Molecular orbitals of cyclobutadiene

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. 

For conjugated (diene)metal complexes, the 7r-molecular orbitals of cyclobutadiene consist of a degenerate eg pair (Figure 3). Because of this orthogonality, there is not a single electronically preferred conformei and barriers for rotation of the cyclobutadiene ligand are generally low . For (cyclobutadiene)Fe(CO)3, in the solid state, NMR spin relaxation data indicate that there are two inequivalent lattice sites. For each of these inequivalent lattice sites, barriers for rotation of the cyclobutadiene have been measured to be 3.63 and... 

Using the polygon-and-circle method to outline the molecular orbitals of cyclobutadiene, explain why cyclobutadiene is... 

The relative energy levels of the molecular orbitals of cyclobutadiene. 

FIGURE 13.20 The relative energies of the molecular orbitals of cyclobutadiene derived from a Frost circle. Electrons have been added to this construct after the energies of the orbitals have been determined. 

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 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],... 

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... 

Fig. 1.39 The three lowest-energy n molecular orbitals of rectangular cyclobutadiene...

Figure 16-8 shows that the first 3 pairs of electrons are in three bonding molecular orbitals of cyclooctatetraene. Electrons 7 and 8, however, are located in two different nonbonding orbitals. As in cyclobutadiene, a planar cyclooctatetraene is predicted to be a diradical, a particularly unstable electron configuration. 

Figure 4.2 Huckel molecular orbitals for cyclobutadiene (3). The 2p AOs are viewed from the top. The radius of the rings is proportional to the size of the AO coefficients cj/JL, so that their area is proportional to cyAL2. The shading indicates the relative sign, i.e. white is used for cyAt>0 and black for cyM< 0 (or vice versa). The coefficients of the NBMOs ij/2 and j/3 are cy/A = V /2 or 0 and those for and j/4 are cy/iJ =0.5...

The distribution of electrons in the tt molecular orbitals of (a) benzene, (b) the cyclopentadienyl anion, (c) the cyclopentadienyl cation, and (d) cyclobutadiene. The reiative energies of the tt molecular orbitals in a cyclic compound correspond to the relative levels of the vertices. Molecular orbitals below the midpoint of the cyclic structure are bonding, those above the midpoint are antibonding, and those at the midpoint are nonbonding. 

Crystal energy matrix, 307 Crystal Hamiltonian, 294, 307 Crystals, organic molecular, 286, 327 Cube, Cn axes of, 19 commutation of, 23 symmetry operations of, 23 symmetry planes of, 20, 21 Cubic point groups, 66ff Current density, 109 Cyclobutadiene, v molecular orbitals of, 178-179... 

The three w orbitals of cyclobutadiene, i, 4 2 and 3 (Section I) which are involved in the bonding are represented in Fig. 1. The highest energy orbital, 4, has a node between each carbon atom and can combine with the nickel orbital. However, the high energy of 4 probably makes the bonding molecular orbital mainly and the antibonding molecular... 

Figure 4.26 shows the FfMOs for cyclopropenyl carbocation, square planar cyclobutadiene, cyclopentadienyl anion, benzene, cycloheptatrienyl carbocation, and planar (Ds/,) cyclooctatetraene. If we place electrons into the molecular orbitals of each species according to the aufbau principle, we notice an important relationship between the stability of the systems and the... 

Figure 8.1. Molecular orbitals of (a) 1,3-dienes, (b) cyclobutadiene, (c) trimethylenemethane. Metal orbitals which may form bonds with the given orbital of the ligand are shown.

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

The distribution of electrons in the rr molecular orbitals of (a) benzene, (b) the cyclopentadienyl anion, (c) the cyclopentadienyl cation, and (d) cyclobutadiene. 

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... 

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