Degenerate states, band splitting

A typical graphical solution of (8.31), for d = 3, is shown in Fig. 8.4. It is noted that, in most cases of double-adsorption, there are two localized states below the band, compared to just one for single-adsorption. This pair of localized states arises due to a splitting of the doubly-degenerate singleadsorption localized state, and is the precursor to the band of such states that would emerge as more adatoms are added to the system. 

At the low-energy side there are three bands centered at 12.0,12.7, and 13.4 eV (96,800, 102,425, and 108,070 cm , respectively). The first band has vibrational fine structure with an parent progression of about 1170 cm. The adiabatic Ip is at 11.56 eV (93,230 cm" ). These three bands can only belong to ionization from either the leg or the 3aig levels the ionization from the leg orbitals yields a positive ion in a degenerate state, so it must be split by the Jahn-Teller effect... 

Later Narayan [63] and Rabalais and Katrib [64] further examined the assignment of the low frequency PE bands as Turner et al. [57] they all came to the conclusion that the first two bands must be due to the components of the Jahn-Teller split g state of C2H6. They pointed out that the vibration causing Jahn-Teller instability must be one of the degenerate CH3 deformation vibrations, Vg (ej or Vj j ( g). Their frequencies in the neutral molecule are 1486 and 1460 cm", respectively. 

Figure 4 Selection rules for the absorption of Icp and rep light based on a transition between an orbitally nondegenerate ground state and an orbitally degenerate excited state within a magnetic field applied parallel to the axis of light propagation (a). A derivative-shaped Faraday Ai term is observed due to the Zeeman splitting of states and the associated energy separation of bands based on the AMl = 1 selection rule (b). (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007.) We note that in this example, since 5 = 0 for closed shell atoms or molecules, J = L, and Mj = Ml. Absorption and MCD spectra of zinc octaethylporphyrin (ZnOEP) in CHCI3 (c). The MCD spectrum is dominated by derivative-shaped Ai terms. (Reproduced with permission from J. Mack, Y. Asano, N. Kobayashi, M. J. Stillman, J. Am. Chem. Soc., 2005,127, 17697-17711. 2005 American Chemical Society)...

The interaction along the c-direction is enhanced in y-BN as compared to a-BN. This leads to the splitting of states in y-BN which are nearly degenerate in a-BN. The band structure of y-BN shows some similarities with those of other wurtzite IIIB-VB compounds (AIN, GaN) and also wurtzite IIB-VIB compounds (CdSe, CdS, ZnS). The reported bandwidth datafory-BN are lower valence band = 6.0 eV, upper valence band =11.0 eV, full valence band = 20.3 eV [1]. 

Hexagonal CdS is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (F). The topmost valence band (F5 - - Fi) is split owing to the crystal field and spin-orbit coupling into three spin-degenerate states. The exciton states formed with holes in these valence band states are referred to as the A, B, and C excitons, respectively. 

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