Electronic states distortions

How do these conclusions fit in with the Jahn-Teller (49) theorem telling us that molecules with orbitally degenerate electronic states distort to lose this degeneracy Some of the distortions we have seen and rationalized are allowed under the Jahn-Teller scheme, but very importantly others are not (50). For example,... 

If there is only significant overlap with one excited vibrational state, equation (Bl.2.11) simplifies fiirther. In fact, if the mitial vibrational state is v. = 0, which is usually the case, and there is not significant distortion of the molecule in the excited electronic state, which may or may not hold true, then tire intensity is given by... 

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. 

In his classical paper, Renner [7] first explained the physical background of the vibronic coupling in triatomic molecules. He concluded that the splitting of the bending potential curves at small distortions of linearity has to depend on p, being thus mostly pronounced in H electronic state. Renner developed the system of two coupled Schrbdinger equations and solved it for H states in the harmonic approximation by means of the perturbation theory. 

Semiconductivity in oxide glasses involves polarons. An electron in a localized state distorts its surroundings to some extent, and this combination of the electron plus its distortion is called a polaron. As the electron moves, the distortion moves with it through the lattice. In oxide glasses the polarons are very localized, because of substantial electrostatic interactions between the electrons and the lattice. Conduction is assisted by electron-phonon coupling, ie, the lattice vibrations help transfer the charge carriers from one site to another. The polarons are said to "hop" between sites. 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

There is a second point to note in dementi s paper above where he speaks of 3d and 4f functions. These atomic orbitals play no part in the description of atomic electronic ground states for first- and second-row atoms, but on molecule formation the atomic electron density distorts and such polarization functions are needed to accurately describe the distortion. 

In conclusion, it can be stated that the observation of structural distortions of compounds with a 6s lone pair is strongly dependent on the electronic states of the bonding partners and the overall structural surroundings in the solid material. 

However, there also exists a third possibility. By using a famous relation due to Dirac, the relativistic effects can be (in a nonunique way) divided into spin-independent and spin-dependent terms. The former are collectively called scalar relativistic effects and the latter are subsumed under the name spin-orbit coupling (SOC). The scalar relativistic effects can be straightforwardly included in the one-electron Hamiltonian operator h. Unless the investigated elements are very heavy, this recovers the major part of the distortion of the orbitals due to relativity. The SOC terms may be treated in a second step by perturbation theory. This is the preferred way of approaching molecular properties and only breaks down in the presence of very heavy elements or near degeneracy of the investigated electronic state. 

Here, we pointed to the problem of theoretical representation, in particular, in two aspects of theory (i) the existence of highly mobile atoms at the surface such as hydrogen, which are usually not considered in the atomistic models and (ii) the importance of bandgaps and relative energy levels of electronic states, which is often distorted in local density approximations. In both respects, a quick fix to the problem is not very likely. However, as both theory and experiment continue to be developed and applied in common research projects, it can be expected that the actual understanding of the processes involved in reaction on model catalysts will substantially improve over the next 10 years. After all, the ability to trace reactions and to account for the position and charge state of each reactant is already a realization of what seemed 20 years ago a fiction rather than fact. 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

This is accompanied by a structural distortion and thus, according to the above model, to an electronic state which, due to the symmetry of the electronic distribution lies precisely at midgap. This single state, having half occupied levels in the gap, has been termed native solitons. 

Figure 6. On the right, the n-system ofTMMand the electronic configuration of the ground state are shown ( 2 labels are used). The left panel presents electronic states of TMM at the ground state equilibrium D h geometry, and at the two Jan-Teller 2 distorted structures (equilibrium geometries of the 1 B and 1 i states). The corresponding adiabatic singlet-triplet gaps are also shown.

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