Dewar Reference Structure

Figure 9. Resonance energies per jt electron in units of electronvolts for the conjugated monocyclic hydrocarbons using the Chung—Dewar reference structure and the Pariser—Parr—Pople computational method.

We have applied the Hess—Schaad version of the Dewar reference structure to the systems listed in Table 2. Theoretical investigations of the REPE index were also published. Changes in the energy of the o electrons in a series of compounds were found to vary linearly with though in opposite direction to ji energies. This provides some explanation of why jr-elec-tron-only models of conjugated systems can be as successful as they are. Reference structures were investigated."" " and comparisons were made with other recent theoretical aromaticity indices. ... 

By contrast, the Dewar resonance energy represents solely the contribution coming from the cyclic electron (bond) delocalization since the model reference structure is represented not by a system of isolated 7r-bonds, but by a hypothetical cyclic polyene with the number of tr- and tr-bonds equal to that in a given molecule. Making use of the additivity of bond energies in acyclic polyenes (65JA692), one may calculate the total energy... 

The Dewar resonance energy (DRE) is found as the difference between the heats of atomization of a given conjugated molecule and the classical Kekule reference structure... 

The main difficulty with the RE concept is the hypothetical nature of the reference structure, its choice being somewhat arbitrary. There are many ways of defining RE (M. Dewar, C. F. Wilcox, and others). Here we shall briefly examine the topological resonance energy (TRE). TRE is a nonparametric index which is directly related to the topology of a molecule and is of great practical value in predicting the aromatic stability of an arbitrary jt-network. 

A particularly interesting case involves the bicyclo[2.2.0]hexa-2,5-diene system. This ring system is a valence isomer of the benzene ring and is often referred to as Dewar benzene. Attempts prior to 1960 to prepare Dewar benzene derivatives failed, and the pessimistic opinion was that such efforts would be fruitless because Dewar benzene would be so unstable as to immediately revert to benzene. Then in 1962, van Tamelen and Pappas isolated a stable Dewar benzene derivative 9 by photolysis of l,2,4-tri-(/-butyl)benzene. The compound was reasonably stable, reverting to the aromatic starting material only on heating. Part of the stability of this particular derivative can be attributed to steric factors. The /-butyl groups are farther apart in the Dewar benzene structure than in the aromatic structure. 

Dewar [67] was the iirst to amend eq, (76) satisf orily, though there have been other, less successful, attempts in this direction [89]. Dewar introduced the polyene reference structure instead of the usual isdated double reference structure. This new RE index was termed the Dewar resonance energy [90], DRE,... 

The calculated values of these indices for several selected reactions are given in Table 9, into which the values corresponding to antiaromatic reference structures, which represent a natural counterpart to ideally aromatic standards, were included for comparison. As can be seen from this Table, the predictions of Dewar classification are indeed confirmed since for allowed reactions the similarity to aromatic reference structures are systematically higher than to the antiaromatic ones. On the other hand, for forbidden reactions the similarity to antiaromatic structures dominates so that these structures can be expected to play the role of transition states in this case. The above conclusions suggesting the important role of antiaromatic reference species as the eventual transition states in forbidden reactions was investigated in the study [158], in which the more detailed specification of the structure of antiaromatic transition states was attempted. The basis of this approach is a straightforward reformulation of the above procedure in terms of second order or pair density matrices. These matrices are generally defined by eq. (105),... 

The reference structure is a nonexisting entity and can be chosen in different ways. This has led to various resonance energies namely Hiickel Resonance Energy (HRE), Dewar Resonance Energy (DRE), Topological Resonance Energy (TRE), and so on. TRE [60] has been extensively used as a measure of aromaticity and is defined as follows ... 

It will be seen that the choice of reference structure turns out to be crucial to the success of Dewar s computation of resonance energy. We show the predicted order of aromaticity of the set of 11 small conjugated hydrocarbons in Figure 6 using various reference structures. Readers may wish first to make their own rankings of these 11 for comparison with the results below. The annulenes, (CH) , will also be examined. 

Dewar and de Llano then used the additivity of eq 10 to define a polyene-like reference structure for computing the resonance energy of any conjugated hydrocarbon. For example, in the case of benzene, the reference is cyclohexatriene whose heat of atomization is given by eq 10 so that... 

In a valence bond calculation, the reference structure is a single Kekule structure, presumably the most important in the actual mixture of such structures for the compound. This is different from the Dewar reference in that it contains any strain energy of the system, whereas Dewar s reference does not. 

In fact Dewar and de Llano concluded their paper that introduced the successful reference structure (column 3 of Figure 6) with there no longer seems any point at all in carrying out calculations by less refined procedures, in particular the HMO method or variants of it . They thus appear to attribute their success to the change in computational method from HMO to Pariser—Parr—Pople rather than to their important switch in reference structure. 

However, use of the HMO computational method together with a Dewar-like reference structure (column 4 of Figure 6) gives an even better result and shows that Dewar and de Llano s success was caused by their new reference structure, not by their use of the PPP instead of the HMO computational method. 

Dewar defined RE as the difference between the total TT-electron energy, Ejt, and the energy of an acyclic polyene-like reference structure obtained by summing over all bonds (the corresponding bond types riij) their energies Ey. 

The treatment of concerted reactions advocated by Dewar (1966) involves a consideration of the aromatic properties of the transition state. In this approach the reference structure is chosen as the corresponding open chain compound. The transition state is classified as aromatic if it is lower in energy than the reference structure, non-aromatic if of the same energy, and antiaromatic if of higher energy. Transition states are too short-lived to permit experimental criteria of aromaticity to be used. However the information can be readily deduced from molecular orbital theory. 

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. 

The scope of this review is a detailed survey of reactions proceeding through vinyl cations and an attempt of a systematic definition of the properties of these intermediates with reference to those of saturated carbonium ions. Although attention will be particularly devoted to linear cations, bridged unsaturated species will be considered as alternative structures of vinyl cations rather than as a distinct type of reactive intermediates. The 77--complex terminology (Dewar, 1949) widely abused in the past decades to indicate especially cyclic cations and recently reassessed by Banthorpe (1970) will be generally avoided. The most recent Btudies not covered by published reviews on the subject (Rappoport, 1969 Richey and Richey, 1970 Richey, 1970 Hanack, 1970) are discussed in greater detail than others and data are collected in pertinent Tables. 

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