Antiaromatic state

The surprising finding is that the strain in 24 and 25 brings about the formation of an intramolecular a-bond as a means of avoiding an unfavorable strained dianionic antiaromatic state. 

The threshold is a tether of eight carbon atoms where no two-electron reduction occurs. It seems that the strain in 26 is large enough that it does not get into an antiaromatic state. Moreover, it seems that the formation of an intramolecular a-bond is not favored either, because insufficient stabilization is gained in this way. 

Stabilizing resonances also occur in other systems. Some well-known ones are the allyl radical and square cyclobutadiene. It has been shown that in these cases, the ground-state wave function is constructed from the out-of-phase combination of the two components [24,30]. In Section HI, it is shown that this is also a necessary result of Pauli s principle and the permutational symmetry of the polyelectronic wave function When the number of electron pairs exchanged in a two-state system is even, the ground state is the out-of-phase combination [28]. Three electrons may be considered as two electron pairs, one of which is half-populated. When both electron pahs are fully populated, an antiaromatic system arises ("Section HI). 

A more general classification considers the phase of the total electronic wave function [13]. We have treated the case of cyclic polyenes in detail [28,48,49] and showed that for Hiickel systems the ground state may be considered as the combination of two Kekule structures. If the number of electron pairs in the system is odd, the ground state is the in-phase combination, and the system is aromatic. If the number of electron pairs is even (as in cyclobutadiene, pentalene, etc.), the ground state is the out-of-phase combination, and the system is antiaromatic. These ideas are in line with previous work on specific systems [40,50]. 

The results of the derivation (which is reproduced in Appendix A) are summarized in Figure 7. This figure applies to both reactive and resonance stabilized (such as benzene) systems. The compounds A and B are the reactant and product in a pericyclic reaction, or the two equivalent Kekule structures in an aromatic system. The parameter t, is the reaction coordinate in a pericyclic reaction or the coordinate interchanging two Kekule structures in aromatic (and antiaromatic) systems. The avoided crossing model [26-28] predicts that the two eigenfunctions of the two-state system may be fomred by in-phase and out-of-phase combinations of the noninteracting basic states A) and B). State A) differs from B) by the spin-pairing scheme. 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

We term the in-phase combination an aromatic transition state (ATS) and the out-of-phase combination an antiaromatic transition state (AATS). An ATS is obtained when an odd number of electron pairs are re-paired in the reaction, and an AATS, when an even number is re-paired. In the context of reactions, a system in which an odd number of electrons (3, 5,...) are exchanged is treated in the same way—one of the electron pairs may contain a single electron. Thus, a three-electron system reacts as a four-electron one, a five-electron system as a six-electron one, and so on. 

The potential surfaces of the ground and excited states in the vicinity of the conical intersection were calculated point by point, along the trajectory leading from the antiaromatic transition state to the benzene and H2 products. In this calculation, the HH distance was varied, and all other coordinates were optimized to obtain the minimum energy of the system in the excited electronic state ( Ai). The energy of the ground state was calculated at the geometry optimized for the excited state. In the calculation of the conical intersection... 

There is another usefiil viewpoint of concerted reactions that is based on the idea that transition states can be classified as aromatic or antiaromatic, just as is the case for ground-state molecules. A stabilized aromatic transition state will lead to a low activation energy, i.e., an allowed reaction. An antiaromatic transition state will result in a high energy barrier and correspond to a forbidden process. The analysis of concerted reactions by this process consists of examining the array of orbitals that would be present in the transition state and classifying the system as aromatic or antiaromatic. 

The selection rules for cycloaddition reactions can also be derived from consideration of the aromaticity of the transition state. The transition states for [2tc -f 2tc] and [4tc -1- 2tc] cycloadditions are depicted in Fig. 11.11. For the [4tc-1-2tc] suprafacial-suprafacial cycloaddition, the transition state is aromatic. For [2tc -F 2tc] cycloaddition, the suprafacial-suprafacial mode is antiaromatic, but the suprafacial-antarafacial mode is aromatic. In order to specify the topology of cycloaddition reactions, subscripts are added to the numerical classification. Thus, a Diels-Alder reaction is a [4tc -f 2 ] cycloaddition. The... 

Ab initio molecular orbital calculations for the model systems RCN3S2 (R = H, NH2) show that these dithiatriazines are predicted to be ground state singlets with low-lying triplet excited states (Section 4.4). The singlet state is stabilized by a Jahn-Teller distortion from C2v to Cj symmetry. In this context the observed dimerization of these antiaromatic (eight r-electron) systems is readily understood. 

Hiickel s rule states that planar cyclic 71 systems involving 4n+2 electrons will be unusually stable ( aromatic ), while cyclic 7i systems with 4n electrons will be unstable ( antiaromatic ). 

In the case of 60, the ion has been prepared and has been shown to be a diradical in the ground state, as predicted by the discussion on page 58. Evidence that 60 is not only nonaromatic but also antiaromatic comes from studies on 64 and 66. When 64 is treated with silver perchlorate in propionic acid, the molecule is rapidly solvolyzed (a reaction in which the intermediate 65 is formed see Chapter 5). Under the same conditions, 66 undergoes no solvolysis at all that is, 60 does not form. If 60 were merely nonaromatic, it should be about as stable as 65 (which of course has no resonance stabilization at all). The fact that it is so much more reluctant to form indicates that 60 is much less stable than 65. It is noted that under certain conditions, 65 can be generated solvolytically. ... 

The aromatic-antiaromatic transition state rules are. another formulation of the Woodward-Hoffmann type rules (Table 8.3). 

The alternate approach of Dewar and Zimmerman can be illustrated by an examination of the 1,3,5-hexatriene system.<81,92> The disrotatory closure has no sign discontinuity (Hiickel system) and has 4n + 2 (where n = 1) ir electrons, so that the transition state for the thermal reaction is aromatic and the reaction is thermally allowed. For the conrotatory closure there is one sign discontinuity (Mobius system) and there are 4u + 2 (n = 1) ir electrons, so that the transition state for the thermal reaction is antiaromatic and forbidden but the transition state for the photochemical reaction is aromatic or allowed (see Chapter 8 and Table 9.8). If we reexamine the butadiene... 

Using the nomenclature of Dewar and Zimmerman, the transition state for the 2, + 2S cycloaddition is a 4n Hiickel system (zero nodes) and is antiaromatic in the ground state and aromatic in the excited state. The transition state for the 2S + 20 cycloaddition is a 4n Mobius system (one node) and is aromatic in the ground state and antiaromatic in the excited state (see Chapter 8). The general cycloaddition rules are given in Table 9.5. 

Aromatic transition state = allowed reaction —, antiaromatic transition state — forbidden reaction. 

Figure 7. Aromatic and antiaromatic systems in the ground state (GS) and the twin excited state (ES). The parameter E, is the coordinate that transforms A to B.

The second mechanism, due to the permutational properties of the electronic wave function is referred to as the permutational mechanism. It was introduced in Section I for the H4 system, and above for pericyclic reactions and is closely related to the aromaticity of the reaction. Following Evans principle, an aromatic transition state is defined in analogy with the hybrid of the two Kekule structures of benzene. A cyclic transition state in pericyclic reactions is defined as aromatic or antiaromatic according to whether it is more stable or less stable than the open chain analogue, respectively. In [32], it was assumed that the in-phase combination in Eq. (14) lies always the on the ground state potential. As discussed above, it can be shown that the ground state of aromatic systems is always represented by the in-phase combination of Eq. (14), and antiaromatic ones—by the out-of-phase combination. 

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