Electric and magnetic dipole transition moments

Denoting the electric and magnetic dipole transition moments of oscillators a and b as p, lUg and m, lUb, respectively, the rotational strength of the coupled oscillator is given by (34)... 

Thus, we feel that the a-helical and the extended" helical structure are well established in VCD, and that there exists a simple method for the interpretation of the data. The VCD features of the B-pleated sheet structure appear reasonably well established, too, although its interpretation is much more difficult. Since the data are mono-signate, the DECO model is not appropriate (it always predicts conservative couplets). Nafie and coworkers explained such monosignate VCD in terms of a model similar to one described earlier by Schellman [24], with nearly co-linear (and antiparallel) electric and magnetic dipole transition moments [30]. 

Optical activity is almost always related to spectroscopic transitions allowed to both electric and magnetic radiation, consequent on the existence of electric and magnetic dipole transition moments /t andm joining the ground state to at least one excited state and with the condition that ft The symmetry... 

Theoretically, can be related to the electric and magnetic dipole transition moments and (g denotes the ground state and n the excited state) ... 

Fig. 15.1 Comparison of the angle between electric and magnetic dipole transition moments of the chirality transfer v(C-D) mode in the 1 1 pulegone-CDas complexes calculated by using diverse computational criteria (a) and 9 diverse complex arrangements (b) (Reproduced from Ref. [80] with kind permission of Wdey-Liss, Inc)...

Meanwhile, CD intensity is proportional to the rotational strength R, the imaginary part of the scalar product of the electric and magnetic dipole transition moments fi and m, respectively. 

Thus, a nonvanishing electronic contribution to the magnetic dipole transition moment is obtained. Assuming nuclear wavefunctions to be harmonic oscillator wavefunaions, the final expressions for the individual electric and magnetic dipole transition moments are obtained respectively as,... 

In practice, the electric and magnetic dipole transition moments are usually expressed as summations of atomic properties, namely the atomic polar tensor (APT), Pgp, and atomic axial tensor (AAT), respectively. In the... 

Hansen, A.E. On evaluation of electric and magnetic dipole transition moments in the zero differential overlap approximation. Theor. Chim. Acta 6, 341-349 (1966)... 

Note that in the simplest quantum mechanical expression, for a CD spectrum to be observed there must be both electric and magnetic dipole transition moments, for which the cosine between the two transition dipole moments must be non-zero (Figure 2). Essentially, this means that the transition dipole moments must have a parallel (or anti-parallel) relationship to one another. Without all three components (the electric dipole transition moment, the magnetic dipole transition moment, and their parallel relationship) there can be no optical activity. 

There is only one other ab initio implementation of the theory of optical activity to calculate optical rotatory strengths, that due to Hansen and Bouman, based on the random-phase approximation (RPA) and implemented in the program package, RPAC. The RPA method is intended to include those first-order correlation effects that are important both for electronic transition intensities and for excitation energies. The electric and magnetic dipole transition moments in RPA are given by equations (14), (15), and (16) (analogous to equations 7, 8, and 9, above). 

MCD spectra of n systems contain a wealth of detailed information about electronically excited states that is not accessible by other means. They reflect particularly clearly the effects of molecular structure on electric and magnetic dipole transition moments, including not only their relative orientation in the molecular framework, but also their relative sense. They also report in exquisite detail the nature of vibronic interactions. 

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