Theoretical resonance energy

The theoretical resonance energy can therefore be calculated either from the localized orbitals or from the canonical orbitals. 

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

Triazine has not yet been prepared, and until fairly recently there were no well-documented examples of monocyclic 1,2,3-triazine derivatives. Early estimates of the potential degree of stability of 1,2,3-triazine were made on the basis of the theoretical resonance energy the results obtained indicated a delocalization energy of about 25 kcal/mole, which implies that the ring system should be reasonably stable and certainly amenable to synthesis. Many other related molecular orbital (MO) calculations have been carried out on similar systems more recently. 

Compound Observed Resonance Energy, (kcal/mol) Theoretical Resonance Energy, Hiickel Approximation -p... 

Finally, we can just use one structure, which for C6H6 gives the elusive cyclohexatriene (D3h symmetry) (fig. 6). Of course, for cyclobutadiene, nothing out of the ordinary is observed and the normal 1,3-cyclobutadiene results. The difference in energy with the two-structure calculation gives the theoretical resonance energy (TRE) [51]. 

At first we define two types of resonance energies, namely vertical resonance energy (VRE) and theoretical resonance energy (TRE). The former is the energy difference between the optimal delocalized molecule such as benzene and the localized reference molecule such as 1,3,5-cyclohexatriene whose geometries are kept the same. The latter is the energy difference between the delocalized molecule and the optimal localized reference molecule, whose geometries are not kept the same. Fig.l shows the relationship between VRE and TRE. The computed results are listed in Table 1. 

With this value of Eq we have calculated some theoretical resonance energies. In Table I they are compared with the empirical values. Besides the case of benzene which apparently plays a singular part in the group of aromatic hydrocarbons, the coincidence is very good. This is an astonishing effect because until now caloric and spectroscopic energy values within the Hiickel theory differed by a factor of 3. 

A modified definition of resonance energy has been introduced by Dewar (66T(S8)75, 69JA6321) in which the reference point is the corresponding open-chain polyene. In principle this overcomes the difficulties inherent in comparing observed stability with that of an idealized molecule with pure single and double bonds, as thermochemical data for the reference acyclic polyenes are capable of direct experimental determination. In practice, as the required data were not available, recourse was made to theoretical calculations using a semiempirical SCF-MO method. The pertinent Dewar Resonance Energies are listed in Table 30. 

Considering their potential antiaromatic character, thiepins are also of theoretical interest. HMO calculations of -resonance energies, using reference data from 27 acyclic polyenes containing sulfur, predict antiaromatic character for thiepin and 2-benzothiepin, whereas 1- and... 

The aromaticity of five-membered rings with two or more heteroatoms was discussed in detail in earlier reviews.52 100 111 In a comprehensive survey on the quantitative measurements of aromaticity,112 it has been shown that basicity-based quantification of aromaticity gave more reproducible resonance energies than other methods, such as heats of formation, ring currents, magnetic susceptibilities, and theoretical indices. 

Other congeners of phosphinins—arsenin, antimonin, and bismin—have been shown to be definitely less aromatic than benzene by diverse theoretical treatments that have been reviewed.236 For instance, the Bird aromaticity index for arsenin was found to be 67, compared to 100 for benzene.123 Table 4 summarizes a few parameters used to estimate the aromaticity of heterobenzenes resonance energies... 

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