Benzene Hiickel theory

In the Hiickel theory the three occupied MO, which determine the it bonds in benzene, PMO = 11, where 1 stands for the unit row matrix, read... 

The CNMR spectrum of quinazoline in benzene was assigned on the basis of a selective decoupling technique and a theoretical treatment using the extended Hiickel theory as well as... 

Aromatic systems provide the most significant applications of Hiickel theory. For benzene, we find the secular equation... 

Hiickel molecular orbital theory benzene, 174 butadiene, 171-173 computational resources, 174 ethylene, 173... 

Furthermore, the HOMO energy of styrene is higher than the HOMO energy of benzene, and this will make the electrophilic substitution of styrene faster than that of benzene. The contribution from the second term of equation 2-7 (the Coulombic term) uses the total electron population on each atom because styrene is a hydrocarbon, and because we have used a very simple Hiickel theory, inevitably the sum of the squares of the coefficients of the filled orbitals must be equal on each atom. Thus the second term of equation 2-7 makes little contribution to the site-selectivity in this compound. A more elaborate theory, no doubt, would lead to a small uneveness of charge distribution, but the contribution of the Coulombic term will still be much less than that of the frontier orbital term. 

Many rings and clusters, however, cannot be understood within the two-center two-electron bond framework. This is sometimes extended by assuming resonance, for example between the two Kekule-type structures for benzene (6). A more natural approach is to extend the molecular orbital (MO) approach (see Topic C6) to many atoms. The so-called Hiickel theory of ring systems makes important predictions relevant to inorganic molecules such as S2N2. Clusters such as boranes also... 

Soon after the appearance of the new view about the driving force for the Dsh structure of benzene, Hiickel theory was reexamined by Kataoka and Nakajima.They concluded that the traditional view, in which the r-electron delocalization energy... 

In this contribution, it was also recognized that a clear dividing line exists between aromatic and antiaromatic species, set to about a Hiickel hardness of -0.2/3, where /3 is the carbon parameter of Hiickel theory. The Hiickel and relative Hiickel hardness of benzene are. e.g., equal to —1.0/3 and —0.428/3, respectively, those of cyclobutadiene are 0/3 and 0.765/3, respectively. For comparison, the values for Ceo are -0.378/3 and -0.316/3, predicting this molecule to be aromatic. ... 

The key assumptions in the Hiickel theory involve the integrals in (17.10). The integral 7/ / is assumed to have the same value for every carbon atom in the molecule. (For benzene the six carbons are equivalent, and this is no assnmption. For 1,3-butadiene, CH2CHCHCH2, one would expect for an end carbon and a middle carbon to differ slightly.) Moreover, is assumed to be the same for carbon atoms in different planar hydrocarbons. The integral is assumed to have the same value for any two carbon atoms bonded to each other and to vanish for two nonbonded carbons. The integral Srr is... 

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. 

FIGURE 15.22 Hiickel theory predicts the above arrangement for the six tt electrons in benzene. The amount of additional stability in the it orbitals of benzene is so great that it defines aromaticity. 

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