Orbitals, molecular cyclobutadiene

High level molecular orbital calculations of cyclobutadiene itself and experimen tally measured bond distances of a stable highly substituted derivative both reveal a pat tern of alternating short and long bonds characteristic of a rectangular rather than square geometry... 

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... 

FIGURE 11 13 Frost s circle and the TT molecular orbitals of (a) square cyclobutadiene (b) ben zene and (c) planar cyclooctatetraene... 

It is in this area that qualitative MO procedures have great success because there are general characteristics of the 77 molecular orbitals of mono-cyclic, conjugated polyene systems that predict differences in the properties of cyclobutadiene, benzene, cyclooctatraene, and other similar compounds that are not obvious from the simple VB method. 

The simple resonance theory fails to explain the singular lack of effectiveness of delocalization in cyclobutadiene and cyclooctatetraene, but we may turn to molecular orbitals for the solution. 

Find the Hiickel energy levels and molecular orbitals for butadiene, cyclobutadiene, and pentatrienyl. 

Figure 3.25. Molecular orbital representations of the bonding structure of the parent bishomoaromatic dication C4H82+ (604) and cyclobutadiene dication C4H42+ (605).

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

Fig. 4.17 The n molecular orbitals and n energy levels for a cyclic four-p-orbital system in the simple Hiickel method. The MOs are composed of the basis functions (four p AOs) and the eigenvectors, while the energies of the MOs follow from the eigenvalues (Eq. 4.69). This particular diagram is for the square cyclobutadiene molecule. The paired arrows represent a pair of electrons of opposite spin, in the fully-occupied lowest MO, i/q, and the single arrows represents unpaired electrons of the same spin, one in each of the two nonbonding MOs, ij/2 and 1//3 the highest n MO, 1I/4, is empty in the neutral molecule...

Antiaromaticity [1] is the phenomenon of destabilization of certain molecules by interelectronic interactions, that is, it is the opposite of aromaticity [2], The SHM indicates that when the n-system of butadiene is closed the energy rises, i.e. that cyclobutadiene is antiaromatic with reference to butadiene. In a related approach, the perturbation molecular orbital (PMO) method of Dewar predicts that union of a C3 and a Ci unit to form cyclobutadiene is less favorable than union to form butadiene [3]. 

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]. 

On the basis of this resonance picture only, organic chemists initially expected that cyclobutadiene, like benzene, would have a large resonance stabilization and would be especially stable. Yet cyclobutadiene proved to be an extraordinarily elusive compound. Many unsuccessful attempts were made to prepare this compound before it was finally synthesized at very low temperature in 1965. The compound is quite unstable and reacts rapidly at temperatures above 35 K. As we shall see, cyclobutadiene is a member of an unusual group of compounds that are actually destabilized by resonance. To understand why benzene is so stable while cyclobutadiene is so unstable, we must examine a molecular orbital picture for these compounds. 

Q Show how to construct the molecular orbitals of a conjugated cyclic system similar to benzene and cyclobutadiene. Predict whether a given heterocyclic structure will be aromatic. For heterocycles containing nitrogen, determine... 

Although we can draw benzene-like resonance structures (Figure 16-3) for cyclobutadiene, experimental evidence shows that cyclobutadiene is unstable. Its instability is explained by the molecular orbitals, shown in Figure 16-6. Four sp2 hybrid carbon atoms form the cyclobutadiene ring, and their four p orbitals overlap to form four molecular orbitals. The lowest-energy MO is 771, the all-bonding MO with no nodes. 

The pi molecular orbitals of cyclobutadiene. There are four MOs the lowest-energy bonding orbital, the highest-energy antibonding orbital, and two degenerate nonbonding orbitals. 

An electronic energy diagram of cyclobutadiene shows that two electrons are unpaired in separate nonbonding molecular orbitals. 

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