Integrated rotatory strength

Experimentally, it has been customary to calculate the so-called rotatory strength, R, of a transition. The integrated rotatory strength of a transition b is related to As as follows ... 

Often the imaginary nature of this quantity is simply ignored or omitted. In some applications the complete numerator and denominator of eq. (21) are integrated over a band , and results are reported in terms of the ratio, Gium, of an integrated rotatory (or rotational) strength and dipole strength, D. ... 

The rotatory strength R can be compared with the measured difference in extinction coefficient for right and left polarized light As = Bl — Sr), integrated over the wavelength region of the absorbing band ... 

The form of eq. (11) is similar to that encountered in CD spectroscopy. Finally, it should be noted that this equation has been derived for measurements at a particular wavelength, X expressions involving integrated (over the electronic band) rotatory and absorption strengths may also be developed [2],... 

By analogy with the dipole strength [Eq. (8)], the rotatory (or rotational) strength Rj of a transition can be obtained from the integrated ellipticity values of a dichroic band. R may be evaluated approximately for a Gaussian curve by [see Ref. (18)]... 

We do not at first consider vibrational effects. These should be of primary importance in determining the shape of the rotatory dispersion curves in an absorption band (Moscowitz, 1957 Moffitt and Moscowitz, 1959), but they need not enter explicitly in the calculation of rotational strengths. This is completely analogous to the theory of electronic absorption spectra. For the integrated absorption one needs to use only the electronic wave functions, but... 

From a theoretical point of view, the leading term contributing to CD in randomly oriented molecules is due to the interference of electric and magnetic dipole transition amplitudes, with the rotatory (R) strength taken as a measure of CD. It is expressed from dipole and angular momentum integrals between initial and final states according to the expressions... 

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