Forbidden band

An interesting point is that infrared absorptions that are symmetry-forbidden and hence that do not appear in the spectrum of the gaseous molecule may appear when that molecule is adsorbed. Thus Sheppard and Yates [74] found that normally forbidden bands could be detected in the case of methane and hydrogen adsorbed on glass this meant that there was a decrease in molecular symmetry. In the case of the methane, it appeared from the band shapes that some reduction in rotational degrees of freedom had occurred. Figure XVII-16 shows the IR spectrum for a physisorbed H2 system, and Refs. 69 and 75 give the IR spectra for adsorbed N2 (on Ni) and O2 (in a zeolite), respectively. 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

The second example in Fig. 4-4 shows how a (spin-allowed or spin-forbidden) band lying close to a charge transfer band may acquire unusually high intensity. We shall discuss charge-transfer bands more in Chapter 6. For the moment, we note that they involve transitions between metal d orbitals and ligands, are often fully allowed and hence intense. On occasion, the symmetry of a charge transfer state... 

Here we comment on the shape of certain spin-forbidden bands. Though not strictly part of the intensity story being discussed in this chapter, an understanding of so-called spin-flip transitions depends upon a perusal of correlation diagrams as did our discussion of two-electron jumps. A typical example of a spin-flip transition is shown inFig. 4-7. Unless totally obscured by a spin-allowed band, the spectra of octahedral nickel (ii) complexes display a relatively sharp spike around 13,000 cmThe spike corresponds to a spin-forbidden transition and, on comparing band areas, is not of unusual intensity for such a transition. It is so noticeable because it is so narrow - say 100 cm wide. It is broad compared with the 1-2 cm of free-ion line spectra but very narrow compared with the 2000-3000 cm of spin-allowed crystal-field bands. 

We should note that expressions (1.28) (1.31) have been obtained without accounting for plausible recharging of biographic surface states [84, 98] which is reasonable in case when above states have fully occupied energy levels positioned deeply inside the forbidden band. 

The adsorption of donor particles can also be accompanied by various situations. In case when kT6 = ltd - x S> 0, but 0 < so> i-C- the level of chemosorbed particle is situated in the forbidden band below the Fermi level of the neutral surface, the function (ar) is described by expressions (1.32) - (1.35) with values of 5 given by relations (1.30) and (1.31). If >0, we can encounter the case with the opposite band bending close to the surface of adsorbent resulting in saturation of the surface-adjacent layers by electrons of conductivity. 

Zinc oxide is a thoroughly studied typical semiconductor of n-type with the width of forbidden band of 3.2 eV, dielectric constant being 10. Centers responsible for the dope electric conductivity in ZnO are provided by interstitial Zn atoms as well as by oxygen vacancies whose total concentration vary within limits 10 - 10 cm. Electron mobility in monocrystals of ZnO at ambient temperature amounts to 200 cm -s". The depth of donor levels corresponding to interstitial Zn and oxygen vacancies under the bottom of conductivity band is several hundredth of electron volt [18]. 

Fig. 2.2 Band structure of a semiconductor. eg denotes the energy gap (width of the forbidden band)... 

For a sufficiently large potential increase, the charge in the interphase finally corresponds to the minority charge carriers (Fig. 4.12D). The greater the width of the forbidden band eg, the broader is the potential range A f in which the space charge region has the character of a depletion layer, i.e. is formed by ionized impurity atoms. 

Figure 5 shows a collection of S j -S0 R2PI spectra near the origin. The weak bands at low frequency are pure torsional transitions. We can extract the barrier height and the absolute phase of the torsional potential in S, from the frequencies and intensities of these bands. The bands labeled m7, wIq+, and are forbidden in the sense that they do not preserve torsional symmetry. In the usual approximation that the electronic transition dipole moment is independent of torsion-vibrational coordinates, band intensities are proportional to an electronic factor times a torsion-vibrational overlap factor (Franck-Condon factor). These forbidden bands have Franck-Condon factors m m") 2 that are zero by symmetry. Nevertheless, they are easily observed in jet-cooled spectra. They are comparably intense in many spectra, about 1-5% of the intensity of the allowed origin band. 

