The absorption spectrum

The interaction of a photon with a molecule can be schematized in a very general form  

As already mentioned, the regions of interest for photochemistry are the UV-vis ones, and this means light radiations in the range 200 nm-1,000 nm. The energy that one molecule can gain with the absorption of a photon is therefore significant and it could take to bond breaking, but there are many different possible deactivation processes and the fate of the molecule depends on their competition, as discussed in detail in Chap.l. 

Very importantly, an excited state must be considered as a new chemical species in comparison with the molecule in its ground state and can present different chemical and physical properties. The excited states and the ground one differ, in fact, for the distribution of the external electrons that are the ones interacting with the environment, and, therefore, the ones determining the chemical reactivity of a substance. An example is reported in Fig. 3.1 that compares some characteristics of formaldehyde in the ground state and in its lower excited state. 

The extra-energy of an excited state that comes from the photon absorbance induces the promotion of an electron from an orbital at lower energy to an orbital at a higher energy level. This means that the absorption of radiant energy 

The two fundamental characteristics of these bands are their position and their intensity. The position of a band is defined by the wavelength of its maximum intensity that is called X maximum (2max), and therefore the energy connected to that electronic transition can be calculated with the Plank equation  

The most averaged quantity is the absorption spectrum or total absorption cross section Ctot(w) which, loosely speaking, measures the capability of a molecule to absorb radiation with frequency u (for a rigorous definition see Chapter 2). As the name suggests, the total cross section is defined irrespective of the fate of the excited complex and the population of the possible fragmentation channels. 

From the overall shape of the spectrum and possible structures one can draw general conclusions about the dissociation dynamics. The A band of H2O is (almost) structureless indicating a mainly direct dissociation mechanism. The B band exhibits some weak undulations which can be attributed to a special type of trapped motion with a lifetime of the order of one internal vibration (see Section 8.2). However, the broad background indicates that the dissociation via the B state also proceeds primarily in a direct way. Finally, the C band consists of rather pronounced structures which immediately tell us that the excited H20(C1Hi) complex lives on the order of at least several internal vibrations. Although the absorption spectrum is a highly averaged quantity it contains a wealth of dynamical information more of this in Chapters 6-8. 

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Since the absorption spectrum is a ratio it is amenable to other interpretations. One such interpretation is that the absorption spectrum is the ratio of energy absorbed to energy incident. From this perspective, the quantity /)co(d/d0< li 0l f 0) is interpreted as the rate of energy absorption (per unit volume), since d E/d t = /)co(d AVd t) while tire quantity E dha is interpreted as the incident energy flux, which depends only on the field intensity and is independent of frequency. 

The above fomuilae for the absorption spectrum can be applied, with minor modifications, to other one-photon spectroscopies, for example, emission spectroscopy, photoionization spectroscopy and photodetachment spectroscopy (photoionization of a negative ion). For stimulated emission spectroscopy, the factor of fflj is simply replaced by cOg, the stimulated light frequency however, for spontaneous emission... 

Note the presence of the ra prefactor in the absorption spectrum, as in equation (Al.6.87) again its origm is essentially the faster rate of the change of the phase of higher frequency light, which in turn is related to a higher rate of energy absorption. The equivalence between the other factors in equation (Al.6.110) and equation (Al.6.87) under linear response will now be established. 

To make a clearer connection to the molecular dynamics, this expression can be transfomied to the time domain. In this picture, which was initially developed by Heller and co-workers [132,133], the absorption spectrum is given by the expression... 

A different example of non-adiabatic effects is found in the absorption spectrum of pyrazine [171,172]. In this spectrum, the, Si state is a weak structured band, whereas the S2 state is an intense broad, fairly featureless band. Importantly, the fluorescence lifetime is seen fo dramatically decrease in fhe energy region of the 82 band. There is thus an efficient nonradiative relaxation path from this state, which results in the broad spectrum. Again, this is due to vibronic coupling between the two states [109,173,174]. 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

Due to the structure of the symmetrical anhydrobase. every time a 2-methylthiazolium undergoes the attack of a base, theoretically it can result in two trimethine thiazolocyanines the mesomethylsubstituted one and the unsubstituted one. For an unexplained reason, it seems that when position 5 of the starting molecule is substituted, only the mesomethyl dye is produced according to the absorption spectrum, 530 nm for the methylmeso and 569 nm for the 4-phenyl substituted derivative (Scheme 29). ... 

