Oscillator strength concept

Closely related to the absorption coefficient is the concept of the oscillator strength for the transition, or the/-number. It is given by... 

The relative success of the binary encounter and Bethe theories, and the relatively well established systematic trends observed in the measured differential cross sections for ionization by fast protons, has stimulated the development of models that can extend the range of data for use in various applications. It is clear that the low-energy portion of the secondary electron spectra are related to the optical oscillator strength and that the ejection of fast electrons can be predicted reasonable well by the binary encounter theory. The question is how to merge these two concepts to predict the full spectrum. 

Si1 The concept of oscillator strength was developed from the classical ffceory of dispersion. It is related to the molar refraction R of a substance... 

Line and multiplet strengths are useful theoretical characteristics of electronic transitions, because they are symmetric, additive and do not depend on the energy parameters. However, they are far from the experimentally measured quantities. In this respect it is much more convenient to utilize the concepts of oscillator strengths and transition probabilities, already directly connected with the quantities measured experimentally (e.g. line intensities). Oscillator strength fk of electric or magnetic electronic transition aJ — a J of multipolarity k is defined as follows ... 

Oscillator strength (f Number) A measure of the intensity of a spectral band a classical concept (giving the effective number of electrons taking part in a certain transition) adapted to wave mechanics. For a transition between state i and state j,... 

Combining the idea of solvent-induced changes in molecular structure with the concept of a solvent continuum around the solvatochromic molecule, a micro-structural model of solvatochromism has been developed by Dahne et al., which reproduces, qualitatively correctly and quantitatively satisfactorily, the solvatochromic behavior of simple merocyanine dyes [95b], The results obtained with this model for 5-(dimethylamino)penta-2,4-dienal are in good agreement with the solvent-dependent experimental data such as transition energies, oscillator strengths, r-electron densities, and r-bond energies [95b] cf. also [326, 327],... 

In a very new report, Fujino et al. challenge the two-isomerization-mechanism concept on the basis of their time-resolved and time-integrated femtosecond fluorescence measurements of B-azobenzene following excitation of the (7t,7t ) State. They use the extremely weak fluorescence (cf. Figure 1.8) as an indicator for the population of the emitting state. From the ratios of their measured fluorescence lifetimes (S2 0.11 ps Sp 0.5 ps) and the radiative lifetimes deduced from the (absorption-spectra-based) oscillator strengths, they determine the fluorescence quantum yields 2.5310 for the emission and 7.5410" for the Si—>So emission. By comparison... 

The first technical problem is encountered immediately upon beginning to test how well a periodic system concept agrees with the data. The problem consists of the surprisingly large errors that often accompany data in journal articles (occasionally as much as 20% for dissociation potentials and 100% for oscillator strengths of diatomic molecules). The errors are far less serious in quality critical tables. 

Intensity variations reveal a variety of effects, both in the bound spectrum and above threshold. In order to study them, one needs to introduce the concept of oscillator strength, as a preliminary to discussing various factors which influence the intensities of spectral lines. 

The concept of intramolecular vibrational energy redistribution (IVR) can be formulated from both time-dependent and time-independent viewpoints (Li et al., 1992 Sibert et al., 1984a). IVR is often viewed as an explicitly time-dependent phenomenon, in which a nonstationary superposition state, as described above, is initially prepared and evolves in time. Energy flows out of the initially excited zero-order mode, which may be localized in one part of the molecule, to other zero-order modes and, consequently, other parts of the molecule. However, delocalized zero-order modes are also possible. The nonstationary state initially prepared is often referred to as the bright state, as it carries oscillator strength for the spectroscopic transition of interest, and IVR results in the flow of amplitude into the manifold of so-called dark states that are not excited directly. It is of interest to understand what physical interactions couple different zero-order modes, allowing energy to flow between them. A particular type of superposition state that has received considerable study are A/-H local modes (overtones), where M is a heavy atom (Child and Halonen, 1984 Hayward and Henry, 1975 Watson et al., 1981). 

In this study, we evaluate the oscillator strength of hypersensitive transitions in LnX3 (X = Cl, Br, I) molecules with the multi-reference spin-orbit (MRSO) Cl method and discuss the origin of hypersensitive transition intensities, especially focusing on the Ln dependence, halogen dependence, and also the effect of LMCT. To compare our ab initio results and the semi-empirical concepts, such as the JO theory and the DC model, we evaluate the oscillator strengths and two kinds of JO intensity parameters T Cdc) and rxC b) in Sect. 4.1. These two parameters T Cdc) T Cab), the details of which are defined in Sect. 3 and Ref. [5], represent the contributions only from the DC theory and those from all the effects considered in the ab initio calculations, respectively. If the origin of hypersensitive transition intensities can be explained by the DC model alone, these two JO intensity parameters T Cdc) and TAC b) are expected to show similar... 

The transition probability can be vividly described by the concept of oscillator strength / which relates the classical model with a more realistic approach. It can be explained as follows ... 

The book begins with a discussion of the fundamental definitions and concepts of classical spectroscopy, such as thermal radiation, induced and spontaneous emission, radiation power and intensity, transition probabilities and oscillator strengths, linear and nonlinear absorption and dispersion, and coherent and incoherent radiation fields. In order to understand the theoretical limitations of spectral resolution in classical spectroscopy, the next chapter treats the different causes of the broadening of spectral lines. Numerical examples at the end of each section illustrate the order of magnitude of the different effects. 

The conclusions of this classical model can be transferred to real molecules in a relatively simple way by introducing the concept of oscillator strength. 

Using the concept of oscillator strength, the absorption and dispersion of real atoms or molecules in a level E. with absorption frequencies can be described by modifying the classical formulas (2.55,56) to... 

We then turn to a consideration of the absorption lines produced by the transmission of a continuous spectrum through an absorbing vapour. The concept of equivalent width is explained and we show that the equivalent width of an absorption line is determined by the product N.f..L. Details are given of the measurement of relative oscillator strengths by the absorption technique using a King furnace. 

However, the concept of group frequencies is applicable only when the vibrations of a particular group are isolated from those of the rest of the molecule. If atoms of similar masses are connected by bonds of similar strength, the amplitudes of oscillation are similar for all atoms. For example, this situation occurs in a system like... 

---