Alternating trans- polyacetylene

The gap in alternating trans-polyacetylene is described on the basis of its quasi-particle band structure and the question of the Bloch-type conduction in DNA (either through doping or the possibility of intrinsic conduction due to charge transfer from the sugar rings to the nucleotide bases) is discussed. This is followed by a brief discussion of the electronic structure of disordered polypeptide chains. 

If one performs a minimal (ST0-3G) basis calculation for alternating trans-polyacetylene (PA) using bond distances determined from geometry optimization with this base, one obtains a gap of 8.91 eV /22/. This is more than four times the experimental value of 2 eV which is the position of the first peak in the absorption spectrum of pure trans PA /30/. (It should be mentioned that in trans PA there is no exciton band /G/ and therefore one can take this value as the gap value.) If one... 

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). 

Fig. 4.1 The chemical structures of several relevant polymers are illustrated. There is a carbon atom at each vertex, and the hydrogen atoms are not shown. PE(CHf polyethylene, or PE, with only the C-H single bonds shown PA trans -polyacetylene PPV poly(p t -phenylenevinylene) and PPP poly(pita -phenylene). The lower three polymers are conjugated, according to the alternating single and double bond system.

When two trans-polyacetylene chains with different phases are put together, an obvious disturbance occurs in the standard conjugation pattern. The bond alternation defect that appears is known as a neutral soliton (Fig. 1.7). This kind of quasi-particle has an unpaired electron but is electrically neutral and is isoenergetically mobile along the polymer chain in both directions. This soliton gives rise to a state in the middle of the otherwise empty energy gap that can be occupied by zero, one or two electrons (Fig. 1.8). 

The experiments showed clear differences of behavior between polyacetylene in the cis and trans forms. Namely, SEE and OE are obtained in the cis and trans forms, respectively. In other words, the electronic spins are fixed in ds-polyacetylene, and they become mobile in the trans form. This result is quite consistent with the soliton picture. In cw-polyacetylene, a bond alternation defect divides the chain into two parts ds-transoid and frans-cisoid, whose energies are different (Fig. 8a). Thus, to minimize energy, the spin defect will be trapped at one end of the chain (Fig. 8b). On the other hand, in trans-polyacetylene the chain is divided into two degenerate parts. The defect should therefore be free to move (Fig. 9). 

Figure 1 Regular (Model I) and alternating (Model II) trans-polyacetylene structures. The unit cells are surrounded by broken lines...

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. 

I. Ciofini, C. Adamo, and H. Chermette (2005) Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory. J. Chem. Phys. 123, p. 121102... 

Figure 3 Structure of trans polyacetylene with (a) non-alternating and (b) alternating C-C bond lengths...

The size of electroconductivity compressed samples MoClj j(C3(, jHgQ j), measured at a direct current at a room temperature-( 1.3 3.3) 10 Ohm -cm is in a range of values for a trans-polyacetylene and characterizes a composite as weak dielectric or the semiconductor. The positioned size of conductivity of samples at an alternating current tr = (3.1 4.7)-10 Ohm cm can answer presence of ionic (proton) conductivity that can be connected with presence of mobile atoms of hydrogen at structure of polymer. 

Figure 7.8 HOCO and LUCO orbital diagrams of trans-polyacetylene, PA. Two unit cells of C2H2 are shown both orbitals correspond to k = it/a. The gap between the two orbitals is primarily due to the bond length alternation (BLA) of the shorter (=) and longer (—) C-C bonds...

As discussed in A Word About... Polyacetylene and Conducting Polymers (p. 421), thin films of all-cis or all-trans polyacetylene have different appearances, being coppery or silvery, respectively. Draw structures of the all-cis or aW-trans isomers of polyacetylene as well as the alternating cis-trans isomer. 

The polymer trans-polyacetylene, trans-(CH)j. contains a very long chain of alternating single and double carbon-carbon bonds. The term trans refers to the configurations of the two hydrogens bonded to each pair of doubly bonded carbons (Fig. 17.7). Analysis of the... 

Figure 5.57. Synthetic routes for cis- and trans-polyacetylene. It should be noted that the trans-isomer of PA is more stable than the cis-isomer since the former has two degenerate ground states (two energetically-equivalent arrangements of alternating double bonds).

In all cases where the question concerning the relative stabilities of equidistant versus bond alternating structures arises (polyyne [20,21, polyacetylene 22-27, polymethineimine 28,29 ) the latter are more stable within the framework of the restricted Hartree Fock approximation. For polyyne and polyacetylene this issue is in accord with the well known concept of a Peierls distortion jsoj. The occurence of Hartree Fock instabilities (see e.g. refs. 31,32 ) in the case of the equidistant, metallic structures of polyyne (cumulene) and all-trans polyacetylene points, however, to the need for improved methods going beyond the independent particle model. First efforts in this direction 27 show that at the level of second order Moller-Plesset perturbation theory the alternant configuration of polyacetylene is still preferred energetically although as expected the energy difference to the equidistant structures becomes smaller. 

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