Peierls dimerization

Resonance depends sensitively on the electron-phonon coupling, which is an important property of CPs. In fact, in the SSH model of PA, it is important in the mere occurrence of the Peierls dimerization. 

Up to recently, in the field of the low dimension compounds, the most peculiar and interesting physical properties had been predicted by the theoretical physicists before the synthesis of the compounds. This is in particular the case for the Peierls instability in the 1 - D conducting systems and for the spin-Peierls dimerization in the 1 - D magnetic systems160. It seems that now the situation is somewhat reversed. The chemists synthesize systems which the physicists had never thought of before, so the quantitative theory comes after. We believe that this process will be more and more frequent. The possibilities of the chemist in terms of new types of compounds are almost without limit, if not his own imagination. In the field of the magnetic systems with subtle spin orders, very spectacular developments may be expected. 

Peierls dimerization in polyacetylene is the result of two opposite effects the CT electrons form a skeleton that opposes dimerization the tt electrons, on the contrary, tend to form alternating bonds [10]. This is modeled by the Hamiltonian (Su-Schriefifer-Heger Hamiltonian [11]) ... 

TTF-TCNQ does not show any sign of Peierls dimerization, which may depend on the fact that the band is much less than half filled, but with charge transfer occurring already in the ground state. The very small activation energy seems to be associated with ET within the stacks. 

Three-quarters localization may be achieved by changing every second carbon atom in PA to a nitrogen atom. Optimization by the one-electron, unrestricted PM3 model leads either to an SDW or a CDW solution. The result is a deformed molecule with a repetition period of four atoms. It is clear that there are two possibilities for the ground state, and that correlation effects have to be included to obtain a correct result. The conclusion is that in the one-dimensional systems, one-half band occupation leads to a trivial Peierls dimerization, while the cases of one-quarter or three-quarters occupation may lead to interesting dynamics. 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

An important property of the dimerized Peierls stale is the existence of gaps in the spectra of spin and charge excitations. For free electrons (//ci-ci=0) both gaps are equal, while in the presence of Coulomb repulsion the spin gap is smaller than the charge gap [23, 24]. In what follows, we will assume the temperature to be much smaller than these two gaps, so that we can neglect electronic excitations and replace Hcl [ A (.v)] by its ground state expectation value. 

Spin-Peierls Compounds. - A good review of the properties of the spin-Peierls compound CuGe03 has been given recently.82 A lattice dimerization,... 

Figure S (a) View at right angles to the molecular plane of TCNQ in the rubidium salt at room temperature, showing displacement and mirror plane shared by stacked anions (b) relationships of the anions in Rb(TCNQ) at 160 K (c) dimerization due to Peierls distortion (d) relationship between pairs...

This note is organized as follows. In section II, the RVA is presented using the example of the two-legspin ladders. In section III, the RVA method is applied to the study of the dimerized chain described by the Extended Peierls-Hubbard model. A nice similarity between the two-leg ladder and this system is pointed out and comparisons with DMRG calculations are made. We conclude in section IV and give some reasonable perspectives. 

We choose as model system the simplest conjugated polymers - the trans-polyacetylene. This compound shows a. dimerized structure with an altemance between double bond (1.35A) and single bond (1.45A) the monomer is then simply a double bond (see figure (8)). The tt electrons are assumed to be effectively describe not by the full PPP Hamiltonian but by the Extended Peierls-Hubbardmodel (EPH) [17, 14], a short version of it) for simplicity... 

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