TT-delocalization energy

In the same paper [208] an approach for partitioning the TChb into two terms (the ring closure energy and the tt-delocalization energy , as schematized in Fig. 7) was also suggested. 

The predictions of relative stability by the various approaches diverge more widely when nonbenzenoid systems are considered. The simple Htickel method using total TT delocalization energies relative to an isolated double-bond reference energy (a + 6) fails. This approach predicts stabilization of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for much more stable aromatics. The HMO , RE, and SCF-MO methods, which use polyene reference energies, do much better. All show drastically reduced stabilization for such systems and, in fact, indicate destabilization of systems such as butalene and pentalene (Scheme 8.2). 

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). 

This molecule provides an interesting and entirely genuine illustration of the predictive power of simple Hfickel MO theory it also serves as a good first example of how to apply symmetry methods in more general cases. The molecule was predicted to have —30 kcal/mol of delocalization energy in 1952 in 1962 it was synthesized and shown to be stable.tt The molecule may oe assumed to be planar, and we shall adopt the numbering scheme shown below. 

An MO study of all twenty pyranopyrandiones has been reported (73MI22200). Use was made of HMO calculations together with the co technique. Calculations were also performed on some methyl-substituted pyranopyrandiones and afforded values for the delocalization energy, 7r- bond orders and tt- charge densities. Empirical resonance energies were obtained... 

This geometry precludes the possibility of two equivalent VB structures, as for benzene, because, as you will see if you try to make a ball-and-stick model, 25b is highly strained and not energetically equivalent to 25a at all. Thus we can conclude that the delocalization energy of cyclooctatetraene is not large enough to overcome the angle strain that would develop if the molecule were to become planar and allow the tt electrons to form equivalent tt bonds between all of the pairs of adjacent carbons. 

P. C. Hiberty, D. Danovich, A. Shurki, S. Shaik, J. Am. Chem. Soc. 117, 7760 (1995). Why Does Benzene Possess a Deh Symmetry A Quasiclassical State Approach for Probing TT-Bonding and Delocalization Energies. 

If the three tt bonds in benzene were independent of each other, i.e., localized, they would have energy 3(2o + 2/3) = 6a + 6/3. Hence the delocalization energy (DE) for benzene is... 

Calculations of tt densities, total electron densities, localization energies, or delocalization energies for pyridine and quinoline by the MINDO/ 2 method give results that are either no better or worse than those calculated by the simple Hiickel method [73JCS(P2)I79], It is generally found that for aromatic reactivity the Hiickel method outperforms other methods often regarded as superior. Ab initio calculations may in due course produce better results, but at present are far too expensive for molecules of this size. 

Metal 77-cyclopentadienyls somewhat resemble the rr-allyl complexes. Initially, when the nature of the metal-allyl bond was not sufficiently clear, the similarity was emphasized many times [see the review by E. O. Fischer (425)]. The similarity shows itself, for example, in the equal antisymmetric C—C stretching frequencies (1640 cm ), which indicate that the force constants, hence the bond orders, are close. The central rr-allyl proton absorbs in the same NMR region as do the protons of coordinated cyclopentadienyl. Both ligands display the symmetrical sandwichlike bond with their metals. Today, however, it is clear that the complexes differ significantly in type, the difference being associated first of all with the fact that TT-allyl complexes are much more efficient than 77-cyclopentadienyls at transforming to o-allyl or 77-olefin compounds. This may be due to the difference between the delocalization energies, 2.472 and 0.828 eV for cyclopentadienyl and allyl anions, respectively (426). 

Do a Hiickel calculation on the conjugated four-carbon ring cyclobutadiene. Calculate the tt-electron delocalization energy. Comment on the applicablity of Hiickel s 4N -b 2 rule for aromaticity. 

The nine-membered lactam representing an intermediate between cis and irons lactams was assumed to be sufficiently flexible to allow the more stable irons amide group to co-exist with the strainless cis form [47]. However, a strainless planar irons form is not possible and the actual conformation is rather a skew structure which drastically reduces the jo—tt overlap and decreases resonance stabilization of the amide group. Therefore, an increased amount of delocalization energy is released in the... 

The weak reactivity of benzene is in part attributed to this additional stabiliza- j tion. That stabilization energy is often called the delocalization energy or reso- nance energy of benzene and is taken as a measure of the aromaticity of the j molecule. The expression resonance energy comes from the description of] the delocalized tt system in valence-bond theory in terms of the resonant hybrid... 

The fact that the C-C bond lengths are shorter and the C-C stretching frequencies and the delocalization energies per tt electron are higher for cyclopropenium than for benzene, is taken as an indication of superaromaticity . 

Let us consider the significance of this stabilization, which is sometimes called the delocalization energy (DE). The stabilization results from the removal of the restriction that the tt electrons be localized between two particular atoms. Comparison of the DE of 1,3,5-hexatriene and benzene would suggest that the triene is stabilized by almost half the extent of benzene, but thermodynamic comparisons do... 

These resonance structures are the nitrogen and oxygen analogs of the allyl cation. The effect of this tt delocalization is to attenuate the polar destabilization by these substituents. These interactions are reflected in MO energies, bond lengths, and charge distributions calculated for such cations (review Section 3.4.1). 

One approach to evaluation of the aromaticity of a molecule is to determine the extent of thermodynamic stabilization. Attempts to describe stabilization of a given aromatic molecule in terms of simple HMO calculations have centered on the delocalization energy. The total rr-electron energy of a molecule is expressed in terms of the energy parameters a and 6 that are used in HMO calculations. This energy value can be compared to that for a hypothetical localized version of the same molecule. The HMO energy for the tt electrons of benzene is 6a + 86. The same quantity for... 

Benzene is a planar molecule. Each of its six carbon atoms is sp hybridized, with bond angles of 120°. A p orbital of each carbon overlaps the p orbitals of both adjacent carbons. The six tt electrons are shared by all six carbons. Compounds such as benzene that are unusually stable because of large delocalization energies are called aromatic compounds. 

There has been no lack of investigations aimed at calculating the Q and e values theoretically. The polarity factor is a measure of electron density. Q is a measure of the resonance stability in the transition state and can be correlated with the delocalization energy accessible from electronic theory calculations. The quantity -RT In Q can then be considered as the contribution to the activation energy for the opening of tt bonds at the ultimate C atom of the monomer. 

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