Cyclobutadiene, degenerate orbitals

The localized structure of cyclobutadiene shows two double bonds, implying four pi electrons. Two electrons fill irh the lowest-lying orbital. Once is filled, two orbitals of equal energy are available for the remaining two electrons. If the two electrons go into the same orbital, they must have paired spins and they must share the same region of space. Since electrons repel each other, less energy is required for the electrons to occupy different degenerate orbitals, with unpaired spins. This principle is another application of Hund s rule (Section 1-2). 

Benzene is aromatic because it has a filled shell of equal-energy orbitals. The degenerate orbitals and 773 are filled, and all the electrons are paired. Cyclobutadiene, by contrast, has an open shell of electrons. There are two half-filled orbitals easily capable of donating or accepting electrons. To derive Hiickel s rule, we must show under what general conditions there is a filled shell of orbitals. 

The Hiickel it MOs of a square planar cyclobutadiene are well known. They are the one below two below one set shown in 81. We have a typical Jahn-Teller situation, i.e., two electrons in a degenerate orbital. (Of course, we need worry about the various states that arise from this occupation, and the Jahn-Teller theorem really applies to only one.67) The Jahn-Teller theorem says that such a situation necessitates a large interaction of vibrational and electronic motion. It states that there must be at least one normal mode of vibration that will break the degeneracy and lower the energy of the system (and, of course, lower its symmetry). It even specifies which vibrations would accomplish this. 

Cyclobutadiene complexes afford a classic example of the stabilization of a ligand by coordination to a metal and. indeed, were predicted theoretically on this basis by H. C. Longuet-Higgins and L. E. Orgel (1956) some 3 y before the first examples were synthesized. In the (hypothetical) free cyclobutadiene molecule 2 of the 4 rr-electrons would occupy and there would be an unpaired electron in each of the 2 degenerate orbitals 2. P l- Coordination to a metal provides further interactions and avoids this unstable configuration. See also the discussion on ferra-boranes (p. 174). 

The pattern for planar conjugated systems established for cyclobutadiene, benzene, and cyclooctatetraene persists for larger rings. All 4 - -2 systems are predicted to have all electrons paired in bonding MOs with net stabilization relative to isolated double bonds. In contrast, planar systems containing 4n tt electrons are predicted to have two degenerate orbitals, each with one unpaired electron. This pattern is the theoretical basis of the Hiickel rule. 

Andaromatic compounds have an even number of pairs of tt electrons. Therefore, either they are unable to fill their bonding orbitals (cylopentadienyl cation) or they have a pair of tt electrons left over after the bonding orbitals are filled (cyclobutadiene). Hund s mle requires that these two elecdons go into two degenerate orbitals (Section... 

In 1956, Longuet-Higgins and Orgel 60) pointed out that since square cyclobutadiene, according to molecular orbital theory, has two unpaired electrons in a doubly degenerate orbital, both could be used to form w bonds to a transition metal. They regarded the situation as analogous to that of a... 

Devise a set of degenerate orbitals for cyclobutadiene that is different from those shown above and meets the other requirements as to energy and average electron distribution. 

For cyclobutadiene, there is another interesting possibility which we have explored before with the case of methylene in Section 8.8. Is it possible to produce a stable structure by allowing the two highest energy electrons of the 4n species to separately occupy the orthogonal pair of degenerate orbitals with their spins parallel The result would be a triplet diradical species as in 12.11. For such an electronic... 

For square cyclobutadiene, the lowest lying singlet state is described by the electron configuration 12.15, in which the degenerate orbitals are singly occupied with opposite spins. The alternative singlet state configurations 12.16 and 12.17,... 

Figure 5.3. SHMO orbitals for cyclopropenyl, cyclobutadiene, cyclopentadienyl, and benzene. The energies are in units of f relative to a. Two alternative but equivalent representations are shown for the degenerate n orbitals of cyclobutadiene. Sizes of the 2p orbitals are shown proportional to the magnitudes of the coefficients whose numerical values are given. Coefficients not specified may be obtained by symmetry.

Compounds with a narrow HOMO-LUMO gap (Figure 5.5d) are kinetically reactive and subject to dimerization (e.g., cyclopentadiene) or reaction with Lewis acids or bases. Polyenes are the dominant organic examples of this group. The difficulty in isolation of cyclobutadiene lies not with any intrinsic instability of the molecule but with the self-reactivity which arises from an extremely narrow HOMO-LUMO gap. A second class of compounds also falls in this category, coordinatively unsaturated transition metal complexes. In transition metals, the atomic n d orbital set may be partially occupied and/or nearly degenerate with the partially occupied n + 1 spn set. Such a configuration permits exceptional reactivity, even toward C—H and C—C bonds. These systems are treated separately in Chapter 13. 

Note that in fact cyclobutadiene does not have degenerate, singly-occupied molecular orbitals, as a Jahn-Teller type (actually a pseudo-Jahn-Teller) distortion lowers its symmetry from square to rectangular and leads to a closed-shell paired-electron molecule [4]. 

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