Jahn-Teller-Peierls distortions

In general, then, a band which is 1/3,1/4. .. l/p occupied is subject to Peierls instability with respect to a tri-, tetra-, / -merisation. It is important to remind you at this point that the possibility of a Jahn-Teller instability does not always mean the distortion occurs. The same applies for Peierls instability. There are several reasons. First of all, Peierls instability holds rigorously for ideal one-dimensional materials and reality is a more complicated three-dimensional space. Second, as in the case of molecules, when high-spin states are preferred, the distortion is not favored (see Problem 7 for an example). Third, even in the case of low-spin systems, the distortion may have additional consequences, e.g., weakening of spectator bonds. Coupled destabilizing effects can dampen or even prevent distortion. In the H2 case described above, there is no effect opposing the distortion, and dimerization is complete, i.e., fully independent H2 molecules result from our hypothetical chain. 

Before leaving this section, we need to tell you a very important point that beginners often forget. As in the case of Jahn-Teller instability, Peierls instability occurs for particular electron counts. For example, dimerization (a distortion leading to the doubling of the elementary unit cell parameter) is expected to occur only in the case of a half-filled band (or nearly half-filled if the material is not stoichiometric), i.e., Peierls instability depends on band population. 

As a result of the second-order effect, also large C4, 4 2 monocycles are expected to be acetylenic as is explained by the Peierls distortion that is seen in one-dimensional electronic systems with periodic potentials [35b-e]. This effect is associated with the distortion of the potential energy surface to lower the total energy of the system through electron-phonon coupling [35b]. For a molecular system, the same effect is also referred to as the second-order Jahn Teller (SOJT) effect that leads to the vibrational-mode... 

Fig. 9.10. The Peierls effect has the same origin as the Jahn-Teller effect in removing the electronic level degeneracy by distorting the tem Jahn, E. Teller, Proc. Roy. Soc. A161 (1937) 220). (a) The electrons occupy half the FEZ, i.e. a standing for the nearest-neighbour dis-...

An important aim of the book is then to show how common orbital situations arise throughout the whole chemical spectrum. For example, there are isomorphisms between the electronic structure of CHj, Fe(CO)4, and Ni(PRj)s and between the Jahn-Teller instability in cyclobutadiene and the Peierls distortion in solids, These relationships will be highlighted, and to a certain extent, we have chosen problems that allow us to make such theoretical connections across the traditional boundaries between the subdisciplines of chemistry,... 

Peierls distortion Distortion that occurs to break the symmetry in order to avoid a degeneracy of states at the Fermi level, similar to the Jahn Teller distortion in molecular compounds... 

Consider the consequences of a Jahn-Teller distortion in each cyclobutadiene unit in poly(l,3-cyclobutadiene) that introduces long and short bonds into the ring (giving a Peierls distortion to the polymer). Sketch how this would change the band structure developed in Exercise 3. 

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