Spectral degeneracy

El Ahrach, H. 1., Bachelot, R., Vial, A., Lerondel, G., Plain, J., Royer, P. and Spooera, O. (2007). Spectral degeneracy breaking of the plasmon resnance of single metal nanoparticles by nanoscale near-field photopolymerization. Phys. Rev. Lett. 98 10741 (007) [4 pages]. 

Keywords Jahn-Teller effect Icosahedral symmetry S5 symmetry Spectral graph-theory Electronic/spectral degeneracy... 

Wall M R, Dieckmann T, Feigon J and Neuhauser D 1998 Two-dimensional filter-diagonalization spectral inversion of 2D NMR time-correlation signals including degeneracies Chem. Phys. Lett. 291 465... 

Most of the complexes to be described here have trigonal symmetry. For a trigonal center, the splitting of the spectral bands due to the lifting of orientational degeneracy is described by two parameters, A1 and A2. The parameter A is proportional to the hydrostatic component of the stress and gives rise to a shift in frequency that is independent of the stress direction, whereas A2 gives rise to a shift that depends on the orientation of the center. 

Here I stands for the intensity of the spectral hnes N is the atom number density in cm Z is the partition function E and y are the energies and degeneracy s of the upper levels, respectively and A and A are the Einstein coefficient and wavelength, respectively, for the observed transitions. When changing the concentration Nt relative to that Nm the line intensities ft and 7m will likewise change, and according to (6.1) one should obtain a cahbration curve with constant slope (Davies et al. 1995 Ciucci et al. 1999 Hou and Jones 2000). 

In his derivation, Frieden uses the concept of a number-count set nm, each member representing the number of photons counted in a spectral interval. The total number of photons m= x nm is taken as known to be N. In terms of frequencies vm, the values of the object spectrum are given by om = nmhvm, where h is Planck s constant. The number of normal modes or degrees of freedom available for occupation by photons of frequency vw is labeled zm. The Bose-Einstein degeneracy factor... 

The presence of two CT bands is typical for complexes with mono-substituted benzenes. Upon substitution, the degeneracy of the HOMOs of benzene is lifted. Therefore, the two CT bands can be associated to two complexes with a distinct geometry. For the DEA/PMDA DAC, the substantially slower CR dynamics observed upon 400 nm excitation should be therefore due to the different geometry of the DAC rather than to the spectral effect. Such a slower CR dynamics might be related to a smaller V and/or to a larger driving force. 

Regarding the photoionization of predominantly ligand MOs, many authors proceed on the assumption that there is a crude relationship between spectral intensity and orbital degeneracy. This assumption should be viewed with caution, however, since the generalization is accurate only for the ionization of electrons with similar localization properties. 

In reality the cylindrical LF has to be added to the octahedral interaction which lifts the degeneracy of the 2D term as described in Sect. 3.1. When combining these two perturbations it matters whether the cylindrical field coincides with the trigonal or with the tetragonal directions of the octahedron, because the remaining D3i or DAh subgroups are not equivalent. Two different spectral patterns thus will result from this superposition of octahedral and cylindrical ligand fields. 

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