In collaboration with E.L. Sibert, we have learned to interpret these Franck-Con-don forbidden, pure torsional band intensities in S,-S0 absorption spectra quantitatively and thus place the key ml+ assignment on firm ground.27 The forbidden bands follow the selection rule Am = 3, so we need a perturbation of the form Vel cos 3a. Working in an adiabatic representation with the S0 and S, electronic states denoted by y0(g a) and /,( a) and the torsional states by m" and m, the electric dipole transition moment is,... 

Fourier expansion of p10(a) allows us to calculate relative intensities of the three forbidden bands m2, m, and m,. These are in quantitative agreement with experiment. The agreement is excellent over a wide range of ratios of the key model parameters V6 and F (effective rotational constant), which are taken from experiment. Previous conformational inferences in S0, S, D0 (ground state cation), including our own, were in fact correct. They now rest on solid ground. 

A representative example of an EL spectrum is shown in Fig. 45. The energy levels from which the emission starts are always inside the forbidden band of A1203. 

Second, we analyze the nature of the next, strong 2PA bands. The positions of their final states correspond to one-photon symmetry forbidden bands and can be found from excitation anisotropy measurements, as illustrated in Figs. 6,19, and 23. Excitation anisotropy spectra for all cyanine-like molecules typically reveal a large alternation of maximum and minimum features suggesting the positions of the 1PA and 2PA transitions. Two-photon excitation into final states involves two dipole moments, fi0i and /i (i. 

Cerny, and Maxova (44, 45) have adopted larger values for C/B, Of these latter the ferrocene assignment (32) is dubious since subsequent reexamination has failed to establish the existence of two of the three spin-forbidden bands there claimed, whilst valid alternative assignments of the spin-forbidden transitions of Ni(Cp)2 and V(Cp)2, on which the higher C/B values were based (44, 45) are readily made (vide infra). 

The assignment of the shoulder at 25 kK. is though rather problematical no other spin-allowed d-d band is expected in this region, and since the crude extinction coefficient no doubt exaggerates its true intensity, it may tentatively be assigned as a spin-forbidden band, the most likely candidate being the 4E (a 52) -> 2A(a2 5) transition. This in turn leads to a B value of about 650 cm 1, with 0 not unreasonably at about 0.70. 

The band at 1600 cm-1 due to a double-bond stretch shows that chemisorbed ethylene is olefinic C—H stretching bands above 3000 cm-1 support this view. Interaction of an olefin with a surface with appreciable heat suggests 7r-bonding is involved. Powell and Sheppard (4-1) have noted that the spectrum of olefins in 7r-bonded transition metal complexes appears to involve fundamentals similar to those of the free olefin. Two striking differences occur. First, infrared forbidden bands for the free olefin become allowed for the lower symmetry complex second, the fundamentals of ethylene corresponding to v and v% shift much more than the other fundamentals. In Table III we compare the fundamentals observed for liquid ethylene (42) and a 7r-complex (43) to those observed for chemisorbed ethylene. Two points are clear from Table III. First, bands forbidden in the IR for gaseous ethylene are observed for chemisorbed ethyl-... 

For AgFl the intensities of the spin-forbidden bands, relative to those of the allowed transitions, are actually smaller than for the analogous 3d complex, CuFi This however is because the larger Dq of the Ad series, and the smaller B value, results in a greater separation between... 

For ruthenium and the following elements of the 4d series the free-ion f values become in excess of 1000 cm-1, and apart from the exceptions mentioned previously, the relative intensities of the spin-forbidden bands are found to be significantly larger than for the 3d elements. For the intra-subshell (t g) transitions 3T g XT%g and 3T g 1Eg some 2%... 

Once again two spectroscopic studies have been made — due to Brown et al. (32) and to Allen et al. (12) respectively — and the same comments apply as for the two investigations of the RuFspin-forbidden bands at 12.2 and 16.1 kK., with spin-allowed transitions at 19—21 kK. and at 26.0 kK., but no other absorptions were found below 40 kK. On the other hand the spectrum of Allen et al., although broadly mirroring these findings, revealed extra absorptions at 32.8,39.6, and 44.6 kK., together with a strong indication of a band below 4 kK. (Fig. 2). 

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