LUMO states

As the number of silicon atoms in the delocalized backbone cr-electron system increases, the number of HOMO and LUMO states increases, resulting in a band structure for high molecular weight polymers. Electronic absorptions from the HOMO (cr) to LUMO (essentially a ) are responsible for the characteristic UV absorption of polysilanes observed between 300 and 400 nm, the transition moment for which is in the direction of the Si chain.198 Polysilanes are... 

Spiropyran merocyanine specffa shift markedly to the blue as the solvent polarity increases [4,25], as shown in Fig. 7a for 6,8-dinitro-BIPS merocyanine. This is generally accepted to imply that they have a zwitterionic character caused by the donation of electron density from the indoline nitrogen to the phenolic C9 oxygen [4,25]. The rational behind this assignment to the zwitterion is based simply on the fact that if the zwitterion is in the highest occupied molecular orbital (HOMO) state, then the corresponding quinoidal resonant form is in the lowest unoccupied molecular orbital (LUMO) state and changing the solvent to a more polar one... 

The opposite direction of spectral shift with solvent polarity is observed for the spiro-oxazine [4] and naphthopyran mero-forms and this is generally accepted to infer a quinoidal HOMO and a zwitterionic LUMO state in their cases. This shift is shown also in Fig. 7b for a naphthopyran TT isomer (CHR2). Of course, H-bonding and other specific interactions will also affect the position of the mero-form spectral maximum. In the case of the substituted BIPS, spiro-oxazine, and CHR2, there is evidence to support their respective assignments to a zwitterionic and quinoidal forms, including x-ray [36,80-85] and NMR [36,55,86-88] data. 

Transport in DNA samples with all bases the same could be either by free carriers, i.e., band transport, or by polarons. As will be further discussed in the next section, the polarons are expected to be large polarons, not small. In the conducting polymers there is overwhelming evidence that electrons (holes) from a metal contact are injected directly into polaron states in the polymer, because the polaron states have lower energies than the LUMO (HOMO) or conduction (valence) band edge. As has recently been shown theoretically [30], the injection takes place preferably into a polaron state made available when a polaron-like fluctuation occurs on the polymer chain close to the interface, rather than into a LUMO state, with subsequent deformation to form the polaron. It could also be expected for DNA that injection... 

Fig. 2. Transient absorption of Pe -Tripod probed at 570 nm (squares). The measured signals a superposition of cation absorption and stimulated emission (negative signal). The data were fitted to a three-exponential rise (solid line) revealing time constants of 30 fs (42%), 720 fs (33%) and 4.3 ps (25%). The inset illustrates the atomic structure of the Pe -Tripod and its LUMO state, both calculated on a semi-empirical level.

Abstract. Equilibrium configurations, total energies, heats of formation, energies of HOMO and LUMO states, densities of one-electron states (DOS) and IR spectra of CNTs T-junctions of the various types are calculated by employing of PC Gamess version of semi-empirical quantum chemistry PM3-method. 

Electrical conduction will occur by the hopping of either electrons or holes within these distributions of energy levels. Charge transport can be either of holes by transfer between the LUMO states or of electrons between the HOMO states. These correspond to the formation of either a radical cation by the removal of an electron to an adjacent electrode or an anion by the injection of an electron. The nature of the majority carriers will, therefore, be determined by the ionisation potentials and electron affinities of the conjugated moieties. A low ionisation potential will favour hole transport while a high electron affinity will favour electron transport. Most of the conductive polymers reported in the literature have low ionisation potentials and are hole, conductors. ... 

When discussing the electronic structure of molecules and solids, one-electron descriptions, such as the molecular orbitals of Equation 8.1, are quite intuitive. It is common to talk about individual electrons occupying particular states. For example, reactions often occur by the mixing of the highest occupied molecular orbital (HOMO) of one species and the lowest unoccupied molecular orbital (LUMO) of another. In such a reaction the electrons in the HOMO state move into the new mixed orbital, lowering their energy. The HOMO and LUMO states are each pairs of one-electron molecular orbitals, since in the simplest case an orbital giving the spahal distribution for a spin up electron has an identical partner for spin down. Mulh-electron wavefunctions that describe the whole electronic structure in this picture are constructed from the one-electron states. So, for example, in a four-electron system in which all the electronic states are doubly occupied (spin up and spin down), based on Hartree-Fock theory we can write ... 

Fig. 4. The anatomy of a p-like state . Two isodensity contour maps (+ 0.01 and + 0.03 a.u." ) of the same LUMO orbital are shown side by side. Unlike the p-Uke orbitals in one-electron models, LUMO states in MQC MD-DFT and CIS models have the lobes pushed outwards between the first and the second solvation shells, with < 20% of the spin density residing inside the cavity. This results in considerable firagmentation of the diffuse part of the wavefunction. The O 2p orbitals are strongly polarized, with opposite signs of the orbitals attained by water molecules on the opposite sides of the cavity in the direction of transition dipole moment.

We now proceed to briefly describe e injection from the metallic electrode into the adjacent band of LUMO states and the hopping transport in this band.134... 

The new states can either be interpreted in the band picture as polarons and/or bipolarons which occur due to electron-phonon coupling after ionization (see below) (electron-electron interaction is neglected) or as the new HOMO and LUMO states in charged particles if localized molecular orbitals are assumed (electron-electron correlation is taken into account, electron-phonon coupling neglected). Both models will be discussed in parallel in the following subsections. However, in general discussions the band stmeture terms will be used as they are more common in literature. 

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