Systems by Simple Hiickel MO Theory

REACTIONS OF AROMATIC COMPOUNDS Cyclic n Systems by Simple Hiickel MO Theory 

Theorists believe that the symmetry of the n system is imposed by the framework of a bonds. Bond alternation in the n system can be forced by the fusion of strained bicyclic rings [248] such as in [4]phenylene [249], tricyclobutabenzene [250], or trisbicyclo[2.1.1]-hexabenzene [251]  

Two novel fonns of carbon, with formulas Cis [252] and Ceo [253] owe their stability to aromaticity with cyclic arrays of p orbitals which do not fall strictly into the class of cyclic systems discussed above  

Theoretical studies indicate that the allotrope, Cis, is a planar cyclic structure and therefore has one planar cyclic array of 18 electrons of the above type. It also has a second cyclic 18-electron array in the a framework, albeit the orbitals overlap in a k fashion [254]. The allotrope, Ceo [255], has a cyclic polyaromatic three-dimensional structure which has also been argued to be aromatic [256]. 

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As shown by the data, the barrier depends upon the metal ion. Explain the basis for the metal ion dependence. Data on the rotational barrier of the allyl cation ( 18 kcal/mol) and allyl radical (>17 kcal/mol) indicate that the barrier for rotation in all three species is similar. According to simple Hiickel MO theory, should the barrier to rotation in the allyl system increase, decrease, or remain the same as electrons are added to the tt system in the progression CH2=CHCH2, CH2=CHCH2, and CH2=CHCH2 ... 

Molecular-orbital theory has taken many forms and has been dealt with by many approximations. In 1963 Hoffmann S presented a formalism which he referred to as extended Hiickel (EH). In the 1930 s, however, this formalism would simply have been called molecular-orbital, since it is a straightforward application of molecular-orbital (MO) theory, using a one-electron Hamiltonian. Hoffmann referred to it as extended Hiickel because it did not limit itself to 7r-electron systems and was able to deal with saturated molecules by including all overlap integrals. In these respects it did extend the usual, or simple Huckel, method, which was customarily applied to 7T-electrons, and assumed complete tt — a separability. 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

An important example of the application of MO theory is to the orbitals that may be formed from the p orbitals perpendicular to a molecular plane, such as that of the phenyl ring of the amino acid phenylalanine. A computational scheme was proposed by Erich Hiickel and provides a simple way of establishing the molecular orbitals of n-electron systems, especially hydrocarbons such as ethene, benzene, and their derivatives. A common procedure is to treat the a-bonding framework using the language of VB theory, and to treat the -electron system separately by MO theory. We use that approach here. 

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