Modern Polymer Spect..

4.4 Geometric Chmges Iiid~lrcecl bjj Dopiiiy 21 3
Figure 4-4. Schematic molecular orbital energy levels. (a) Neutral conjugated system; (b) its radical
cation; (c) its dication; (d) neutral radical of an odd oligoene. HOMO, highest occupied molecular
orbital; LUMO, lowest unoccupied molecular orbital; SOMO, singly occupied molecular orbital;
0. electron.
tonian with an electron-lattice interaction teiin (SSH model), their model being
essentially the same as the Huckel approximation. The continuuin versions of the
SSH niodel are very useful for describing polarons and bipolarons as well as solitons,
because analytic solutions can be obtained for physical parameters (creation
energy, electronic absorption, etc.) relating to the excitations [21, 47-49].
4.4.2 Electronic States of Poiarons, Bipoiarons, and Solitons
We will first discuss the electronic states of linear conjugated molecules at the
Huckel level with electron-lattice interaction [7], as models of self-localized excitations.
The MO energy levels of these systems are schematically shown in Figure 4-4.
In a neutral conjugated molecule (e.g., p-terphenyl), the bonding and antibonding
levels are formed as the result of interaction between n-electron levels (Figure 4-4a).
In its radical cation, geometric changes lead to an upward shift of the highest
occupied molecular orbital (HOMO) and a downward shift of the lowest unoccupied
molecular orbital (LUMO), and one electron is removed from the HOMO
level (Figure 4-4b); the singly occupied molecular orbital (SOMO) is then formed.
In its radical anion, the HOMO level is occupied by two electrons and the LUMO
has one electron. Since geometric changes in the dication, where another electron
is removed from the HOMO level (Figure 4-4c), are larger than those in the radical
cation, the HOMO and LUMO levels shift further. In the dianion, each of the
HOMO and LUMO levels is occupied by two electrons. In the MO energy levels of
an odd trans-oligoene radical, CllHJ1+2' (where n is an odd number), a nonbonding
level, which is occupied by one electron, is formed in the center of the band gap as
shown in Figure 4-4d [36]. In its cation and anion, the nonbonding level IS occupied
by null and two electrons, respectively.