Topological resonance energy aromaticity

The concept of relative hardness and topological resonance energy per electron as a measure of aromaticity, with a relative hardness value of zero as the border for antiaromaticity, failed for 1-benzothiepin,3 2... 

Topological resonance energy studies of the three isomeric thienopyrimidines show that while all of the ring systems are aromatic, the thieno[3,4-, pyrimidine class of compounds is less aromatic by approximately 20%. Correspondingly this system is believed to be considerably more reactive than its isomers <1997CCA841>. 

Results of MNDO calculation of lA-azonine (35 X=NH) are in agreement with experimental evidence that this is a planar, aromatic molecule. The calculated geometry of oxonin (35 X = 0), as a buckled, unsymmetrical polyenic heterocycle, is also in agreement with its known properties. The MNDO calculations on thionin (35 X = S) indicate that this molecule is planar, which should allow effective tt delocalization, and at least some aromatic character (86MI927-OI). The topological resonance energy model also predicts lA-azonine and thionin to be aromatic, and oxonin nonaromatic (84JHC273). 

A theoretical investigation of [njcydophenacenes was reported by Aihara, who discussed stability of [njcyclophenacenes with a topological resonance energy (TRE) method [10] and proposed that the cydophenacenes are aromatic and stable... 

The abbreviation TRE comes from topological resonance energy , as this measure of the overall cyclic conjugation in a polycyclic conjugated molecule was originally named [35,44], The TRE-concept was introduced in 1976 independently by Aihara [34] and by Milun, Trinajstic and the present author [35, 44, 45], Aromatic conjugated molecules have positive whereas antiaromatic molecules have negative TRE-values. 

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. 

The concept of topological resonance energy was introduced to provide a relative measure of aromaticity <77JA1692>. In a newer approach, the absolute hardness, or HOMO-LUMO gap, as the measure of aromaticity is defined to be in the ionization potential of the species minus its electron affinity. The parameters of the absolute hardness and a related relative hardness for (152) are consistent with the high reactivity of this compound <89JA737l>. 

Gimarc et al. have calculated topological resonance energies for a series of sulfur-nitrogen rings and have suggested that the hypothetical species should be planar and aromatic <85rCA105>. 

The topological resonance energy model has also been used to study the aromatic stabilities of the heteronins. l//-Azonine (1) and thionin (14) were predicted to be aromatic, whereas oxonin (11) was predicted to be nonaromatic <84JHC273>. Hiickel energy levels have been calculated for the neutral S5N4 ring system <80PAC1443>. 

In particular, Heilbronner questioned the compatibility of the topological resonance energy with the HMO model and with chemical experience. Quite disturbing was also the failure to account for the properties of oxocarbon systems. It was claimed not only that C3O3 is aromatic, but also that C3O3 is aromatic or nonaromatic depending on the parameters used. This was criticized by one of us, because C3O3 should be antiaromatic by the Hiickel... 

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 ... 

V2 is the edge weight of G °. Topological resonance energy can be normalized to per n electron TRE(PE) or per ring bond TRE (PRB) and used to classify molecules as aromatic or not as follows ... 

Topological resonance energy has been used as a qualitative measure of aromaticity of not only organic compounds [61,62] but also inorganic macrocycles [63]. Topological resonance energy for Hiickel annulenes, are given below in closed analytical form... 

Analytical forms for Topological resonance energy of annulene cations and anions are also available [64,65], Topological resonance energy very well predicts aromaticity and antiaromaticity of annulenes and their ions and show that with increasing ring size they all become nonaromatic. 

This has been very well extended to Mobius systems and hetero [66-69] and homoaromatic [70] systems. The concept of Topological resonance energy as a mea-snre of aromaticity has been extended to the lowest excited state of annnlenes. Here the excited state in the lowest n-n triplet state and the reference strnctnre is the most stable biradical. 

The topological resonance energy (TRE) is considered to be a useful measure of aromatic stabil-... 

Attachment of substituents to the cage has been a blossoming branch from the onset of fullerene chemistry. " The concomitant removal of electrons from the n system (by localizing them in o bonds) is bound to affect any resonance mechanism that might be operative. For multiple adducts of Ceo, the aromatic character is indicated, by Fluckel-type calculations of the topological resonance energy, to depend notably on the addition pattern, and the same is to be expected for the magnetic and NMR proper-... 

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