Integrated absorption intensities

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. 

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). 

Thus, for diethylamine, (7—4 x 10 3 for methylaniline, 13 x 10 3 for pyrrole [1], 44 X 10 3. Combining these figures with appropriate integrated absorption intensities given by Russell and Thompson [5], we may follow Rayliss, Cole and Little [8] in assuming the model of a point dipole in a spherical cavity and calculating the cavity radii. These turn out to be 4-5 (diethylamine), 9 7 (methylaniline) and 9 8 A (pyrrole). 

Thus the integrated absorption intensity is found to depend on the square of the transition moment integral defined as... 

Figure 3.3a). The total area under the curve gives the integrated absorption intensity, J ej [Pg.63]

The natural radiative lifetime gives an upper limit to the lifetime of an excited molecule and can be calculated from the integrated absorption intensity. The quantity to be plotted is e vs v if (3.96) is used and... 

The natural radiative lifetime is independent of temperature, but is susceptible to environmental perturbations. Under environmental perturbation, such as collisions with the solvent molecules or any other molecules present in the system, the system may lose its electronic excitation energy by nonradiative processes. Any process which tends to compete with spontaneous emission process reduces the life of an excited state. In an actual system the average lifetime t is less than the natural radiative lifetime as obtained from integrated absorption intensity. In many polyatomic molecules, nonradiative intramolecular dissipation of energy may occur even in the absence of any outside perturbation, lowering the inherent lifetime. 

A totally allowed transition has oscillator strength /=1 and molar extinction coefficient 105. Different factors may reduce the / values to different extents. Oscillator strengths / are related to integrated absorption intensities by the expression... 

Fig. 3.15. The variation of the integrated absorption intensity of hydrogen with the density [213], Q, of the perturbing gas, in the region 300-1400 cm-1. Reproduced with permission from the National Research Council of Canada from [213],...

Analysis of Defined Fractions. Quantitative infrared analysis was used for those fractional groups that have definitive bands average absorptivities were estimated using model compounds (12, 16, 17). Table I lists the infrared bands and the apparent integrated absorption intensities (B) used. Quantitative IR spectra were measured in methylene chloride with 0.05 cm sodium chloride cells, using a Perkin-Elmer 521 infrared spectrophotometer. Peak area was measured by planimetry. Molecular weights were determined by vapor-pressure osmometry in benzene. 

Table I. Infrared Assignments and Apparent Integrated Absorption Intensity...

The data reported by Basila et al. (221,224) lead to a value of 1.6 03. Using the apparent integrated absorption intensities as given by Hughes and White (198), Ward and Hansford (226) estimated the limits of detection of Br nsted acidity to be of the order of magnitude of 10 2 meq g-1 for silica-aluminas with Brunauer-Emmett-Teller (BET) surface areas between 350 and 500 m2 /g. 

Because of the use of finite slit widths, the radiation is not monochromatic (and covers an appreciable part of the band envelope) and the measured quantity is an apparent integrated absorption intensity (B),... 

Having established both a probable mathematical form of the true shape of an infrared absorption band and its relationship to its apparent or observed profile, Ramsay outlined three methods for determining true integrated absorption intensities. As these methods have been used exclusively in all reported studies of absolute intensities of metal carbonyl stretching vibrations, they are now described in some detail. ... 

Since the two ratios of the right-hand side of Eq. (14) have been tabulated, it is easy to present K in the same form so that by measuring the apparent peak intensity and the apparent half-intensity band width of an absorption band and consulting the relevant tables, the true integrated absorption intensity can be calculated from Eq. (13). 

If a spectrometer with a linear wavelength scale is used, the experimental absorption curve has to be replotted as fractional absorption (Tq — T)ITq against v in cm , and the area under the band for a range (r — i g) determined. A correction for the band wings is applied to obtain A, and then the true integrated absorption intensity is calculated from Eq. (20). Wing corrections are presented in tabular form in terms of the quantity (i — and are to be found in the original paper 121). 

In molecules such as the aromatic hydrocarbons for which the most experimental data are available, it was found that the fluorescence lifetimes were much shorter than that which could be deduced from the integrated absorption intensity. The latter provides the oscillator strength f, and a radiative lifetime... 

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