrays of n systems...

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. 

Whereas in the Frost mnemonic for Hiickel systems the polygon is inscribed with a vertex down, in the Zimmerman mnemonic for Mobius systems the inscription is with the polygon side down. Three examples of each type are shown in Figure 9. Note that each intersection of the polygon with the inscribed circle corresponds to an MO and that the vertical positioning of the intersection gives the MO energy analytically. Thus, all of the Hiickel systems, with one vertex at the bottom, have in common one MO at —2 P. Also the odd-sized arrays have their Hiickel and Mobius relatives turned upside down from one another, while in the even series there is no such relationship. 

In a pericyclic reaction the array of basis orbitals of the reacting molecule is cyclic halfway along the reaction coordinate. The array will either be of the Mobius or the Hiickel type. Since the circle mnemonics give the distribution of MO energies... 

According to Zimmermann [101] and Dewar [102], the allowedness of a concerted pericyclic reaction can be predicted in the following way A cyclic array of orbitals belongs to the Hiickel system if it has zero or an even-number phase inversions. For such a system, a transition state with An+ 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

Both the Woodward-Hoffmann approach and the Hiickel-Mobius concept are useful for predicting the course of concerted reactions. They both have their limitations as well. The application of the Hiickel-Mobius concept is probably preferable for systems with low symmetry. On the other hand, this concept can only be applied when there is a cyclic array of orbitals. The conservation of orbital symmetry approach does not have this limitation. 

Another array of orbitals with the same sort of linear combinations is that of the tr system of cyclopolyenes (benzene, naphthalene) with which you are probably already familiar. The molecular orbitals constructed from sets of parallel p orbitals are both bonding and antibonding at various energies. The system is particularly stable if Hiickel s rule (2/ + 2 electrons see also Chapter 15) is obeyed. In the ease of an infinite arr.iy of hydrogen atoms (l.v ). the situation is unstable (as you should have questioned immediately) it reverts to an array of molecules ... 

Mobius aromaticity A monocyclic array of orbitals in which a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps) reveals the opposite pattern of aromatic character to Hiickel systems with 4n electrons it is stabilized (aromatic), whereas with 4n + 2 it is destabilized (antiaromatic). In the excited state 4n + 2, Mobius pi-electron systems are stabilized, and 4n systems are destabilized. No examples of ground-state Mobius pi systems are known, but the concept has been applied to transition states of PERI-CYCLIC REACTIONS (see AROMATIC [3]). 

The energy levels of Hiickel and Mobius orbital arrays are easily generated. (In Ref. 14 we show in detail how the orbital energies of Mobius cyclobutadiene are obtained... 

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