Benzene Huckel molecular orbitals

We start with some biographical notes on Erich Huckel, in the context of which we also mention the merits of Otto Schmidt, the inventor of the free-electron model. The basic assumptions behind the HMO (Huckel Molecular Orbital) model are discussed, and those aspects of this model are reviewed that make it still a powerful tool in Theoretical Chemistry. We ask whether HMO should be regarded as semiempirical or parameter-free. We present closed solutions for special classes of molecules, review the important concept of alternant hydrocarbons and point out how useful perturbation theory within the HMO model is. We then come to bond alternation and the question whether the pi or the sigma bonds are responsible for bond delocalization in benzene and related molecules. Mobius hydrocarbons and diamagnetic ring currents are other topics. We come to optimistic conclusions as to the further role of the HMO model, not as an approximation for the solution of the Schrodinger equation, but as a way towards the understanding of some aspects of the Chemical Bond. 

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

We will consider the application of the Huckel 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 w-electron. The -electron MOs will be constructed from six 2pf atomic orbitals, each located at one of the carbon atoms, thus, e... 

These calculations are of special interest because Purcell and coworkers have been interested in the structure-activity relationships of this series of compounds for several years and have compared several approaches to structure-activity relationships with the same compounds. Earlier they (27, 28) reported on detailed studies of the effect of partition coefficients (benzene-water), electric moments, and electronic structures on the relative activity of the congeners. Purcell (28) used Huckel molecular orbital theory to calculate the net charges on all the atoms of each compound. The only apparent success was the apparent correlation of the net charge at the amide nitrogen atom with activity. This was later shown to be caused by the statistically significant correlation between the 7T value and the net charge on the nitrogen atom (29). 

HMO theory (Huckel Molecular Orbital theory) A simple molecular orbital theory applied to planar 7i-conjugated systems. A key simplification involves treatment of the n-system independently from the cr-system. The HMO molecular orbital energies are in terms of a and p, where a is equated with the energy of an isolated orbital, and P is the resonance integral, equated to the energy associated with having electrons shared by atoms. As reference, benzene is 4P more stable than an isolated orbital. 

Use Huckel molecular orbital theory to construct molecular orbitals for conjugated hydrocarbon molecules such as butadiene and benzene... 

Figure 8.32 The Huckel molecular orbitals of benzene, viewed from above the plane of the molecule. There will be two components to each lobe shown, one above the plane of the molecule and the other below the plane with an opposite sign...

Schematic representation of Huckel molecular orbitals of benzene.

Huckel benzene Mdbius benzene FIGURE 5.11 Benzene k molecular orbitals. 

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

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 m 1931 when Erich Huckel dis covered an interesting pattern m 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 Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Huckel realized that his molecular orbital analysis of conjugated systems could be extended beyond neutral hydrocarbons He pointed out that cycloheptatrienyl cation also called tropyhum ion contained a completely conjugated closed shell six tt electron sys tern 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... 

Figure 6.4. Energy-level diagram for the molecular orbitals of benzene evaluated in the Huckel approximation.

The benzene derivatives presented an enigma to structural chemists in that although the benzene rings had three double bonds, they underwent substitution rather than addition when treated with reagents such as bromine and nitric acid. No adequate explanation for their behavior was presented prior to the development of quantum mechanics. In the early 1930 s, two explanations were presented. One was by Pauling making use of valence bond theory,2 and the other was by E. Huckel making use of molecular orbital theory.3... 

Huckel realized that his molecular orbital analysis of conjugated systems could be extended beyond the realm of neutral hydrocarbons. He pointed out that cycloheptatrienyl cation contained a tt system with a closed-shell electron configuration similar to that of benzene (Figure 11.13). Cycloheptatrienyl cation has a set of seven tt molecular orbitals. Three of these are bonding and contain the six tt electrons of the cation. These six tt electrons are delocalized over seven carbon atoms, each of which contributes one 2p orbital to a planar, monocyclic, completely conjugated tt system. Therefore, cycloheptatrienyl cation should be aromatic. It should be appreciably more stable than expected on the basis of any Lewis structure written for it. 

German physicist Erich Hiickel used the molecular orbital theory to explain the stability of benzene and other aromatic compounds. Huckel s rule determines the number of ir electrons that give stability to an unsaturated planar ring according to the formula 4n -I- 2. Eor benzene and its analogs,... 

Benzene is described by molecular orbital theory as a planar, cyclic, conjugated molecule with six it electrons. According to the Huckel rule, a molecule must have 4 + 2 it electrons, where n = 0,1, 2, 3, and so on, to be aromatic. Planar, cyclic, conjugated molecules with other numbers of ir electrons are antiaroraatic. 

Bloch s treatment was incorporated in the molecular orbital study of the benzene mdecule by Huckel [149,150]. The latter showed that the ener es of the x-electrons in unsaturated molecules such as benzene could be approximated by solving secular determinants containing the Coulomb integral, a, for a carbon atom and the resonance int al, for a pair of carbon atoms. In the case of benzene, the determinant assumes the form shown in Figure 16. 

Fig. 35. The n molecular orbitals according to Huckel MO calculations (kfi), energy level diagram (center) and term diagram of benzene with electronic transitions indicated (right). Quoted from [6]. Copyright John Wiley and Sons, Ltd. Reproduced with permission. The other parts are taken from Chang R (1971) Basic principles of spectroscopy. McGraw-Hill Kogakushi, Ltd, Tokyo. Reproduced with permission of the McGraw-Hill Companies...

The Huckel method has been used to obtain n molecular orbitals, and their associated enei gies, for butadiene and benzene. The n electron energy is found to be lower than it would be for localized n bonding, and this difference is known as the delocalization energy. 

Abstract. Guided by an intuitive choice of approximations which shows remarkable chemical insight into the topic of aromaticity, Huckel mastered the difficult mathematical treatment of a complex molecule like benzene at a very early stage of quantum theory using method 1 (now valence bond theory) and method 2 (now molecular orbital theory). He concluded that methoci 2 is clearly superior to method 1 because the results of this method explain directly the peculiar behaviour of planar molecules with 6 n electrons. 

Various aromatic and conjugated polyunsaturated hydrocarbons undergo one-electron reduction by alkali metals." Benzene and naphthalene are examples. The EPR spectrum of the benzene radical anion was shown in Fig. 12.2a (p. 657). These reductions must be carried out in aprotic solvents, and ethers are usually used. The ease of formation of the radical anion increases as the number of fused rings increases. The electrochemical reduction potentials of some representitive compounds are given in Table 12.1. The potentials correlate with the energy of the LUMO as calculated by simple Huckel MO theory." A correlation that includes a more extensive series of compounds can be observed with the use of somewhat more sophisticated molecular orbital methods." ... 

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