Containing Delocalized Electronic Systems

It should be clear that everything that has been said thus far applies to molecules for which a single Kekule structure can be written. Thus atoms are either bound together, or not bound together, and there is no confusion on the point. With delocalized systems, the binding is much less easy to define. 

Suppose we first consider benzene, and decide how we might deal with it in a force-field calculation. Can we find a natural bond length and a force constant for bond stretching, which would presumably be somewhere in between those for a carbon- carbon single bond and a carbon- carbon double bond, and which will adequately reproduce the structure of benzene The answer is that we can, and simple benzene derivatives can then be dealt with using these parameters by the methods previously discussed. We only need to call the benzene bond a special kind of carbon-carbon bond with its own parameters. 

Benzenoid compounds have been treated in this way by Boyd, who has looked at such molecules without considering the quantum mechanics of the electronic system (Boyd, 1968 Shieh et al., 1969 Boyd et al., 1971 Chang et al., 1970). He has treated a variety of paracyclophanes and related compounds with generally good results. Thus it seems clear that simple benzenoid hydrocarbons can be treated in the usual way, if a special set of parameters is assigned to the benzene ring. 

What will happen, then, if we use these same parameters and try to calculate the geometry of naphthalene We find that, on this basis, naphthalene has essentially all of the bond lengths equal (Allinger and Sprague, 1972, 1973), in contrast to the experimental situation where it is known that the individual bond lengths are proportional to their bond orders. The conclusion is that we cannot apply force-field calculations as discussed up to this point directly to delocalized systems, except in special cases like benzene where we are able adequately to pick the necessary parameters. If we want to deal in a general way with delocalized molecules, something more is needed. 

Returning to naphthalene, there seems to be no calculational way to arrive at the correct structure without doing some kind of a quantum mechanical treatment of the 7r-system. The bond orders of the 7T-system determine what the structure will be, and it seems unavoidable. While a quantum mechanical calculation on naphthalene is a problem of sizable dimensions (48 valence orbitals or 58 total orbitals as a minimum basis set), the 7T-system of naphthalene contains but 10 orbitals. Before quantum chemists had computers, they studied in great detail the question of -a separation, and a great body of lore is available to us from those studies (see, for example, Flurry, 1968). It is well known just how to treat planar delocalized hydrocarbons by existing methods, to take advantage of the - separation, and yet obtain accurate results. There are restrictions, however, planarity being a particularly important one. 

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N.L. Allinger and J.T. Sprague, Calculation of the structures of hydrocarbons containing delocalized electronic systems by the molecular mechanics method, J. Am. Chem. Soc., 95 (1973) 3893-3907. 

Allinger, N.L. and Sprague, J.T. (1973) Calculations of the Structures of Hydrocarbons Containing Delocalized Electronic Systems by the Molecular Mechanics Method, J. Am. Chem. Soc. 95, 3893-3907. 

Something additional will be needed to calculate heats of formation for compounds that contain delocalized electronic systems, particularly aromatic compounds, and related substances. Tlie problem with the methods previously described when applied to these systems is that one cannot expect to have constant bond energy or bond enthalpy units, because conjugated bonds come with various kinds of bond orders essentially from zero to one in the jr-bond component (or up to two if acetylenes are included), and these different bond orders correspond to different bond lengths and to different bond energies. Somehow this all has to be taken into account if one is to apply the calculation schemes described previously to these conjugated systems. 

The fourth paper in this volume is devoted to some extensions and generalizations of the algebra of the be- and r-matrices. The latter is only valid for the chemistry of molecular systems that are representable by integer bond orders and thus is not applicable to the great variety of molecules with multi-center bonds and delocalized electron systems. This deficiency is overcome by the introduction of the so-called extended be- and r-matrices the xbe- and xr-matrices. They contain additional rows/columns which refer to the delocalized electron systems. Some corresponding data structures are presented that also account for stereochemical aspects. 

In the case of 1,3-butadiene, RAMSES combines the two double bonds to form a single, delocalized r-electron system containing four electrons over all four atoms (Figure 2-50a). The same concept is applied to benzene. As shown in Figure 2-50b, the three double bonds of the Kekule representation form one electron system with six atoms and six electrons. 

The porphyrin ring system (the parent compound 1 is also known as porphin) consists of four pyrrole-type subunits joined by four methine ( = CH-) bridges to give a macrotetracycle. The macrocycle contains 227i-electrons from which 1871-electrons form a delocalized aromatic system according to Huckel s 4n + 2 rule for aromaticity. The aromaticity of the porphyrin determines the characteristic physical and chemical properties of this class of compounds. The aromatic character of porphyrins has been confirmed by determination of their heats of combustion.1"3 X-ray investigations4 of numerous porphyrins have shown the planarity of the nucleus which is a prerequisite for the aromatic character. 

Aromatic hydrocarbons that contain ring systems with delocalized electrons, for example, benzene. 

If the molecule contains multiple bonds, construct the n bonding system using molecular orbital theory, as described in this section and in the remaining pages of Chapter 10. Watch for resonance structures, which signal the presence of delocalized electrons. 

Butadiene, used in the chemical industiy as a precursor of synthetic mbber, is a hydrocarbon with the formula C4 Hg. (See Box 13-1 to learn more about the mbber industry.) The Lewis stmcture of butadiene contains two double bonds on sequential pairs of carbon atoms. The chemistry of butadiene, including its ability to form mbber, can be traced to the delocalized electrons in the tt system of the molecule. 

Stabilization of the redox cycle is relatively important in construction of potentially useful electrochromic materials, because the molecules needed for application require high redox-stability. Recently, S. Hiinig et al. proposed the concept of violene-cyanine hybrid to produce stabilized organic electrochromic materials (3). The hybrid is constructed by a violene-type redox system containing delocalized closed-shell polymethine dyes as end groups. The hybrid is expected to exhibit the color of a cyanine dye, by an overall two-electron... 

The following presentation is limited to closed-shell molecular orbital wave-functions. The first section discusses the unique ability of molecular orbital theory to make chemical comparisons. The second section contains a discussion of the underlying basic concepts. The next two sections describe characteristics of canonical and localized orbitals. The fifth section examines illustrative examples from the field of diatomic molecules, and the last section demonstrates how the approach can be valuable even for the delocalized electrons in aromatic ir-systems. All localized orbitals considered here are based on the self-energy criterion, since only for these do the authors possess detailed information of the type illustrated. We plan to give elsewhere a survey of work involving other types of localization criteria. 

Heteroatom-containing derivatives of pentalene and azulene are 8- and 10-jr-electron systems, respectively, and have been extensively studied by Hafner and co-workers.301-304 A few examples are presented in Schemes 30, 47, and 86. Electron-rich azapentalenes 247—249305 306 and various aza-azu-lenes 250—252300-302 have intense colors and are stable but oxygen-sensitive compounds. Azulenes with nitrogen heteroatoms placed in positions with high electron density, such as position 5, or positions 5 and 7, present a hypsochromic effect, while a heteroatom in position 6, with low electron density, exerts a bathochromic effect. When both types of positions are substituted by heteroatoms, their effect is canceled out.307 The bond lengths in 252 (Scheme 86), as determined by X-ray, indicate delocalization as in 252a and 252b.308 309... 

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