Intensity oscillator strengths

The vast majority of single-molecule optical experiments employ one-photon excited spontaneous fluorescence as the spectroscopic observable because of its relative simplicity and inlierently high sensitivity. Many molecules fluoresce with quantum yields near unity, and spontaneous fluorescence lifetimes for chromophores with large oscillator strengths are a few nanoseconds, implying that with a sufficiently intense excitation source a single... 

If the absorption is due to an electronic transition then/, , the oscillator strength, is often used to quantify the intensity and is related to the area under the curve by... 

Note added in proof. J. C. Strijland and A. J. Nanassy (Physica 24, 935 (1958)) have shown recently that there are no changes of oscillator strength in argon + mercury. Increases in spectral intensity are entirely accounted for by increases in mercury concentration. 

Figure 12. Electronic spectra and the results of open-shell PPP-like semiempirical calculations for radical ions. The vertical lines represent the allowed transitions, the wavy lines with arrows the forbidden ones. The right side scales denote the calculated spectral intensities, where f stands for the oscillator strength. Top left the absorption curve (146) redrawn to the log e vs. 0 (cm ) form calculations are taken from (59). Top right taken from (11). Bottom left taken from (143). Bottom right taken from (136), the absorption curve redrawn to the log e vs, 0 (cm" ) form.

Experimentally guanine shows spectral features with similarities to those of adenine. There are two peaks at 4.51 and 4.95 eV with relatively low intensity and much stronger bands higher than 6 eV. The oscillator strengths for the first two peaks are similar also, 0.14 and 0.21, respectively [143, 146],... 

The ESA spectra of asymmetrical dyes in toluene are shown in Fig. 25. They show broad structureless bands in the NIR region (750-1,100 nm for G19, 850-1,100 nm for G40, and 950-1,100 nm for G188) and more intense transitions in the visible range (400-550 nm for G19, 400-600 nm for G40, and 450-650 nm for G188). Similarly to symmetrical anionic polymethine dyes (Fig. 20), the increase of conjugation length leads to a small red shift of ESA spectra, and to an enhancement of ESA cross sections and the ratio between the ESA and linear absorption oscillator strengths by approximately a factor of two. More detailed experimental description and quantum-chemical analysis can be found in [86]. 

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

FIGURE 6.2 Absorption spectrum of the hydrated electron. The spectrum is structureless, broad (half-width 0.84 eV), intense (oscillator strength 0.75), and has a single peak at 1.725 eV. (See text for details.)... 

The authors also calculated the band structure expected for the fully oxidised form, taken as 33% doping or 2 charges per 6 rings, and the result is depicted in Figure 3.72(c). Continued removal of the states from the valence and conduction bands widens the gap to 3,56eV, with the two intense absorptions in the gap observed in the optical spectra now accounted for by the presence of wide bipolaron bands. The authors stated that, on the basis of other workers calculations, the lowest energy absorption should have the most intense oscillator strength, as is indeed observed. 

The benzofuran-naphthyridine linked dye compound (ABAN, see Fig. 1) has been successfully converted to fluorescent organic nanoparticles [34], for which their photophysical properties such as spectral features and emission intensity are remarkably different from those at the molecular level (solution). The results are rationalized by coplanarization of the benzofuran-naphthyridine molecule in the nanoparticle to extend its effective conjugation length and hence increase the oscillator strength, as is similar to the cases described above. 

It should be noted that no such difficulty appears with the integral of an absorption spectrum because the absorption coefficient is proportional to the logarithm of a ratio of intensities, so that e(A) = e(v). For instance, in the calculation of an oscillator strength (defined in Chapter 2), integration can be done either in the wavelength scale or in the wavenumber scale. 

In some aromatic molecules that have a high degree of symmetry, i.e. with a minimum D2h symmetry (e.g. benzene, triphenylene, naphthalene, pyrene, coronene), the first singlet absorption (So —> Si) may be symmetry forbidden61 and the corresponding oscillator strength is weak. The intensities of the various forbidden vibronic bands are highly sensitive to solvent polarity (Ham effect). In polar solvents, the intensity of the 0-0 band increases at the expense of the others. 

The very weak Tm - So transitions are hard to observe directly by absorption spectroscopy. Even with long cells, the high concentrations required present solubility — and what is more important — purity problems. An impurity of 1 10 may give rise to absorption bands which have the same intensity as the expected Ti So absorption. The experimental conditions, therefore, have to be chosen to allow an increase of the Ti- - So oscillator strength to be achieved through perturbation by paramagnetic species (O2 or NO) or heavy atoms. Alternatively, an indirect method, phosphorescence excitation spectroscopy, which has high sensitivity and selectivity, may be applied. 

Spectral lines are often characterized by their wavelength and intensity. The line intensity is a source-dependent quantity, but it is related to an atomic constant, the transition probability or oscillator strength. Transition probabilities are known much less accurately than wavelengths. This imbalance is mainly due to the complexity of both theoretical and experimental approaches to determine transition probability data. Detailed descriptions of the spectra of the halogens have been made by Radziemski and Kaufman [5] for Cl I, by Tech [3] for BrIwA by Minnhagen [6] for II. However, the existing data on /-values for those atomic systems are extremely sparse. 

In this section we shall give the mathematical expressions for the properties object of the present calculations. One of the measurements of the intensity of an electronic transition is given by the oscillator strength. For an absorption transition between states i and/, it can be defined as follows... 

In the trans conformation (a), the CH2CH2 moiety is achiral, pi and fi2 colinear and no VCD can be generated, that is, the rotational strength is zero. In the two gauche conformations (b) and (c), the CH2CH2 units have opposite chirality, and generate coupled oscillator VCD intensity of opposite sign. 

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