Antibonding tt MOs

The antibonding tt MO results when orbital lobes of opposite sign overlap between adjacent carbon atoms => there is a node between each pair of carbon atoms. 

The n-type interachons within each individual (CH)2 unit generate the bonding (tt) and antibonding (tt ) MOs of each individual unit. The first one is occupied (two tt electrons per unit cell), whereas the second is empty. Except for the fact that... 

The lowest-energy n molecular orbital (denoted Greek psi) has no nodes between the nuclei and is therefore bonding. The tt MO of next lowest energy, ip2, has one node between nuclei and is also bonding.. Above t//] and 1//2 in energy are the two antibonding tt MOs, and (The asterisks indicate... 

Fig. 1.9 Formation of sigma bonding (u) and antibonding (u ) molecular orbitals (MOs) from combination of s and p atomic orbitals (AOs) and of pi bonding (tt) and antibonding (tt ) MOs for combination of p AOs...

However, its isoelectronic unsymmetrical counterpart, 7r-cyclopen-tadienyl-7r-cycloheptatrienylchromium(0) can be reduced to a stable anion radical (41). The orbital occupied by the unpaired electron has dominant ligand tt character. It appears to consist of a combination of the antibonding e2 MO s of the cyclopentadienyl (Cp) and cyclohepta-trienyl (Tr) 7r-systems with about one-third Cp and two-thirds Tr, respectively (41). Reduction of 7r-cyclopentadienyl-7r-methylcyclohepta-trienylchromium leads to an unstable radical anion that decomposes by loss of the seven-membered ligand (41). 

Excited MOs whose main contributions come from AOs with principal quantum numbers equal to the atomic valence-shell quantum numbers are called sub-Rydberg (or valence) MOs. For example, the excited (antibonding) it MOs (symbolized by tt ) of conjugated molecules for which Clpir AOs make the main contribution are valence MOs. Another example is the o 15 MO of H2. Of course, there is not a sharp dividing line between Rydberg and valence MOs. One way to decide how much Rydberg character an MO has is to calculate for it. 

It has a node between each bonded pair of carbons and is antibonding. Figure 1.18 shows these tt MO s in an energy-level diagram. 

First, the irreducible part of the Brillouin zone now varies from k = 0 to k = Tr/d = tt/2d. Indeed, doubling the parameter of the unit cell in real space halves the size of the Brillouin zone (or the reciprocal-space unit cell). Second, recall that orbital interactions are additive and that the final MO diagram (or band structure) is just the result of the sum of all the orbital interactions. Within each individual H2 unit the interactions simply correspond to the bonding (a) and antibonding (a ) MOs of each individual H2 unit. There are three types of interactions involving the MOs of different H2 units interactions between all the a orbitals interactions between all the a orbitals and interactions between the a and the a orbitals. Since all the an orbitals are equivalent by translational symmetry, their interaction is described by the Bloch function ... 

Just as bonding and antibonding a molecular orbitals result from the combination of two s atomic orbitals in H2 (Section 1.6), so bonding and antibonding tt molecular orbitals result from the combination of two p atomic orbitals in ethylene. As shown in Figure 1.17, the n bonding MO has no node between nuclei and results from combination of p orbital lobes with... 

FIGURE 8.5 Bonding and antibonding molecular orbitals (MOs) formed from d-orbital overlap, (a) orbitals along the internuclear axis, (b) tt and tt MOs formed from side-by-side overlap of orbitals in the x-z plane (there is a corresponding pair of MOs formed from side-by-side overlap of c/ orbitals in the y-z plane), (c) S and S orbitals from the face-to-face overlap of a pair of MOs (there is a corresponding pair of MOs constructed from the orbitals, which are rotated 45 from the set shown here). 

The UV spectrum of benzene is interpreted as the excitation of an electron from the highest occupied molecular orbital (HOIMO, bonding n MO) to the lowest unoccupied molecular orbital (LUIMO, antibonding n MO ). The bond order of the TT-system changes from 3 to 2. 

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