Lowest unoccupied molecular orbital splitting

Conjugated polymers are generally poor conductors unless they have been doped (oxidized or reduced) to generate mobile charge carriers. This can be explained by the schematic band diagrams shown in Fig. I.23 Polymerization causes the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the monomer to split into n and n bands. In solid-state terminology these are the valence and conduction bands, respectively. In the neutral forms shown in Structures 1-4, the valence band is filled, the conduction band is empty, and the band gap (Eg) is typically 2-3 eV.24 There is therefore little intrinsic conductivity. 

The features in Figure 15.2 are believed to be due to electron transitions from the highest occupied molecular orbital states to lowest unoccupied molecular orbital states (HOMO-LUMO). Specifically, for single molecules and dilute solutions, the absorption in the blue part of the spectrum is proposed to be caused by the aromatic structure of TNT [4], probably involving it to it transitions.1 In the solid state, where the molecules are stacked up on top of each other, interactions between the molecules occur causing the energy levels to split into higher... 

In view of their similarity the heterobenzenes may be treated as perturbed benzenes. Figure 4 illustrates the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of benzene. In the C2v symmetry of the heterobenzenes these orbitals split into iion-degenerate a2- and bt-orbitals. To the first approximation replacement of by a heteroatom E should leave the a2-orbitals unchanged since they have a node at this position. However, the bj-orbitals which have an antinode at the heteroatom should be strongly effected. 

Figure 15 depicts the splittings of the central metal d-orbitals for (a) an octahedral and a distorted octahedral compound and for (b) a square planar and a distorted square planar compound. For this model discussion, one 7i -orbital is introduced to represent the lowest unoccupied molecular orbital (LUMO). In these simplified schemes, other unoccupied 7i -orbitals and occupied 7i-orbitals are neglected for clarity. Thus, all considered electronic states are MLCT states with a central metal d-orbital as highest occupied molecular orbital (HOMO). 

One always begins with the monomer. What are its frontier levels The classical crystal field or molecular orbital picture of a square planar complex (Fig. 2) leads to a 4 below 1 splitting of the d block.11 For 16 electrons we have z2, xz, yz, and xy occupied and x2-y2 empty. Competing with the ligand field-destabilized x2-y2 orbital for being the lowest unoccupied molecular orbital (LUMO) of the molecule is the metal z. These two orbitals can be manipulated in understandable ways x acceptors push z down, x donors push it up. Better a donors push x2-y2 up. 

Another approach is to use Koopman s theorem and to estimate (in the context of a one-electron picture) the transfer integrals t for holes or electrons as half the splitting of the highest occupied molecular orbital (HOMO) or lowest unoccupied molecular orbital (LUMO) levels, respectively, in a system made of two chains in the neutral state. 

Electron transmission spectroscopy of 3 and 4, which measures gas-phase electron affinities, reveals an even larger splitting (ca. 1.6 eV) of the nonbonding orbitals in these pericyclynes [9]. The lowest unoccupied molecular orbitals (LUMOs) are stabilized by 0.4-0.7 eV relative to the LUMO of acetylene. 

Popov, A. A., Dunsch, L. (2008). Hindered cluster rotation and Sc hyperfine splitting constant in distonoid anion radical Sc3N C8o> and spatial spin charge separation as a general principle for anions of endohedral fullerenes with metal-localized lowest unoccupied molecular orbitals. Journal of the American Chemical Society, 130(52), 17726-17742. 

As seen for the octahedral splitting pattern in Figure 15.1, it is the highest occupied molecular orbital (HOMO), t2g, and the lowest unoccupied molecular orbital (LUMO), 2eg, which are the focus of our attention in the rest of this book. They are shown in 15.1 I. The energy gap between t2g and leg is a function of the ligand a donor strength... 

---