Hiickel theory cyclobutadiene

Problem 11-17. What is the resonance stabilization energy of cyclobutadiene, according to Hiickel theory Express your answer in terms of / . 

In this contribution, it was also recognized that a clear dividing line exists between aromatic and antiaromatic species, set to about a Hiickel hardness of -0.2/3, where /3 is the carbon parameter of Hiickel theory. The Hiickel and relative Hiickel hardness of benzene are. e.g., equal to —1.0/3 and —0.428/3, respectively, those of cyclobutadiene are 0/3 and 0.765/3, respectively. For comparison, the values for Ceo are -0.378/3 and -0.316/3, predicting this molecule to be aromatic. ... 

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 ... 

The most obvious compound in which to look for a closed loop of four electrons is cyclobutadiene (44).135 Hiickel s rule predicts no aromatic character here, since 4 is not a number of the form 4n + 2. There is a long history of attempts to prepare this compound and its simple derivatives, and, as we shall see, the evidence fully bears out Hiickel s prediction— cyclobutadienes display none of the characteristics that would lead us to call them aromatic. More surprisingly, there is evidence that a closed loop of four electrons is actually ami-aromatic.1 If such compounds simply lacked aromaticity, we would expect them to be about as stable as similar nonaromatic compounds, but both theory and experiment show that they are much less stable.137 An antiaromatic compound may be defined as a compound that is destabilized by a closed loop of electrons. 

We have seen so far that MOs resulting from the LCAO approximation are delocalized among the various nuclei in the polyatomic molecule even for the so-called saturated a bonds. The effect of delocalization is even more important when looking to the n electron systems of conjugated and aromatic hydrocarbons, the systems for which the theory was originally developed by Hiickel (1930, 1931, 1932). In the following, we shall consider four typical systems with N n electrons, two linear hydrocarbon chains, the allyl radical (N = 3) and the butadiene molecule (N = 4), and two closed hydrocarbon chains (rings), cyclobutadiene (N = 4) and the benzene molecule (N = 6). The case of the ethylene molecule, considered as a two n electron system, will however be considered first since it is the reference basis for the n bond in the theory. 

The annulenes are that series of monocyclic polyolefins (C H ) containing a complete system of contiguous double bonds. While benzene (the best known member of this class of compounds) has been in evidence for some time it is only of late that interest in the higher members has become apparent. This interest has its origins in the LCAO-MO theory of re-elec-tron systems as formulated by E. Hiickel (in particular the "Hiickel rule relating aromatic stability to structure). Although the non-classical chemistry of the benzenoid hydrocarbons had previously been the subject of some conjecture, Httckel s theoretical studies provided the first satisfactory explanation of the peculiar stability of this class of compounds and, incidently, the elusiveness of cyclobutadiene. 

The success of simple HMO theory in dealing with the relative stabilities of cyclic conjugated polyenes is impressive. Simple resonance arguments lead to confusion when one tries to compare the unique stability of benzene with the elusive and unstable nature of cyclobutadiene. (Two apparently analogous resonance structures can be drawn in each case.) This contrast is readily explained by Hiickel s rule, which states that a species composed of a planar monocyclic array of atoms. 

In this section, we will use MO theory to explain the source of Hiickel s rule for planar, conjugated ring systems. We already analyzed the MOs of benzene (Figure 18.4) to explain its stability. Let s now turn our attention to the MOs of cyclobutadiene (C4H4) and cyclooctatetraene (C3H3) to see how MO theory can explain the observed instability of these compounds. We will start with square cyclobutadiene, which is a system constructed from the overlap of four atomicp orbitals (Figure 18.5). 

Before we leave this chapter, let s look at one important application of group theory to chemistry. The rr-electron systems of aromatic compounds provide an excellent example of the application of group theory to molecules of low symmetry. Hiickel s 4 -f 2 rule predicts that a symmetric, monocyclic compound with 4 -f 2 rr-electrons, where n is any whole number, is substantially more stable than a corresponding compound with An rr-electrons. Benzene, for example, has six TT-electrons ( = 1) and is much less reactive than the An ir-electron compounds cyclobutadiene n = 1) and cyclooctatetraene ( = 2). This seems at odds with the fact that all three of these compounds—cyclobutadiene, benzene, and cyclooctatetraene—may be drawn with two equivalent resonance structures and therefore may be presumed to have similar resonance stabilization. 

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