Benzene Hiickel molecular orbitals

Figure 7.35 Energies of Hiickel molecular orbitals for benzene...

We will consider the application of the Hiickel molecular orbital method to the benzene molecule and we will first see what happens when we do not make use of symmetry. The benzene molecule has a framework of six carbon atoms at the comers of a hexagon and each carbon atom contributes one 7r-electron. The tt-electron MOs will be constructed from six 2pc atomic orbitals, each located at one of the carbon atoms, thus, c... 

Hiickel molecular orbital method, 205 for benzene, 206 for trivinylmethyl radical, 212. 

If you compare the orbital energies of the Hiickel and Mobius cyclic 7r systems (Figures 21-13 and 21-16), you will see that the Hiickel systems have only one lowest-energy MO, whereas the Mobius systems have two. Hiickel systems have an odd number of bonding orbitals (which, when full, accommodate 2, 6, 10, 14, or An + 2 electrons) and the Mobius systems have an even number of bonding orbitals (which, when full, accommodate 4, 8, 12, or An electrons). The Hiickel molecular orbitals have zero or an even number of nodes (see, for example, the benzene MOs, Figure 21-5) the Mobius molecular orbitals are not shown, but they have one or an odd number of nodes. 

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

Shown above is the energy-level diagram for the n orbitals of benzene, calculated on the basis of Hiickel molecular orbital theory. According to this theory, the total energy of the six n electrons of ground-state benzene is given by... 

Figure 1.2. The Hiickel molecular orbitals of benzene and cyclobutadiene...

This model is today known as the Hiickel molecular orbital (HMO) method [1]. Less known is that Hiickel adopted the so-called hard ball potential of Bloch, used in a simplified theory of metals [14]. As mentioned, Hiickel was able to explain the fundamental difference between the aromaticity of benzene and the lack of aromatic character in the behavior of eight % electrons of cyclooctatetraene, CgHg, known today as the Hiickel 4n + 2 rule. This has been one of the most outstanding and significant accomplishments for early quantum chemistry that follows from the Hiickel An+ 2 rule ... 

The concept of the Mobius strip was explained earlier (see p. 55). The basis of the Zimmerman analysis is an extension of this idea. A cyclic polyene is defined as a Hiickel system if its basis molecular orbital (i.e. the lowest filled TT-level as in the case of benzene, for example) contains zero or an even number of phase dislocations. Mbbius systems possess an odd number of phase dislocations in the basis molecular orbitals. In accordance with the rules predicting aromaticity for these systems, which results from the application of the Hiickel molecular orbital theory, it may be inferred that since cyclic conjugation also arises in the transition states of pericyclic reactions, the foDowing conclusions apply ... 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

One of molecular- orbital theories early successes came in 1931 when Erich Hiickel discovered an interesting pattern in the tt orbital energy levels of benzene, cyclobutadiene, and cyclooctatetraene. By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar- geometries, Hiickel found that whether a hydrocar bon of this type was aromatic depended on its number of tt electrons. He set forth what we now call Hiickel s rule ... 

Hiickel realized that his molecular- orbital analysis of conjugated systems could be extended beyond neutral hydrocarbons. He pointed out that cycloheptatrienyl cation, also called twpylium ion, contained a completely conjugated closed-shell six-ir electron system analogous to that of benzene. 

In the 1930 s HiickeP proposed, on the basis of molecular-orbital calculations, a theoretical criterion for aromaticity of cyclic polyenes, known as Hiickers rule, which states that cyclic polyenes should be aromatic if, and only if, they contain 4n- -2 Jt-electrons. At that time only two of such cyclic polyenes were known benzene and cyclo-pentadienyl anion, each having six rc-electrons and satisfying Huckel s rule. Since then, the validity of Hiickel s rule had not been challenged... 

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