VEH band structure

Figure 5-5. Valence band spectra of r/wu-polyacetyienc, recorded using synchrotron radiation at 27 eV and 50 eV photon energy, and the corresponding DOVS derived from Vl-H calculations. The VEH band structure is shown in the lower part of the figure (from Ref. 1281).

Two Hell UPS spectra of poly(3-hexylthiophene), or P3HT, compared with the DOVS derived from VEH band structure calculations 83], arc shown in Figure 5-14. The general chemical structure of poIy(3-a ky thiophcne) is sketched in Figure 5-4. The two UPS spectra, were recorded at two different temperatures, +190°C and -60 "C, respectively, and the DOVS was derived from VEH calculations on a planar conformation of P3HT. Compared to unsubslitutcd polythio-phene, the main influence in the UPS spectra due to the presence of the hexyl... 

The experimental UPS spectra of the emeraldine base form of polyaniline is compared with VEH-derived DOVS in Figure 5-18 97. The DOVS were derived from the VEH band structure calculations shown at the bottom of Figure 5-18. 

The electronic structure of poly(p-phenylenevinylene), or PPV, has several similarities to DP7 hence DP7 is used as a model molecule for PPV34. The VEH band structure of an isolated chain of PPV, and... 

The measurements were carried out using polarized-light from synchrotron radiation. The angle-resolved UPS spectra were recorded for specific directions of photon incidence, photon polarization, and electron exit, chosen in order to resolve the momentum dependence of the 7t-electron energy bands which could be observed in this experiment. Details are available elsewhere63. The UPS results are analysed not only with the help of the valence effective Hamiltonian (VEH) method, but also with the help of new quantum-chemical calculations based upon the excitation model method64. The full VEH band structure is shown in Fig. 7.32. 

The VEH band structure calculations have been carried out using the geometries depicted in Fig. 2 as unit cells, and assuming a fully coplanar conformation,with all the vinyl groups in trans position with respect to adjacent rings (see Fig. 3a). This assumption has been taken on the basis of the accurate ab initio calculations performed to study the rotation potential of the vinyl group in 2-VT, 2-VF, and 2-VPy. For all of these monomers, the trans rotamer is predicted as the most stable conformation. The VEH band structures calculated for the all-cis conformations displayed in Fig 3b show no significant difference with respect to those obtained for trans conformations and they will not be discussed here. 

The VEH band structure computed for PTV is presented in Fig. 4, where all the crossings among k bands and among a bands are avoided due to the low symmetry of the unit cell. The HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands are, as expected, n bands, and show the same atomic orbital composition patterns as those reported for PT. The HOMO band of PTV corresponds to wave functions delocalized over the carbon backbone,with essentially no contribution from... 

Fig. 4. VEH band structure calculated for PTV. Energies are in atomic units. Unoccupied bands with energies larger than 0.0 a.u. are not shown. Solid lines indicate a bands. Dashed lines indicate K bands. HOMO and LUMO denote the highest occupied and lowest unoccupied molecular orbital bands, respectively.

Fig. 5. VEH band structures calculated for PFV (a) and PPyV (b). See Fig 4 for further details.

The VEH band structures calculated for PFV and PPy V are very similar to that of PTV and are displayed in Fig. 5. The most relevant VEH electronic parameters calculated for PFV and PPyV are collected in Table I. For the sake of comparison, the VEH parameters discussed above for PTY and those previously reported for PT i 25 pf,14 and PPy22,are included in Table I. As it was previously observed for PF and PPy, the HOMO bands show similar widths for PFV(2.92 eV) and PPyV (2.81 eV>but now are narrower by about 1 eV. 

FIGURE 21.6 Valence band spectra of trans-polyacetylene, recorded using synchrotron radiation at 27 and 50 eV of photon energy, and the corresponding DOVS derived from VEH calculations. The VEH band structure is shown in the lower part of the figure. (From Logdlund, M., Salaneck, W.R., Meyers, F., Bredas, J.L., Arbuckle, G.A., Friend, R.H., Holmes, A.B., and Froyer, G., Macromolecules, 26, 3815-3820, 1993.)... 

Subsequently, Br das et al. [25] calculated the band structures of polyisothianaphthene (1) and the 5,6-di-methyl, 5,6-dimethoxy, and 5,6-dicyano derivatives, 13-15, using the MNDO-optimized geometry of isothia-naphthene (3) corresponding to the aromatic structures and the VEH band structure methodology. 

Since 1987 calculations have been done on a variety of systems, some of which had previously been prepared and others that were predicted to have low band gaps. Some of these predicted systems were subsequently prepared, whereas others remain unknown. Thus, the pyrrole polymer derivative of 22 (.v = y = 1), namely 23, was calculated (MNDO geometry/Hiickel band calculations) to have a band gap of 0.99 eV [64] and 1.10 eV using MNDO geometry and VEH band structure calculations [65]. A related vinylogous system (24) was calcu-... 

Dougherty s group also calculated polycyclobutadiene-1,3-diyl (45) (MNDO geometry/Hiickel and VEH band structure) and found a band gap of 0.68 eV for structure 45a and a band gap of 0.00 eV for both structures 45b and 45c. Structure 45a was calculated to be a little more stable than 45b and 45c, but a clear choice... 

In Fig. 23.12, the experimental UPS He I and He II valence band spectra of PPV prepared by the tetrahy-drothiophenium precursor route are compared with the DOVS as calculated from the VEH band structure [45J. XPS core-level spectroscopy (not shown) indicates a complete conversion of the precursor polymer. The corresponding band structure is shown in Fig. 23.12b. The energy scale is fixed relative to the experimental Fermi level. The PPV is taken to be planar in the VEH calculations used here, since neutron diffraction measurements on oriented PPV at room temperature have shown that the ring torsion angles, i.e., the twist of the phenyl rings out of the vinylene plane, are on the order of T 6° [71). Such small torsion angles result in negligible effects on the calculated electronic band structure compared with that for the fully coplanar conformation. 

Fig. 23.12 He I and He II UPS valence band spectra of PPV compared with DOVS derived from VEH calculations. The VEH band structure is shown in (b). (From Ref. 45.)...

Fig. 23.30 A portion of the VEH band structure of 4BCMU-PDA, covering the energy region of the upper tt band, in comparison with the ARUPS results. (From Ref. 107.)...

Fig. 7-13 (a) VEH band structure, (b) DOS, of PoIy(acetylene). After Reference [228], reproduced with permission. 

Fig. 7-16 illustrates the computed VEH band structure for P(Py), showing 12 occupied valence bands. Fig. 7-17 in contrast shows a schematic, composite band structure picture of P(Py), assembled firom various theoretical and experimental studies. Fig. 7-18 shows VEH band structures using ab initio STO-3G optimized geometries for, respectively, P(PP) at 0% doping. Fig. 7-19 shows the VEH band... 

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