Oscillators strength

The oscillator strength can be calculated theoretically and determined experimentally, and so its importance lies in the cormection it provides between theory and reality, as well as its usefulness for classifying the strength and nature of transitions. 

The following equation that is given in most textbooks (Atkins, 1970 Eyring et al., 1944 McGlynn et al., 1972 Pauling and Wilson, 1935) relates the dimensionless oscillator strength/to the dipole matrix elements for an isotropic radiation bath (see Section 3.4.3 and Eq. (126))  

It is noteworthy that two transitions which have the same oscillator strength do not have the same dipole strength because the value of/is divided by Vo in the expression of D. It is even possible that a transition having a larger oscillator strength than a second one has the lowest dipole strength. 

This relationship is independent of the convention used for the dipole strength. It depends only on the integrated spectral intensity. 

In some books, for example, Wyboume (1965), the expression of/is given separately for ED and MD transitions as 

In contrast to the harmonic oscillator of our classical model for absorption, real atoms or molecules have many energy levels and therefore also many possible transitions from lower thermally populated levels. This means that there are many absorption lines at different frequencies coi. The magnitude of the absorption coefficient a depends on the population density of the absorbing level and on the transition probabilities for the different transitions. These transition probabilities can be only calculated by using quantum mechanical methods, but there are several experimental techniques for their determination (see next section). 

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  

An atom with an electron in an outer shell, J eucht-Electron ) which can be excited by absorption of a photon from a lower state Ei into higher electronic states Ek can be treated as classical oscillator with the oscillator strength / = 1. However, the total absorption of the atom in level Ei is due to the sum of all transitions into the levels Ek. Each of these transitions contribute only a fraction fik 1 to the 

Since the sum of all transitions from level Ei should have the absorption strength of a classical oscillator we obtain the relation 

The summation extends to all upper levels Ek which can be reached by allowed transitions from level Ei including the ionization or dissociation continuum. 

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Many methods for the evaluation of from equation ( Al.5.20) use moments of the dipole oscillator strength distribution (DOSD) defined, for molecule A, by... 

Kumar A, Fairley G R G and Meath W J 1985 Dipole properties, dispersion energy coefficients and integrated oscillator strengths for SFg J. Chem. Phys. 83 70... 

Kumar A and Meath W J 1992 Dipole oscillator strength properties and dispersion energies for acetylene and benzene Mol. Phys. 75 311... 

Meath W J and Kumar A 1990 Reliable isotropic and anisotropic dipole dispersion energies, evaluated using constrained dipole oscillator strength techniques, with application to interactions involving H2, N2 and the rare gases Int. J. Quantum Chem. Symp. 24 501... 

Kutzelnigg W and Maeder F 1978 Natural states of interacting systems and their use for the calculation of intermolecular forces. III. One-term approximations of oscillator strength sums and dynamic polarizabilities Chem. Phys. 35 397... 

Kuhn H 1958 Oscillator strength of absorption bands in dye molecules J. Chem. Phys. 29 958-9... 

The Bom approximation for the differential cross section provides the basis for the interpretation of many experimental observations. The discussion is often couched in temis of the generalized oscillator strength. 

Assuming the validity of the Bom approximation, an effective generalized oscillator strength can be derived in temis of experimentally accessible quantities ... 

A particularly important property of the generalized oscillator strength is that, for high-energy, small-angle... 

A succinct picture of the nature of high-energy electron scattering is provided by the Bethe surface [4], a tlnee-dimensional plot of the generalized oscillator strength as a fiinction of the logaritlnn of the square of the... 

B2.2.5.5 ATOMIC FORM FACTOR AND GENERALIZED OSCILLATOR STRENGTH... 

In temis of the fonn factor the generalized oscillator strength is defined as... 

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... 

An alkyl group in the chain of a monoraethine thiazolocyanine prevents the molecule from being planar. It gives a bathochromic shift of 40 nm and a decrease of the oscillator strength (26), as is the case for other methine dyes. 

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... 

One characteristic property of dyes is their colour due to absorption from the ground electronic state Sq to the first excited singlet state Sj lying in the visible region. Also typical of a dye is a high absorbing power characterized by a value of the oscillator strength/ (see Equation 2.18) close to 1, and also a value of the fluorescence quantum yield (see Equation 7.135) close to 1. 

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