The Valence Hole Spectrum of

Quasi-Particle Properties of Hole Levels in Molecules 

Judging from experiment (Fig. 46), the 20g total relaxation shift is 5 eV (assuming 

Finally, it should be mentioned that the present assignment of the peak structure in Fig. 46 agrees with the recent measurements by Weigold et al.128). Therefore, the gross features of the valence hole spectrum of N2 can be said to be fairly well understood even though the region above 20 eV cannot yet be well reproduced by first principles calculations. 

The CO molecule has the same number of electrons as N2 but because it is heteronuclear, the bonds are markedly localized towards either nucleus. All holes are therefore created predominantly on one nucleus or the other, and a HF MO A SCF calculation will directly give a larger fraction of the total relaxation energy than in N2. In particular, the HF MO scheme gives the correct ordering of the valence hole levels in contrast to the case of N2. 

Having discussed hole level spectra in N2 in considerable detail, we only give a brief presentation of the corresponding results in CO and a few other systems. Fig. 47 shows 

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Fig. S a Valence band spectra of Gd C82 (grey) and C82 (black) measured with Al Ka x-rays, b Symbols Gd 4f photoemission after subtraction of the empty C82 C 2s/2p spectrum. The vertical lines are individual components of atomic calculations for a 4f> multiplet, and the solid curve is their broadened sum. c Gd-N4>5 x-ray absorption spectrum (Gd 4d-4f excitations) of Gd C82. The complex lineshape comes from the widely spaced multiplet components resulting from the strong Coulomb interaction between the single hole in the 4d shell and the eight electrons present in the 4f shell in the x-ray absorption final state [see Fig. lc]. The arrows represent the two photon energies used for the data shown in panel d. d Resonant photoemission data of the valence band region of Gd C82 recorded off (hv=137 eV) and on (hv=149 eV) the Gd 4d-4f giant resonance...

Fig. 44. (a) Schematic picture of the real part of the self-energy for a valence hole, together with graphical solutions , and of the Dyson equation (Eq. (15)). (b) is meant to represent a typical outer-valence hole spectrum while (c) and (d) describe the possible behaviour of inner-valence holes. (bHd) are connected with the solutions -( ) resp. Note that in principle the self-energy is different for different valence holes, contrary to what is suggested in (a)... 

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

Thus the spectrum which arises when Eq. (8) is Fourier transformed consists of a set of -functions at the energies corresponding to the stationary states of the ion (which via the theorem of Koopmans) are the one-electron eigenvalues of the Hartree-Fock equations). The valence bond description of photoelectron spectroscopy provides a novel perspective of the origin of the canonical molecular orbitals of a molecule. Tlie CMOs are seen to arise as a linear combination of LMOs (which can be considered as imcorrelated VB pairs) and coefficients in this combination are the probability amplitudes for a hole to be found in the various LMOs of the molecule. 

In course of subsequent work Bubeck, Tieke, and Wegner discovered that the action spectrum for photopolymerization of undoped diacetylene multilayers extends into the visible provided some polymer formed in course of previous UV-irradiation is present. Since obviously excitation of the polymer can sensitize the reaction this effect has been termed self-sensitization. Checking the absorption spectrum of the polymer produced via self-sensitization assured that the final product is identical with the product obtained under UV excitation of the monomer. Later work by Braunschweig and Bassler demonstrated, that the effect is not confined to multilayer systems but is also present in partially polymerized single crystalline TS-6, albeit with lower efficiency. Interestingly, the action spectrum of self-sensitization follows the action spectrum for excitation of an electron from the valence band of the polymer backbone to the conduction band rather than the excitonic absorption spectrum of the polymer which is the dominant spectral feature in the visible (see Fig. 21). The quantum yield is independent of the electric field, whereas in a onedimensional system the yield of free carriers, determined by thermal dissociation of optically produced, weakly bound geminate electron-hole pairs, is an linear function of an applied electric field 29.30,32,129) Apparently, the sensitizing action does not... 

When, in an Auger transition, one or both of the final state holes lie in the valence band of a solid, the spectrum observed is simply the selfconvolution of the valence band density of states (DOS) so the shape of a core-valence (core W) AES profile should contain information about the valence band. Chemisorption induces modifications of the local DOS at the surface that lead to changes in the line shapes of the ejected electrons ( fine structure )) for example, sulfur as a monolayer on a Ni(lOO) surface in the structure c(2 x 2) S is characterized as having a residual d-band... 

The p3/2 spectrum of Be-II shows no evidence of a split ground state and it has been suggested that this centre could be a pair of nn substitutional Be atoms (Be2), whose trigonal symmetry has been confirmed by the piezospectroscopic measurements of [77], It may be seen [45] as a divacancy V2 into which two Be atoms are placed the two valence electrons of each Be atom satisfies four of the six dangling bonds of V2 and the two remaining bonds are completed by two electrons of the VB, leaving two holes. Within this scheme, the Be2 pair should then be a double acceptor. An unusual feature is the observation of a much weaker replica of the main spectrum, blue-shifted by... 

In conventional LEDs, the spectral characteristics of the devices reflect the thermal distribution of electrons and holes in the conduction and valence band. The spectral characteristics of light emission from microcavities are as intriguing as they are complex. However, restricting our considerations to the optical axis of the cavity simplifies the cavity physics considerably. If we assume that the cavity resonance is much narrower than the natural emission spectrum of the semiconductor, then the on-resonance luminescence is enhanced whereas the off-resonance luminescence is suppressed. The on-axis emission spectrum should therefore reflect the enhancement, that is, the resonance spectrum of the cavity. The experimental results shown in Fig. 1.9 confirm this conjecture. 

Intensity of Emission from the Vaience Band. In principle, the intensity of the electron emission from the valence state of the atom in the first-order process is determined by equations identical to those for the intensity of the emission from the core level [Eq. (23)]. The distinction lies in the matrix elements describing the atomic amplitude of this process. As mentioned above, the electron emission from the valence band may result from both the first- and the second-order processes. If the final state of the system formed as a result of these transitions is the same, these two processes must interfere. This interference is ignored in the present work. Such an approximation is justified by the fact that the final state of the system is determined by the secondary electron and the many-electron subsystem of the sample with a hole in the valence band. Neglect of the interference of the first- and second-order processes corresponds to the assumption that those processes give rise to different final states of the many-electron subsystem of the sample. Moreover, the contribution from the first-order processes of emission from the valence band is neglected in this work. The reason for that approximation is discussed in detail in Section 4. Thus, of all processes forming the spectrum of the secondary electron emission from the valence band of an atom, we shall consider only the second-order process. 

Another feature in PES spectra is the so-called shake-up structures, appearing as weak satellites on the high binding energy side of the main line. The shake-up structure reflects the spectrum of the 1 -electron-2-hole states generated in connection with pholoionization, and can give useful information about the valence n-electronic structure of a molecular ion. 

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