Spontaneous distortion

Non-adiabatic coupling is also termed vibronic coupling as the resulting breakdown of the adiabatic picture is due to coupling between the nuclear and electi onic motion. A well-known special case of vibronic coupling is the Jahn-Teller effect [14,164-168], in which a symmetrical molecule in a doubly degenerate electronic state will spontaneously distort so as to break the symmetry and remove the degeneracy. 

Cu and Mn, systems that have partially filled d shells with a degenerate ground state. According to the Jahn-Teller theorem, any degenerate electronic system will spontaneously distort in such a way as to remove the degeneracy (Dunitz and Orgel 1960). The distortions around Cu " have been extensively studied and may play a role in the superconductivity found in some copper oxides (Section 13.3.2), while the distortions around Mn + play an important role in the potentially useful magnetoresistive properties of LaMnOs (Section 13.3.3). 

What is not shown in the tables, are spontaneous distortions of the crystal symmetry, which are usually very small (i.e. < 10-4) and have only been observed in cubic systems, where the detection of symmetry distortions is easier. To our knowledge the largest symmetry breaking effect has been observed for cubic GdZn by Rouchy et al. (1981), namely a tetragonal distortion of (A///)ooi -3.7 x 10-4 (see section 5). 

Hexacoordinate Mn(III) and Cr(II) complexes exhibit a strong JT effect the orbitally degenerate state Eg does not correspond to the energy minimum and the geometry is spontaneously distorted along the eg-modc to a tetragonal bipyramid (eventually a rhombic component of the eg-mode admixes). 

There are several obvious mechanisms that lower both the internal energy and symmetry. These are first of all electron-nuclear bonding and interatomic and intermolecular interactions. They underlie the formation of condensed matter (atoms, molecules, and solids) by cooling which takes place in a series of typical SB. Beside these cases there are many SB that are at first sight not associated with bonding, but with spontaneous distortions of high-symmetry configurations (which... 

An important question is whether the JT vibronic coupling (JT, RT, and PJT) mechanism of SB is unique, or it is applicable to a limited number of special cases and hence there may be other mechanisms of SB that are in principle different from the JT one. The answer is that the JT mechanism of spontaneous distortions of high-symmetry configurations (chemically stable systems and transition states of chemical reactions) that leads to SB is unique, and there is no other in principle different mechanism that produces such distortions [1,2,5,11], It was also shown that in ensembles of systems (e.g. local centers in crystals), just the interaction between them (e.g. mutual polarization) cannot produce SB without local (JT) distortions of each system [12]. The JT effects provide thus the necessary and sufficient condition of SB in the systems under consideration. 

Many ferroelectric materials were found in the past. However, there is a limited number of structures that are adopted by the majority of the commercially important ferroelectric materials. In each of these structures, the ferroelectricity is tied to distortion of the coordination polyhedra of one or more of the cations in the structure. One example is the perovskite structure. Cations that seem to be especially susceptible to forming such distorted polyhedra include Ti, Zr, Nb, Ta, and Hf. All of these ions lie near crossover points between the stability of different electronic orbitals, and so may be likely to form distorted coordination polyhedra [5], Polarizable cations such as Pb and Bi are also common to many ferroelectric materials. In this case, it has been suggested that the lone pair electrons may play an important role in stabilizing ferroelectric structures. Thus the ferroelectric transition temperature and spontaneous distortion of PbTiC>3 is much larger than that of BaTiC>3. 

The Jahn-Teller (JT) effect occurs in the presence of degenerate electronic states. A spontaneous distortion of the lattice (or here of the C60 molecule) would lift the degeneracy between these states, if it reduces the symmetry at the origin of the degeneracy. If these levels are only partially occupied, the electrons occupy the... 

Here k is the wave vector of an electron in the it band and a is the spacing between the nearest C atoms on the polymer backbone. The energy dispersion given by Eq. (2.2) is shown by the dashed line in Fig. 2.2(c). Since each C atom gives only one electron, the n band is half filled and the r-PA should be a metal. However as was first shown by Pieirls, degeneracy of the band in the one dimensional (ID) metals is removed by spontaneous distortion of the ID chain. In the case of r-PA the distortion consists of dimerization shown in Fig. 2.2(b). Dimerization opens up a gap ( 1.4 eV) and the r-PA becomes a semiconductor. The band structure of the dimerized chain is shown by the solid lines in Fig. 2.2(c). 

As shown in the Sect. 2, the JT theorem predicts a spontaneous distortion of the high symmetry configuration. Group theory allows finding the irreducible representation of the non-totally symmetric vibrations in the HS conformation, which are JT active and remove the degeneracy and lead to a stabilization of the system by lowering the... 

Tetrahedral complexes generally have more intense absorptions than octahedral complexes. This is a consequence of the first (Laporte) selection rule (Section 11.3.1) transitions between d orbitals in a complex having a center of symmetry are forbidden. As a result, absorption bands for octahedral complexes are weak (small molar absorptivities) that they absorb at all is partly the result of vibrational motions that spontaneously distort complexes slightly from pure symmetry. 

Although SrTiOs, which undergoes a spontaneous distortion at low temperature, has received recent attention in band theory calculations (see Section VII. B), few of these interesting systems have yet been thoroughly investigated by many of the techniques described in this article. 

Crosslinking liquid crystalline polymers yield materials with exceptional properties due to the coupling between elastic properties and mesomorphous behavior. These compounds, especially the mesogenic elastomers, have attracted considerable attention in recent years. Like conventional elastomers, they can sustain very large deformations causing molecular extension and orientation, but they can also exhibit spontaneous distortions, some memory effects, an unusual mechanical response, and coupling between mechanical, optical and electric fields. 

Peierls Instability an instability prominent in quasi-one-dimensional systems with strong electron-phonon interactions due to which the lattice spontaneously distorts with a 2 f ( F is the Fermi wavevector) periodicity, forming a gap at the Fermi level which lowers the total energy of the system. 

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