Polyacetylene electronic structures

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

Contrary to naive expectation, an extended ir-electron system snch as that in the original silvery polyacetylene film does not imply perfect bond conjngation or perfectly like bonds, or conduction along the chain It only implies a degree of charge-density delocalization. Such a material has the electronic structure of a... 

Both theoretical and experimental evidence suggest that the precise nature of the charge carriers in conjugated polymer systems varies from material to material, and it is still a subject of debate in many cases. A discussion of the various theoretical models for the electronic structure of conjugated polymers is given below, using polyacetylene and poly(paraphenylene) as examples. More detailed information on these materials and the applicability of these theoretical models is given in subsequent sections. 

When the 7r-systerns of two or more double bonds overlap, as in conjugated dienes and polyenes, the 7r-clccIrons will be delocalized. This has chemical consequences, which implies that the range of possible chemical reactions is vastly extended over that of the alkenes. Examples are various pericyclic reactions or charge transport in doped polyacetylenes. A detailed understanding of the electronic structure of polyenes is therefore of utmost importance for development within this field. We will first discuss the structure of dienes and polyenes based on theoretical studies. Thereafter the results from experimental studies are presented and discussed. 

Because the extension of the polaron in polyene radical cations is finite (10-20 double bonds depending on the type of calculation), its electronic structure is independent of the number of double bonds attached to either side of it, so that the two lines in Figure 29 must bend at some point to meet the abscissa horizontally, as indicated by the dashed curves. Apparently, the point of inflection has not been reached for n = 15, but it is of interest that the curve for the first excited state could well extrapolate to 0.35 eV, which happens to be where the absorption of a polaron in polyacetylene has been observed300. If this is true, a second, more intense absorption band should occur between 0.5 and 0.7 eV, but the corresponding experiments have not yet been carried out. 

In real tran -polyacetylene, the structure is dimerized with two carbon atoms in the repeat unit. Thus the tt band is divided into occupied tt and unoccupied n bands. The bond-alternated structure of polyacetylene is characterishc of conjugated polymers. Consequently, since there are no partially filled bands, conjugated polymers are expected to be semiconductors, as pointed out earlier. However, for conducting polymers the interconnection of chemical and electronic structure is much more complex because of the relevance of non-linear excitations such as solitons (Heeger, 2001). 

Many phenomena such as dislocations, electronic structures of polyacetylenes and other solids, Josephson junctions, spin dynamics and charge density waves in low-dimensional solids, fast ion conduction and phase transitions are being explained by invoking the concept of solitons. Solitons are exact analytical solutions of non-linear wave equations corresponding to bell-shaped or step-like changes in the variable (Ogurtani, 1983). They can move through a material with constant amplitude and velocity or remain stationary when two of them collide they are unmodified. The soliton concept has been employed in solid state chemistry to explain diverse phenomena. 

This shows that the TB MO calculation correctly predicts the origin of the chemical shift and electronic structure associated with the structure of the polymers. Furthermore, TB INDO/S calculations have been carried out on the seven polyacetylene chains which take an orthorhombic form(9). From these results it has been demonstrated that the chemical shift is very sensitive to intermolecular interactions and the TB MO calculation provides useful information about the band structure. 

The change that converts the polyacetylene molecule from a nonconductive to a conductive state involves the addition of some foreign material, a dopant, to the polymer. Two kinds of dopants are used those that attract electrons and remove them from the bonds that make up a polymer molecule, and those that donate electrons to the molecule. In either case, the normal electronic structure of the molecule is disrupted, and individual electrons within the molecule become more mobile. As their mobility increases, they tend to flow through a molecule and from one molecule to the next when an external electrical potential is applied to the polymer. 

Another well-known example of the same problem of semiempirical DFT is electronic structures of /ran.v-polacetylene [99-105], This is a one-dimensional system subject to a Pierels distortion. Therefore, it is an insulator with a bond-alternated structure at a sufficiently low temperature. However, semiempirical DFT fails to reproduce a large band gap or bond-alternated structure, predicting incorrectly that frans-polyacetylene is (nearly) metallic at zero temperature. This is another manifestation of DFT s nonphysical tendency to favor delocalized wave functions. The HF or HF-based correlated theories do not exhibit this problem. 

Impurity and Aperiodicity Effects in Polymers.—The presence of various impurity centres (cations and water in DNA, halogens in polyacetylenes, etc.) contributes basically to the physics of polymeric materials. Many polymers (like proteins or DNA) are, however, by their very nature aperiodic. The inclusion of these effects considerably complicates the electronic structure investigations both from the conceptual and computational points of view. We briefly mentioned earlier the theoretical possibilities of accounting for such effects. Apart from the simplest ones, periodic cluster calculations, virtual crystal approximation, and Dean s method in its simplest form, the application of these theoretical methods [the coherent potential approximation (CPA),103 Dean s method in its SCF form,51 the Hartree-Fock Green s matrix (resolvent) method, etc.] is a tedious work, usually necessitating more computational effort than the periodic calculations... 

H3NBH3 is isoelectronic with ethane, H2NBH2 is isoelectronic with ethylene, andHNBH is isoelectronic with acetylene. Derive the band structure and the DOS for planar poly- -BHNH- (isoelectronic to polyacetylene) with a single B-N distance and predict its conductivity and stability with respect to a Peierls distortion. Only consider the tt electronic structure. 

In the case of a conjugated polymer like polyacetylene, as shown in Figs. 1.8(a) and 1.8(b), the situation with respect to rotation about the nominally single bonds is very different it is controlled by the electronic structure of the backbone bonds rather than by steric hindrance. As will become clear later, when this type of polymer is discussed in relation to conduction, the partial... 

The simplest polymer with a conjugated backbone is polyacetylene. Its structure is similar to that of the saturated polymer polyethylene, but has one of the hydrogen atoms removed from each carbon of the polyethylene chain. Each carbon atom in the polyacetylene chain thus has one excess electron which is not involved in the basic chemical binding. And if the separation of the carbon were constant, polyacetylene would conduct along the chain in other words it would behave like a metal in one dimension. But unfortunately this is not true as the free electrons tend to get localized in shorter double bonds. Conjugated polymers can at best be expected to display semiconducting properties. 

Questions that had been of fundamental importance to quantum chemistry for many decades were addressed. When the existence of bond alternation in trans-polyacetylene was been demonstrated [14,15], a fundamental issue that dates to the beginnings of quantum chemistry was resolved. The relative importance of the electron-electron and electron-lattice interactions in Ti-electron macromolecules quickly emerged as an issue and continues to be vigorously debated even today. Aspects of the theory of one-dimensional electronic structures were applied to these real systems. The important role of disorder on the electronic structure and properties of these low dimensional metals and semiconductors was immediately evident. The importance of structural relaxation in the excited state (solitons, polarons and bipolarons) quickly emerged. 

Shortly after the initial discovery of doping and the metal-insulator transition in polyacetylene, a theoretical description of the electronic structure was... 

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