Energy levels cyclobutadiene

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... 

A useful mnemonic device for quickly setting down the HMOs for cyclic systems is Frosts circle.If a regular polygon of n sides is inscribed in a circle of diameter 4/3 with one comer at the lowest point, the points at which the comers of the polygon touch the circle define the energy levels. The energy levels obtained for benzene and cyclobutadiene with Frost s circle are shown in Fig. 1.12. 

Fig. 1.12. Energy level diagrams for cyclobutadiene and benzene, illustrating the application of Frost s circle.

Problem 10.30 Design a table showing the structure, number of tt electrons, energy levels of tt MO s and electron distribution, and state of aromaticity of (a) cyclopropienyl cation, b) cyclopropenyl anion, (c) cyclobutadiene, (d) cyclobutadienyl dication, (c) cyclopentadienyl anion, (/) cyclopentadienyl cation, (g) benzene, (h) cycloheptatrienyl anion, (/) cyclooctatetraene, (/ ) cyclooctatetraenyl dianion. ... 

The (An + 2) n electron standard follows from the pattern of orbital energies in monocyclic, completely conjugated polyenes. The tt energy levels were shown for benzene earlier in Figure 11.4 and are repeated in Figure 11.13b. Figure 11.13a and 11.13c show the T7 energy levels for square cyclobutadiene and planar cyclooctatetraene, respectively. 

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...

Figure 5. MO energy level diagram for square-planar (D4I) cyclobutadiene.

In the case of the square conformation of cyclobutadiene, the energy levels would be... 

Figure 2.28 Coordinate system (top), energy levels (left) and real Huckel MOs (right) for cyclobutadiene (ring with N = 4)...

Fig. 4a-c. Enumeration of the moments of the pn levels of cyclobutadiene, a) Shows the energy levels referred to a = 0. b) enumerates the walks explicitly, c) Shows how the same result maybe obtained by propagating a unit vector around the ring... 

The energy levels of Hiickel and Mobius orbital arrays are easily generated. (In Ref. 14 we show in detail how the orbital energies of Mobius cyclobutadiene are obtained... 

Fig. 5-4 rc-Electron energy-levels of cyclobutadiene (a) in its ideal , symmetrical form, in which all carbon-carbon bond-lengths are equal, and (b) in its rectangular form, caused by a pseudo Jahn-Teller or Renner distortion. 

Use group theory to solve for the energy levels of cyclobutadiene. Calculate values for DE. ., py, and q.. Use Hand s rule (p. 4 ) to determine the proper electronic configuration. 

Application of the simple molecular orbital theory to cyclobutadiene (cf Exercise 4-6) leads to prediction of four one-electron energy levels a + 2p, a, a, and a 2p. Use of Hund s rule leads to the following electronic configuration for the four tt electrons ... 

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