Integrated absorption

Section BT1.2 provides a brief summary of experimental methods and instmmentation, including definitions of some of the standard measured spectroscopic quantities. Section BT1.3 reviews some of the theory of spectroscopic transitions, especially the relationships between transition moments calculated from wavefiinctions and integrated absorption intensities or radiative rate constants. Because units can be so confusing, numerical factors with their units are included in some of the equations to make them easier to use. Vibrational effects, die Franck-Condon principle and selection mles are also discussed briefly. In the final section, BT1.4. a few applications are mentioned to particular aspects of electronic spectroscopy. 

In this expression the only variable is N0 and it is this which governs the extent of absorption. Thus it follows that the integrated absorption coefficient is directly proportional to the concentration of the absorbing species. 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

Fig. 21. Integrated intensity OH and OD bands versus time for adsorbed labeled propylene. CH3- CH=CD2 O, OH , OD. CD3—CH=CH2 A, OH A, OD. The integrated intensity for OD was multiplied by 1.35, the isotopic shift, in an attempt to correct for expected differences in the integrated absorption coefficient.

The attribution of lines 1 and 2 in n-type GaAs Si is further substantiated by 1) the value of the ratio of the integrated absorptions A (1-H)/Aj(2-H), which is approximately equal to three (a ratio of about two is expected since lines 1-H and 2-H are attributed to doubly and singly degenerate modes respectively), and 2) the r-factor of 1.398 for line 1, explained by the small contribution of the Si atoms to the wagging motion. 

A spectroscopic calibration of the P—H concentration in InP Zn is obtained from the relation between the concentration of neutralized holes and the integrated absorption Ar of the 2287.7 cm-1 line rising after hydrogen neutralization ... 

Chapter 3 is devoted to dipole dispersion laws for collective excitations on various planar lattices. For several orientationally inequivalent molecules in the unit cell of a two-dimensional lattice, a corresponding number of colective excitation bands arise and hence Davydov-split spectral lines are observed. Constructing the theory for these phenomena, we exemplify it by simple chain-like orientational structures on planar lattices and by the system CO2/NaCl(100). The latter is characterized by Davydov-split asymmetric stretching vibrations and two bending modes. An analytical theoretical analysis of vibrational frequencies and integrated absorptions for six spectral lines observed in the spectrum of this system provides an excellent agreement between calculated and measured data. 

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

To make accurate measurements of the integrated absorption associated with such narrow lines requires that the linewidth of the radiation source be appreciably smaller than that of the absorption line. In practice, this could be achieved with a continuum source only if expensive instrumentation of extremely high resolving power were used, and it is doubtful whether conventional photomultiplier detectors would be sufficiently sensitive at the resulting low radiation intensities. An alternative arrangement is to... 

Using this theory of the dipole-dipole interaction it was then possible to get a good description of the experimentally measured integrated absorptance and vibration frequency as function of coverage. This is shown in Fig. 5 for CO/Ru(001). The solid lines are calculated using... 

Figure 26. Dimerization of butadiene in the crystalline phase. Lower panel Logarithmic plots of the room-temperature evolution of the integrated absorption of characteristic vinylcyclohexene absorption bands at different pressures. The linear evolution unambiguously demonstrates the first-order kinetics of the reaction. Upper panel Evolution of the natural logarithm of the dimerization rate constant as a function of pressure (full squares, left axis the dotted line is intended as a guide for the eye) and evolution of the intensity ratio between selected polymer and dimer (vinylcyclohexene) bands (empty dots, right axis).

Figure 27. Evolution of the IR integrated absorption of the C—H stretching modes involving sp carbon atoms. The corresponding absorption band is indicated by the star in the IR spectra reported in the inset during a compression (full dots)-decompression (empty dots) cycle.

However, central to any truly accurate determination of the radiative rate are the integrated absorption (emission) intensities, A", which for gaseous ions are almost completely unknown as are, usually, the vibrational frequencies. Fortunately, however, ab initio and density functional methods have recently been shown to be quite accurate in their predictions of vibrational spectra for a wide variety of systems, and there is no reason to suspect that this accuracy would not carry over to comparable data for gaseous ions. The one caveat must be that the low-frequency modes that are common in cluster ions will be decidedly anharmonic, and prediction of both these frequencies and their intensities may be suspect. However, these modes are not generally expected to be dominant contributors to the overall radiative rate. In addition, standard RRKM procedures can be applied to the unimolecular dissociation of the same adduct ions and, in principle therefore, the overall kinetics of formation of stabilized association complexes can be accurately modeled. 

For more oareful identification of types of Lewis (aprotic) centres, CO adsorption was carried out in small doses (1-10 Jinol per cell) up to satiiration of active surface achieved. To reveal individual lines the separation of IR-spectra was carried out using CK-2 curve synthesiser. Concentration of aprotic centres was determined using coefficients of integral absorption from ref.[9J. The strength of aprotic centres was characterized by the heat of CO adsorbtion according to eq. (2). Concentration of Bronsted (pro-... 

Newnham, D. A., and J. Ballard, Visible Absorption Cross Sections and Integrated Absorption Intensities of Molecular Oxygen (02 and 04), /. Geophys. Res., 103, 28801-28816 (1998). 

Let us return now to a single oriented ellipsoid. Integrated absorption is sometimes of interest ... 

There are several interesting observations that can be made about (12.32). Integrated absorption is independent of the damping constant y the only bulk parameter that affects it is the plasma frequency. If the particles are in air, then integrated absorption is independent of the shape this is true not only for a single oriented ellipsoid but also for a collection of randomly oriented ellipsoids. It is instructive to rewrite (12.32) using (12.29) ... 

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