Core excitation spectra

Fronzoni G, Decleva P (1998) Ab-initio Cl calculations of the C Is and Cl Is and 2p core excitation spectra of the freon molecules CC14, CFC13, CF2C12, and CF3C1. Chem Phys 237 21-42 Fronzoni G, Stener M, Decleva P, De Alti G (1998) Theoretical study of the Cl Is and 2p near edge photoabsorption spectra of HC1 by accurate ab-initio configuration interaction and density functional approaches. Chem Phys 232 9-23... 

Fig. 23b. Calculated and measured 3d core-excitation spectra. In the spectra with coupling the solid curves correspond to XPS and the dotted curves to EELS. The calculated spectra have been convoluted by a Lorentzian of 1.2eV FWHM to include lifetime broadening. The total energy of the core hole has been subtracted. The experimental spectra have been taken from the following works. XPS Ba (Hufner and Steiner 1985) LaFj (Suzuki et al. 1974) LajO, La (Schneider et al. 1985) Ce02 (Wuilloud et al. 1984b). EELS Ba (Kanski and Wendin 1981) LajOj, La (Schneider et al. 1985) CeOj (Wuilloud et al. 1984b). The XPS and EELS spectra have a common energy scale and the centers of gravity of the EELS final states are indicated by arrows in the corresponding XPS and EELS spectra (Schneider et al. 1985).

In this chapter we aim to diseuss the requirements, challenges, and pitfalls associated with attempting to theoretically model molecular properties for such systems that can be directly compared to experimental data, such as valence excitation spectra, core-excitation spectra, thermodynamics of chemical reactions, and redox properties. 

Gibbons, R, Bradley, C.R., and Eraundorf, P.B. (1987). How to remove multiple scattering from core-excitation spectra iii Varying the mean free path. Ultramicroscopy 21 305-312. 

XAS, on the other hand has a core-excited final state for which the effect of the core-hole must be taken into account. To obtain the full spectrum, i.e., valence, Rydberg and continuum excitations, we use the Slater transition-state approach [22,23] with a half-occupied core-hole. This provides a balanced description of both initial and final states allowing the same orbitals to be used to describe both initial and final states and all transitions are obtained in one calculation [23,24]. Details of the computational procedure can be found in the original papers as referenced in the following sections. In the present chapter, the focus is on the surface chemical bond and the spectra, measured or calculated, will mainly be used to obtain the required information on the electronic structure. 

Fig. 9 Resonant photoemission data from a film of Ce2 C72 recorded at photon energies crossing the Ce-N4 3 core-level excitation spectrum. The numbers refer to the energy positions as indicated in the right panel of Fig. 8 and are 1 94 eV 2 107.2 eV 3 110.2 eV 4 123 eV (at the maximum of the giant resonance, spectrum shown in black) 5 150 eV...

Now the question arises, as before, of the degree to which the rare earth s valence electrons (and in particular 5d) are populated by hybridisation with the electron-rich 7T-MO system of the C72 host molecule. Figure 9 shows resonant photoemission spectra of Ce2 C72, with photon energies selected to span the N4>5 core level excitation spectrum, as indicated in Fig. 8. 

Before we proceed to discuss the valence spectrum in greater detail, it is very instructive first to consider the Is deep core level spectrum, which is not complicated by the presence of several overlapping satellite spectra and therefore gives direct information about the ionic excitation level structure. If the core level spectrum is experimentally available, this may then be of great help for interpreting valence level spectra. 

Fig. 48. Experimental valence level ESCA spectrum for C0124). Ionic excitation levels (top of picture) inferred from the core hole spectrum in Fig. 47...

Since the accuracy of the asymptotic expansion rapidly gets even better with increasing L, there is clearly no need to perform numerical solutions to the Schrodinger equation for L > 7. The entire singly excited spectrum of helium is covered by a combination of high precision variational solutions for small n and L, quantum defect extrapolations for high n, and asymptotic expansions based on the core polarization model for high L. The complete asymptotic expansion for helium up to (r-10) is [36,29]... 

The core loss structure in electron energy loss spectroscopy (EELS) is known to be very similar to XANES, because the core loss spectrum is caused by physically the same process as that of x-ray absorption, corresponding to the electronic transition from core level to unoccupied excited states. Therefore, the theoretical analysis for ELNES can be carried out by almost the same procedure used for that of XANES. For the chemical state analysis of oxide ceramics, ELNES has also been proved to be very efficient with theoretical analysis by DV-Xa cluster calculation . The cluster calculation indicates that the core-hole effect due to the electronic transition is sometimes very important and the ground state calculation gives a serious errors in excited electronic state. 

Donor-7i)3-Donor chromophores are another group of propeller-shaped chromophores. TPA studies of 117 indicated only a small 5 of 30 GM at 740 nm. The shape of the excitation spectrum showed that the maximum must be located at X < 740 nm [505]. Chromophore 117 has an amino nitrogen at the central core as donor, which combines three unsaturated arms with end capped amino... 

The spectrum serves to Illuminate several of the characteristics of core-excited resonances. The "doublet" structure, repeated at intervals of approximately 170 meV, is characteristic of the >2 C-C symmetric stretch. The spacing between the first and second features in each pair is 60 meV. We attribute these to two quanta of the CH2 torsional mode, l.e. 2V1,. These characteristic energies in the anion are quite close to those of the Rydberg "parent" state, as expected. The existence of the low frequency modes is a clear indication of the long lifetime of the Feshbach resonance relative to that of the B2g shape resonance discussed previously. 

In Figure 4 we show the transmission spectrum of benzene at higher energies. The lowest feature Is the second "shape" resonance ( B2g). Above this lie several smaller features which must correspond primarily to core-excited states. Detailed studies of the decay channels of these resonances have not yet been carried out, although some Information is available. The vertical arrows in Figure 4 indicate the energies at which maxima occur in the excitation functions for Vi of the ground electronic state of ben-... 

Fig. 7.2. A typical inner-shell excitation spectrum the 3p spectrum of Ca. Note the wide doublet splitting between the two series limits due to the large spin-orbit interaction of the nearly-closed core, the prominent Rydberg series and the broad, asymmetric autoionising resonances (after J.-P. Connerade et aL [302]).

For excitation from core states of atoms to a final continuum state in the solid, an important observation is the occurrence of quasiperiodic modulations in the intensity of the observed continuous spectrum. These modulations are readily explained as arising from interference between the wave of the escaping electron, and a backscattering off the nearest neighbour atoms. They are called extended X-ray absorption fine structure or EXAFS for short. They are very important, because they can be rather simply analysed to yield the distance between the atom on which the core excitation has taken place and its nearest neihbours. There is an extensive literature on this technique [643] which is a very powerful one, since it can be applied to all kinds of compounds each atom has its own particular, quasiatomic core states, and so the method is atom-specific. The only complication is when the same atom can occupy two different sites with different nearest neighbours. 

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