Electronic transitions, forbidden oscillator strength

We saw earlier that the probability of electric dipole absorption is related to the transition dipole moment. However, there are a variety of terms commonly used to describe the strength or probability of absorption. The allowedness or forbiddenness of the transition, and oscillator strength, /, are useful ideas where the relative, rather than absolute value, of the strength of coupling is required. These terms are factors used to describe how likely absorption is by reference to the ideal oscillator of a free electron where the transition is fully allowed and both the allowedness and oscillator strength are unity. 

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.

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

Rate Constants of Radiative Transitions. The natural radiative rate constant kr of an electronic transition from a state to a state Sf is related to the transition moment M and thereby to the oscillator strength f. It is convenient to factorize f to highlight the various factors which determine to what extent a transition is allowed if near 1) or forbidden (f near 0). The transition moment includes the displacement of all particles of the molecule during the transition, nuclei as well as electrons. The heavy nuclei move much more slowly than the light electrons so that their motions can be considered to be independent. Within this approximation the transition moment is given as... 

Having accurate semi-empirical values of the energy levels and eigenfunctions one is in a position to calculate wavelengths and oscillator strengths of allowed and forbidden electronic transitions in the inter-... 

Experimentally, the oscillator strength is given by the integrated intensity (area) under the absorption band, while theoretically it is given by the square of the transition moment integral J gM s. dr. This leads to the selection rules for electronic transitions when jTgMTedi is nonzero, there is absorption intensity and the transition is allowed when this integral is required to be zero, the transition is forbidden. ... 

Since the relaxation of the higher exciton states occurs on an ultrafast timescale of about 100 fs [23,26], the absorption spectrum for a closed structure, Fig. 26.4, top and centre, consists of either one or a few relatively broad spectral bands, respectively. For both cases, i.e., circular and elliptical arrangement, the transitions from the k = 1 exciton states are polarized perpendicular with respect to each other. Moreover, the lowest exciton state is optically forbidden, because a C2-type symmetry reduction alone, i.e., an ellipse, does not give rise to oscillator strength in the k = 0 state. This situation is reminescent to the electronically excited states of the B850 BChl a... 

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