Absorption bandwidth

A possible method for predicting absorption bandwidths of chromogenic molecules or FBAs using PPP-MO theory (section 1.5) has been devised. It is based on the empirical linear relationship stated by the Pestemer rule. Thus theoretical Stokes shifts are computed by the PPP-MO method and related to bandwidths. The requisite MO parameters for various typical absorption bands have been developed for use in these calculations. Reasonable correlation between calculated and experimental half-bandwidth data was found, suggesting that this approach has practical potential in predicting colour tone and brightness intensity [ 19]. 

The magnitude of the interaction is even more important than its nature, and it is thus convenient to make a distinction, as proposed by Forster, between three main classes of coupling (strong, weak and very weak), depending on the relative values of the interaction energy (U), the electronic energy difference between D and A (AE), the absorption bandwidth (Aw) and the vibronic bandwidth (As) (Figure 4.15). 

Weak coupling (U AE, Aw U As) The interaction energy is much lower than the absorption bandwidth but larger than the width of an isolated vibronic level. The electronic excitation in this case is more localized than under strong coupling. Nevertheless, the vibronic excitation is still to be considered as delocalized so that the system can be described in terms of stationary vibronic exciton states. 

A third example can be taken from analytical chemistry. Absorption and resonance Raman spectra of phenol blue were measured in liquid and supercritical solvents to determine the solvent dependence of absorption bandwidth and spectral shifts. Good correlation between absorption peak shift and resonance Raman bands and between Raman bands and bandwidth of C-N stretching mode were observed while anomalous solvent effect on the absorption bandwidth occnrred in liquid solvents. Large band-widths of absorption and resonance Raman spectra were seen in supercritical solvents as compared to liquid solvents. This was dne to the small refractive indices of the supercritical solvents. The large refractive index of the liqnid solvents only make the absorption peak shifts withont broadening the absorption spectra (Yamaguchi et al., 1997). 

There are experimental evidence for the assignment of Sj to the ttct state for both HFB and PFB. Figure 15-33(a) presents the fluorescence excitation and dispersed fluorescence spectra of HFB in supersonic free jet [74], The fluorescence excitation spectra very closely mimic the vapor-phase irir S0 absorption spectra of the compound. It is evident that there is no spectral overlap between the fluorescence and the tht <- S0 absorption spectra of HFB. The energy difference between the absorption and emission maxima is greater than 11 000 cm-1. Moreover, the full width at half maximum (FWHM) of the absorption is about 3000 cm-1, whereas that of the dispersed emission is about 5500 cm-1. For fluorinated benzenes with four or less F atoms, the absorption and emission bands overlap with the Stokes shift of about 4000 cm-1, and the FWHM of both bands is about 3000 cm-1. The FWHM absorption bandwidth of 3000 cm-1 is characteristic of tht (Lft) S0... 

When the donor and acceptor are sufficiently close, as in an ion pair or in covalently linked complexes, electron transfer can be promoted by the absorption of light. An absorption band corresponding to the light induced electron transfer is usnally called a charge transfer (CT) absorption band . The molecnlar parameters that determine the CT absorptivity, bandwidth, and band shape are the same molecular parameters that determine the magnitude of the electron-transfer rate constant.In the weak-coupling limit, the absorptivity of the CT absorption band is small (much less than 10 cm ) in the strong-... 

The absorption bandwidth is usually formulated as a function of the reorganiza-tional energies that also contribute to Eq. 15. For a band with a Gaussian shape... 

Let us touch now the opposite case of a rather narrow translational band. By a physical reasoning, the absorption bandwidth Av cannot become extremely narrow, whatever the lifetime t. We relate with v the period Tmd of electromagnetic radiation Tmd = (cv), where c is the speed of light in vacuum. We have ATrad Av(cv2)-1, where min(Arrad) is meant to be positive and v is an average of v value in the frequency interval under investigation. 

The size-dependence of the width and energy of surface plasmon absorption band at 293 K and 77 K we reported earlier [1]. In this paper we discuss the temperature dependence of SPR absorption bandwidth and its energy. 

Fig. 2 depicts the temperature dependence of SPR absorption bandwidth for small particles (< 20 nm), where the monotonic increase of plasmon peak width with temperature takes place. This is similar to the dependences observed for SP in small (1.6-20 nm) gold nanoparticles [2]. 

Figure 2. Temperature dependence of the SP absorption bandwidth normalized to SP bandwidth at 77 K (left) and SP absorption band shift from the spectral position corresponding to 77 K (right) for Cu nanoparticles of different sizes.

To find out the stabilization effect of polyelectrolytes, silver nanoparticles coated with PAH or PEG at concentrations either 1 mg/ml or 5 mg/ml were examined in 0.5 M NaCl, 0.1 M NaCl or 0.01 M NaCl by UV-Vis spectroscopy. For each type of polyelectrolytes prepared at the concentration of 1 mg/ml independently from their molecular weight and sodium chloride concentration the UV-Vis measurement data revealed most broad absorption bandwidth. The narrow absorption bandwidths were related to both PAH (15 kDa) and PEG (8 kDa) at the same concentration 5 mg/ml in 0.01 M NaCl. Silver nanoparticles modified with 5 mg/ml PAH and 5 mg/ml PEG in 0.1 M NaCl presented narrow absorption widths and relatively high absorbance intensity. Furthermore, PEG coated silver nanoparticles revealed better UV-Vis absorption results among mentioned polyelectrolytes. 

Since ead > da when Eda°° > 0> the emission bandwidth is expected to be smaller than the absorption bandwidth. The reorganizational energy appropriate to the thermally activated electron transfer process is Ar(g) not Ai.(e). 

The selectivity of the Shpol skii effect lies in the inherently sharp absorption bandwidths of PAHs (FWHM 1-10 cm ) in appropriate frozen n-alkane hosts. Techniques based on this effect are usually very sensitive provided an optimal photomultiplier tube is used, the detection limit for pyrene in a mixture of 10 PAHs in -octane can be made as low as 5 X 10 °moll using an ordinary excitation lamp. The detection limit for benzo[a]pyrene is even lower by one order of magnitude two orders... 

Fig. I. Two limiting cases of resonance scattering, (a) If the incident light (dark band) has a frequency spread much larger than the absorption bandwidth of the resonant state (white band), the emitted (scattered) light decays exponentially in time with the characteristic decay time of this resonant molecular state. This is the resonance fluorescence limit, (b) If the incident light is much narrower than the absorption band, the scattered light follows the time dependence of the incident light. This is the Rayleigh and Raman scattering limit.

Fig. 45. Excitation profiles (solid lines) and depolarization dispersion curves (broken lines) of a nontotally symmetric fundamental for different homogeneous (F) and inhomogeneous (A) contributions to the same absorption bandwidth (F + A).

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