Cyclobutadiene Hiickel molecular orbitals

Figure 1.2. The Hiickel molecular orbitals of benzene and cyclobutadiene...

Trimethylenemethane (1) is a cross-conjugated it system with a diradical ground state. Its chemistry has been reviewed as early as 1972 by Dowd [8]. The Hiickel molecular orbital (MO) scheme resembles that of cyclobutadiene, and accordingly trimethylenemethane can be stabilized as a ligand in transition metal complexes. Trimethylenemethane complexes can generally be obtained by treatment of a trimethylenemethane dianion with a metal halide or by treatment of organic halides with low-valent metal complexes. In addition to these general methods, there are some more specialized procedures. 

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 ... 

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

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...

Then we set up the six simultaneous equations for the coefficients and the corresponding 6x6 secular determinant and apply the Hiickel approximations. Its form resembles that for cyclobutadiene in Exercise 10.33, but with six rows and six columns. Full-frontal attack on it to determine the six values of E is rather tedious, especially as there are procedures that make use of symmetry that greatly simplifies the solution. As should be verified, the energies and the corresponding (unnormalized) molecular orbitals obtained are as follows (Fig. 10.39) ... 

The alternating behavior of the annulenes between aromatic and antiaromatic had been predicted earlier by the theoretical chanist Hiickel, who formulated this (4n + 2) rule in 1931. Hiickel s rule expresses the regular molecular-orbital patterns calculated for planar, cyclic conjugated polyenes. The p orbitals mix to give an equal number of tt molecular orbitals, as shown in Figure 15-18. For example, the four p orbitals of cyclobutadiene result... 

Is cyclobutadiene dication (C4H4 ) aromatic according to Hiickel s rule Sketch its ir molecular orbital diagram to illustrate your answer. 

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