Global aromaticity

As done in MO theory, REPE values can be computed within the VB model if an appropriate reference structure and its energy are determined [22], Then 

The E j values (in units of J) determined by a least-square procedure 

According to the JTH scheme, the calculated RE and REPE values are listed in Table 8. Encouragingly, our VB RE values bear an excellent linear correlation with the delocalization energies obtained by Wiberg [59] at the B3LYP/6-311G level (the correlation coefficient=0.994) for the first four members of polyacene and polyphenanthrene series, respectively. Thus it appears that the VB RE is a good measure of the thermodynamic stability for isomeric BHs. 

The inconsistency between predictions made by MO REPEs and VB REPEs may be attributed to the different natures of simple MO and VB theories, i.e., the simple MO theory is a one-electron model, free of electron correlation, but VB theory is a many-electron, correlation model. This difference may result in the different topological dependence of -conjugation in MO and VB models, as illustrated by the [n]phenanthrene series. 

As stated above, a new scale is desirable to describe quantitatively the global aromaticity in the VB model. Since the global aromaticity measures the average benzene character of a conjugated system, resonance energy per hexagon (REPH), as defined by Eq. (48), may be a natural choice for BHs [22], 

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The polyurethane industry is dominated by the multinational isocyanate producers. Several of the principal isocyanate producers, including BASF, Bayer, Dow, ICI, and Olin, also manufacture polyols, the other significant building block for polyurethanes. Annual production capacities of the global aromatic isocyanate producers are Hsted in Table 11. Polyols, mainly used for flexible foam production, account for 65 wt % in a flexible foam formulation, 35% in rigid polyurethane foams, and even less in PUIR foams. 

Some indices aim to measure the local aromaticity of an individual ring in a polycyclic system, while others measure the global aromaticity of the whole molecule. 

In Table 29.1, we summarized our results of electronic structure calculations for Bf -Bjj. We reported symmetry, spectroscopic state, valence electronic configuration, number of 2c-2e peripheral B-B a-bonds, number of delocalized o- and TT-bonds, and assignment of global aromaticity/antiaromaticity. The description of chemical bonding in terms of 2c-2e peripheral B-B a-bonds and nc-2e delocalized a- and tt-bonds was obtained via AdNDP method at... 

It is also instructive to look into the global aromaticity of a BH by averaging the local aromaticity of all hexagon rings. Accordingly, the global aromaticity may be measured by an average ... 

ELFct and LI,F bifurcations was used to construct a general scale to measure the global aromatic character of a molecular system.57 This general scale predicted the electron delocalization characteristic of known organic and metallic aromatic and antiaromatic systems. 

Recent synthesis of pyrenophanes ° allowed us to study the dependence of the global aromaticity of the pyrene moiety on the degree of its bending and also how individual rings react to bending. ... 

A final average of EC values over all rings then provides a global aromaticity index per benzenoid ring. We recall that all catafusenes have the molecular formula C4r+2H2r+ and that each of the n = 4R -h 2 carbon atoms contributes with one... 

Figure 14.9 clearly shows that the cation cluster has the expected lS lPj IP configuration, whereas the IPj, level is unoccupied. The CMO-NICS values demonstrate that the IS level has an aromatic contribution, but the IP and IP, levels induce an antiaromatic character. In general, the shell orbitals are nonaromatic, and the global aromaticity is due to the orbitals bearing high contributions from the d AOs (Figure 14.9). As these orbitals have a similar shape to that of the P shell orbitals, these are labeled by IP/ and IP/, respectively. They provide some support for an aromatic behavior.

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