Whereas ATR spectroscopy is most commonly applied in obtaining infrared absorption spectra of opaque materials, reflection-absorption infrared spectroscopy (RAIRS) is usually used to obtain the absorption spectrum of a thin layer of material adsorbed on an opaque metal surface. An example would be carbon monoxide adsorbed on copper. The metal surface may be either in the form of a film or, of greaf imporfance in fhe sfudy of cafalysfs, one of fhe parficular crysfal faces of fhe mefal. 

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

Because of the relatively high population of the u" = 0 level the v" = 0 progression is likely to be prominent in the absorption spectrum. In emission the relative populations of the i/ levels depend on the method of excitation. In a low-pressure discharge, in which there are not many collisions to provide a channel for vibrational deactivation, the populations may be somewhat random. However, higher pressure may result in most of the molecules being in the v = 0 state and the v = 0 progression being prominent. 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

Figure 9.32 Isotopic enrichment of SFg by multiphoton dissociation following irradiation in the vibrational band of SFg. The absorption spectrum is shown (a) before and (b) after irradiation. (Reproduced, with permission, from Letokhov, V S., Nature, Land., Ill, 605, 1979 Copyright 1979 Macmillan Journals Limited)...

Electronic transitions in molecules in supersonic jets may be investigated by intersecting the jet with a tunable dye laser in the region of molecular flow and observing the total fluorescence intensity. As the laser is tuned across the absorption band system a fluorescence excitation spectrum results which strongly resembles the absorption spectrum. The spectrum... 

Molecules and atoms interact with photons of solar radiation under certain conditions to absorb photons of light of various wavelengths. Figure 10-4 shows the absorption spectrum of NO2 as a function of the wavelength of light from 240 to 500 nm. This molecule absorbs solar radiation from... 

In Modulation Spectroscopy, which is mosdy used to characterize semiconductor materials, the peak positions, intensities and widths of features in the absorption spectrum are monitored. The positions, particularly the band edge (which defines the band gap)> are the most useful, allowing determination of alloy concentration. 

RAIRS spectra contain absorption band structures related to electronic transitions and vibrations of the bulk, the surface, or adsorbed molecules. In reflectance spectroscopy the ahsorhance is usually determined hy calculating -log(Rs/Ro), where Rs represents the reflectance from the adsorhate-covered substrate and Rq is the reflectance from the bare substrate. For thin films with strong dipole oscillators, the Berre-man effect, which can lead to an additional feature in the reflectance spectrum, must also be considered (Sect. 4.9 Ellipsometry). The frequencies, intensities, full widths at half maximum, and band line-shapes in the absorption spectrum yield information about adsorption states, chemical environment, ordering effects, and vibrational coupling. 

Many other measures of solvent polarity have been developed. One of the most useful is based on shifts in the absorption spectrum of a reference dye. The positions of absorption bands are, in general, sensitive to solvent polarity because the electronic distribution, and therefore the polarity, of the excited state is different from that of the ground state. The shift in the absorption maximum reflects the effect of solvent on the energy gap between the ground-state and excited-state molecules. An empirical solvent polarity measure called y(30) is based on this concept. Some values of this measure for common solvents are given in Table 4.12 along with the dielectric constants for the solvents. It can be seen that there is a rather different order of polarity given by these two quantities. 

In Pedersen s early experiments, the relative binding of cations by crown ethers was assessed by extraction of alkali metal picrates into an organic phase. In these experiments, the crown ether served to draw into the organic phase a colored molecule which was ordinarily insoluble in this medium. An extension and elaboration of this notion has been developed by Dix and Vdgtle and Nakamura, Takagi, and Ueno In efforts by both of these groups, crown ether molecules were appended to chromophoric or colored residues. Ion-selective extraction and interaction with the crown and/or chromophore could produce changes in the absorption spectrum. Examples of molecules so constructed are illustrated below as 7 7 and 18 from refs. 32 and 131, respectively. 

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