Phenylenes ground-state energy

Consider the stracture of other condnctive polymers snch as poly(p-phenylene), poly(pyrrole), poly(thiophene), and poly(artiline). These polymers do not support soli-ton-like defects becanse the ground state energy of the quinoid form is substantially higher than the aromatic benzenoid stracture. As a result, the charge defects on these polymers are different. As an example, consider the oxidation of polypyrrole (Figure 3). 

The determination of the ground-state energies of the [Njphenylenes is of crucial importance in the evaluation of their aromaticity [3] and strain. On the other hand, their frontier orbital separation constitutes a measure of their kinetic stability [123] and is central to organic conductor applications [124]. The excited states of the phenylenes are also of interest for probing the changes in aromaticity that occur... 

Like their para isomers, 43,47, and 53 have open-shell singlet (M ) ground states (Table 4). The triplet ( A ) and quintet ( A ) states are predicted to be about 2 and 20-25 kcal/mol higher in energy, respectively. Thus, the S-Q splittings are approximately 5 kcal/mol smaller than the corresponding ones of the para isomers (13, 16 and 8, respectively), but qualitatively very similar, as expected due to the similar electronic properties of the o- and p-phenylene linkers. 

Inherently, the orf/zo-phenylene spacer induces only a weak energy difference between the closed and open forms, but the ground-state structure of all MPB 7b-d was found to be well-defined, with or without P-B interaction. A different situation was observed for the related DPB 8a and TPB 9.24 The corresponding nB NMR signals (<5 = 43.1 ppm for 8a and 50.1 ppm for 9) are in between those of triarylboranes ( 70 ppm) and tetracoordinate derivatives thereof ( 0 ppm), suggesting a rapid equilibrium in solution between the open and closed forms (Figure 12). This hypothesis was further corroborated by low-temperature NMR experiments and DFT calculations. The minima associated with the open and closed forms were found to be almost isoenergetic (AG < 3 kcal/mol at 25 °C). 

Yang, S.I., R.K. Lammi, J. Seth, J.A. Riggs, T. Aral, D. Kim, D.F. Bocian, D. Holten, and J.S. Lindsey (1998). Excited-state energy transfer and ground-state hole/electron hopping in p-phenylene-linked porphyrin dimers. J. Phys. Chem. B 102(47), 9426-9436. 

Figure 4-2. Total energy as a function of a structural deformation coordinate. (a) 7Van5-polyacetylene (degenerate ground-state system) (b) poly( p-phenylene) nondegenerate ground-state system).

Although VEH uses a set of parameterized one-electron orbitals, its accuracy approaches that of true ab initio methods. VEH gives ground-state properties, ionization potentials and energy gaps typically within 0.1 eV of the experimental values. The evolution of the band structure of poly(l,4-phenylene) (10 poly(p-phenylene), PPP) during inclusion of sodium is shown in Figure 3. The relaxation of the polymer chain in the vicinity of added electrons produces states in the band gap. These eventually fuse with the valence and conduction bands as Na content increases. These states and their relevance to the properties of real systems has been the focus of much excitement and debate. 

Initially, the calculated results for finite phenylene vinylene, which is A in Fig. 2, are shown. The first virtual transition of the sequence is from ground to Bu state. This transition is mainly composed of that from the highest occupied molecular orbital to the lowest unoccupied orbital, where a Jt-electron which is distributed on C=C double bonds and their alternating bonds, moves into another orbital which is distributed mainly on the other alternating bonds. This type of transition occurs not only for this finite phenylene vinylene but also for all of the molecules we have calculated in Fig 2. The next virtual transition in the sequence is from By to Ag excited state. This mainly comprises three orbital transitions, because the Ag excited states of this energy area are expressed mainly as a linear combination of three configurations according to the result of Cl. The three orbital transitions are HOMO-1 to HOMO, HOMO to LUMO and LUMO to LUMO+1, as shown in Fig. 3, where HOMO-1 represents the otbital level just below HOMO, and LUMO+1 represents the level above LUMO. 

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