The benzene molecule

The Huckel secular equation for the closed chain (ring) with N = 6 is  

As a general rule, the number of nodal planes increases for the higher n orbitals, while the deepest bonding MO has no nodal planes (except for the molecular plane, which is common to all molecules considered here). 

The first degenerate MOs35 f 2 and 4 3 transform like (x, y) and are bonding MOs (HOMOs), the second degenerate MOs 4 and j 5 transform like (x1 — y2, xy) and are antibonding MOs (LUMOs). 

35 Loosely speaking, we attribute to MOs a property (degeneracy) of energy levels. 

The pa and components of the electron distribution function for benzene are equal  

In the case of the benzene molecule, CgHe, we consider 24 a molecular orbitals of which 12 are bonding. These can be transformed into a set of quasi-localized molecular orbitals which, according to the geometry of the molecule, can be defined approximately in terms of sp hybrid orbitals of the C atoms together with the Is orbitals of the H atoms  

The six 2p atomic orbitals whose axes are perpendicular to the nuclear plane (the xy plane) 

These m.o.s are symbolically represented in Fig. 9.8. We have non-localized molecular orbitals that are again non-localizable. 

The weak reactivity of benzene is in part attributed to this additional stabiliza- j tion. That stabilization energy is often called the delocalization energy or reso- nance energy of benzene and is taken as a measure of the aromaticity of the j molecule. The expression resonance energy comes from the description of] the delocalized tt system in valence-bond theory in terms of the resonant hybrid 

Problem 9.11 Relate the additional stabilization associated with delocalized m.o.s with the model of the particle in the box studied in Chapter 2. 

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The napthanes (C H2n), or cycloalkanes, are ring or cyclic saturated structures, such as cyclo-hexane (CgH 2) though rings of other sizes are also possible. An important series of cyclic structures is the arenes (or aromatics, so called because of their commonly fragrant odours), which contain carbon-carbon double bonds and are based on the benzene molecule. 

Now consider die case where Ais itself a time-independent operator, such as that for the position, momenPiin or angidar momenPiin of a particle or even the energy of the benzene molecule. In these cases, the time-dependent expansion coefficients are unaffected by application of the operator, and one obtains... 

However, many adsorbates caimot reach a coverage of 1 ML as defined in this way this occurs most clearly when the adsorbate is too large to fit in one unit cell of the surface. For example, benzene molecules nonnally lie flat on a metal surface, but the size of the benzene molecule is much larger than typical unit cell areas on many metal surfaces. Thus, such an adsorbate will saturate the surface at a lower coverage than 1 ML deposition beyond this coverage can only be achieved by starting the growdi of a second layer on top of the first layer. 

The first study was made on the benzene molecule [79], The S ISi photochemistry of benzene involves a conical intersection, as the fluorescence vanishes if the molecule is excited with an excess of 3000 crn of energy over the excitation energy, indicating that a pathway is opened with efficient nonradiative decay to the ground state. After irradiation, most of the molecules return to benzene. A low yield of benzvalene, which can lead further to fulvene, is, however, also obtained. 

Cooper D L, J Gerratt and M Raimondi 1986. The Electronic Structure of the Benzene Molecule. Nature 323 699-701. 

There is a small peak one mass unit higher than M m the mass spectrum of ben zene What is the origin of this peak d What we see m Figure 13 40 as a single mass spectrum is actually a superposition of the spectra of three isotopically distinct benzenes Most of the benzene molecules contain only and H and have a molecular mass of 78 Smaller proportions of benzene molecules contain m place of one of the atoms or m place of one of the protons Both these species have a molecular mass of 79... 

Structure. The representation of the benzene molecule has evolved from the Kekule ring formula (1) to the more electronically accurate (2), which iadicates all carbon—carbon bonds are identical. 

There are three compounds with the formula C6H4ClBr in which two of the hydrogen atoms of the benzene molecule have been replaced by halogen atoms. Draw structures for these compounds. 

We can use the concept of resonance to explain these characteristics of the benzene molecule. There are two Kekule structures with exactly the same energy they differ only in the positions of the double bonds. As a result of resonance... 

The convenience and usefulness of the concept of resonance in the discussion of chemical problems are so great as to make the disadvantage of the element of arbitrariness of little significance. Also, it must not be forgotten that the element of arbitrariness occurs in essentially the same way in the simple structure theory of organic chemistry as in the theory of resonance — there is the same use of idealized, hypothetical structural elements. In the resonance discussion of the benzene molecule the two Kekule structures have to be described as hypothetical it is not possible to synthesize molecules with one or the other of the two Kekule structures. In the same way, however, the concept of the carbon-carbon single bond is an idealization. The benzene molecule has its own structure, which cannot be exactly composed of structural elements from other molecules. The propane molecule also has its own structure, which cannot be composed of structural elements from other molecules — it is not possible to isolate a portion of the propane molecule, involving parts of two carbon atoms... 

It may be mentioned that the three-electron bond developed above is not present in the benzene molecule, for which certain investigators have suggested the structure... 

The benzene molecule can now be treated very simply by the Slater method, with the help of the rules formulated by one of us4 for finding the matrix elements occurring in the secular equation. The bonds between the six eigenfunctions can be drawn so as to give the independent canonical structures shown in Fig. 1. Any other... 

Fig. 1. The five canonical structures contributing to the normal state of the benzene molecule.

Now the magnitude of the resonance integral, which determines the resonance energy and the resonance frequency, depends on the nature of the structures involved. In benzene it is large (about 36 kcal./mole) but it might have been much smaller. Let us consider what the benzene molecule would be like if the value of the resonance integral were very small, so that the resonance frequency were less than the frequency of nuclear... 

It is often asked whether or not the constituent structures of a resonating system, such as the Kekul4 structures for the benzene molecule, are to be considered as having reality. There is one sense in which this question may be answered in the affirmative but the answer is definitely negative if the usual chemical significance is attributed to the structures. A substance showing resonance between two or more valence-bond structures does not contain molecules with the configurations and properties usually associated with these structures. The constituent structures of the resonance hybrid do not have reality in this sense. 

Numerical results for the shielding field of the benzene molecule are collected in Table 1 for the center of the molecule (labelled COM), and for points along a quarter circle of radius 2.47 A from the -ajcis to the x-axis, see Figure 3 for specification of axes. The radius of the circle corresponds to the distance from the ring center to a proton but, as defined, the points lie in the entirely nucleus-free xz-plane. Except for COM, the entries in the table are labelled by the angle between the z-axes and the direction to the field point. The table includes the isotropic part of the shielding, and the principal... 

Table 1 Isotropic and Principal Value Shieldings, and Intensity Measures for the Benzene Molecule. See text.

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