Degeneracy, removal

The regular octahedron of a d9 system is an abstraction since the JT effect applies the electronic ground state cannot be orbitally degenerate so that the tetragonal (eg-mode) distortion leads to the degeneracy removal. 

Sampling and Rigid-Body Minimization in Molecular Docking Revisited—On-the-Fly Optimization and Degeneracy Removal. 

D. A. Gschwend and I. D. Kuntz. Orientational sampling and rigid-body minimization in molecular docking revisited On-the-fly optimization and degeneracy removal. Journal of Computer-Aided Molecular Design, 10 123-132, 1996. 

The enumeration becomes more compHcated in the case where the electrons are equivalent, as here the exclusion principle must be taken into account. Hence it is necessary to write down the complete system of eight quantum numbers and strike out all the cases where all the quantum numbers of the two electrons are the same. In the first instance, therefore, we imagine the directional degeneracy removed... 

The first term of Eq. 12.3 represents the interaction of the nuclear quadrupole moment with a non-cubic external electric field in the (0,0,0) coordinates and determines the nuclear quadrupole splitting, the conseqnence of the degeneracy removal of the excited state. The second term describes the interaction of the nuclear charge with the electronic clond around the nuclens, and determines the shift of the nuclear level energies. 

If A 0, each state is doubly degenerate, a degeneracy removed by rotational interaction to give A doubling. When /I = 0, if Lj + 2 + /i + X 4 is even there will be one more 27+ state than 27 state and if it is odd, one more 27 state than 27+ state. 

Two other examples will sufhce. Methane physisorbs on NaCl(lOO) and an early study showed that the symmetrical, IR-inactive v mode could now be observed [97]. In more recent work, polarized FTIR rehection spectroscopy was used to determine that on being adsorbed, the three-fold degeneracies of the vs and v modes were partially removed [98]. This hnding allowed consideration of possible adsorbate-adsorbent geometries one was that of a tripod with three of the methane hydrogens on the surface. The systems were at between 4 and 40 K so that the equilibrium pressure was very low, about 10 atm. 

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. 

If the solution of the zero-order Schiodinger equation [i.e., all teiins in (17) except V(r,Ro) are neglected] yields an/-fold degenerate electronic term, the degeneracy may be removed by the vibronic coupling tenns. If F) and T ) are the two degenerate wave functions, then the vibronic coupling constant... 

Accepting the Longuet-Higgins rule as the basis for the search of conical intersection, it is necessary to look for the appropriate loop. The -type degeneracy of a Jahn-Teller system is removed by a nonsymmetric motion. 

Figure 25 shows the results of the 2 distortion induced by a degenerate e 2 vibration that removes the Dsa degeneracy (compare Fig. 23). By symmetry, five...

Introduction of the vibronic coupling (s / 0) causes removal of the above degeneracy and leads to the general vibronic-spin-orbit pattern presented in the central part of Figure 3. Each vibronic level is characterized by a particular K... 

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

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