Features of the Absorption Spectrum

Let us now turn to the relation between energy bands and the spectrum. For this, see Fig. 4-3, which shows the absorption spectrum for InAs the corresponding energy bands are shown in Fig. 4-4. InAs is convenient for identifying features of the spectrum. 

Notice first that the minimum gap between the valence and conduction bands in Fig. 4-4 occurs at F this is the minimum gap for the entire Brillouin Zone. The corresponding energy difference, in this case less than 1 eV, is called Eq and, as indicated in E ig. 4-3, is the minimum energy at which absorption occurs. It is the same Eq evaluated in Eq. (3-39) and discussed there. The situation has a complication in the homopolar semiconductors in that the minimum energy in the conduction band does not occur at F where the valence-band maximum is. The difference is called an indirect gap and absorption cannot occur at that energy in the absence of other perturbations such as thermal vibrations. For this reason we ghose InAs as better suited for discussion than silicon. 

Imaginary part of the dielectric susceptibility of InAs as a function of energy. [After Cardona and Poliak, 1972,] 

Energy bands of InAs. [After Chelikowsky and Cohen, 1976b.] 

The largest peak in Fig. 4-3, labelled 2. can be easily identified with the fairly parallel bands separated by between 4 and 6 eV over most of the region shown in Fig. 4-4. (A careful study of this was made recently by Kondo and Moritani, 1977.) These bands arise from the Jones Zone, which will be discussed in detail in the treatment of tetrahedral semiconductors with pseudopotentials in Chapter 18. The energy at which this peak occurs was used earlier as a basis for obtaining experimental values for the covalent energy Fj (Harrison and Ciraci, 1974). 

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All the above considerations reveal that the absorption spectrum of 112 will be a complexity of overlapping bands and, therefore, the assignment of electronic features of the absorption spectrum of 112 is still far from being clear. This also complicates the discussion of the CD of the cyclopropane chromophore. 

The Eq. (9.1.16) alternative form for Ivn io) is mathematically equivalent to the standard Eq. (9.1.9) form, but in many cases Eq. (9.1.16) is both more convenient to use and provides deeper insights into how local features of the e-state potential energy surface affect the dynamical processes that are encoded in the absorption spectrum (see Figs. 9.1 and 9.2). The keys to these insights are (i) that k, (0)) is the initially localized state-function that would be produced by a sufficiently short excitation pulse and (ii) that the early time evolution of ti) generates the most prominent features of the absorption spectrum, Iv<< u)). 

The surprising feature of the absorption spectrum of phenylalanine is that it is sensitive to acid and alkali. This indicates that an appreciable change in the vibrational levels of the benzyl chromophor occurs, due to inductive effects brought about by ionization of the carboxyl or amino group. As will be shown later, such an influence on the vibrational levels can be shown to occur when an aromatic amino acid is combined in peptide linkage (Section VI, 2). The absorption curves of phenylalanine in acid and alkali are shown in Fig. 3. 

A standard UV-VIS spectrophotometer will irradiate a sample with UV and visible light and will generate an absorption spectrum, which plots absorbance as a function of wavelength. The most important feature of the absorption spectrum is the Xmax (pronounced lambda max), which indicates the wavelength of maximum absorption. 

In the present example, the electronic QM computations have been performed with the DFT/N07D model while the effect of the methanol solvent has been included by means of the polarizable continuum model, where the solvent is represented by a homogeneous dielectric polarized by the solute, placed within a cavity built as an envelope of spheres centered on the solute atoms [ 154] (see Chapter 1 for details). The solvent has been described in the nonequilibrium hmit where only its fast (electronic) degrees of freedom are equilibrated with the excited-state charge density while the slow (nuclear) degrees of freedom remain equilibrated with the ground state. This assumption is well suited to describe the broad features of the absorption spectrum in solution due to the different time scales of the electronic and nuclear response components of the solvent reaction field [89]. 

Figure 1 shows the absorption spectra recorded at room temperature and at lOK for a suspension of reaction centers isolated from the thermophilic species of R. sulfoviridis. Very similar spectra are obtained from the mesophilic species (data not shown). In the near infrared region, the general features of the absorption spectrum of the reaction centers of R. viridis (3) are observed for the R. sulfoviridis species ... 

The most important feature of the absorption spectrum is the, which indicates the... 

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