Dipole transition moment, electric magnetic

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. 

Vibrational circular dichroism arises from the interference of the electric dipole transition moment (p joi and the magnetic dipole transition moment (m )io and is proportional to the rotational strength, / ,o, where... 

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)... 

The spectra in this figure represent one of the strongest cases for the ring current mechanism of VCD intensity enhancement. In this case, currents increase the magnetic dipole transition moment without altering the relative arrangement of electric dipole transition moments and the relative intensity pattern is preserved. In the structures 42 and 43, we show that in the A complex, 42,... 

The formulation of magnetic dipole transition moments is unfortunately less straightforward. Compare the electronic contributions to the electric and magnetic dipole moments of G ... 

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]. 

The origin of the electric dipole intensity for the AMj = 1 transitions studied merits further consideration. If the static magnetic field is 5 kG, the motional electric field has a magnitude of approximately 3 V cm-1 and is perpendicular to the applied magnetic field. This electric field mixes a state [./, Mj) with the states. J 1, Mj 1) and in order to obtain non-zero electric dipole transition moments for the transitions. /. Mj) o IJ, Mj 1), the oscillating electric field must be applied parallel to the static magnetic field. 

Here i//0 is the ground vibrational wave function and ij/ is the wavefunction corresponding to the first excited vibrational state of the th normal mode /< is the electric dipole moment operator Qj is the normal coordinate for the /th vibrational mode the subscript 0 at derivative indicates that the term is evaluated at the equilibrium geometry. The related rotational strength or VCD intensity is determined by the dot product between the electric dipole and magnetic dipole transition moment vectors, as given in (2) ... 

For a carbonyl group in a Cjv symmetry environment, such as in formaldehyde, the dipole approximation for the n- r transition yields JWo f > 0 and Mo f = 0. Although the transition is magnetically strongly allowed and polarized along the CO axis, it is electrically forbidden. The absorption therefore is of very weak intensity and the rotational strength is equal to zero. Perturbations by vibrations or by an achiral solvent can affect and to such an extent that a small nonzero electric dipole transition moment results but again this produces only a very small absorption intensity and... 

We can deduce the symmetry of a response tensor by considering the operators that enter the numerator of its quantum mechanical expression. For example, the product of three electric-dipole transition moment operators in Eq. (14) render SFG a parity-odd and time-even process. It follows that a third-order process requires nonlocal magnetic-dipole contributions in order to be parity-odd and that a local fourth-order process is parity-odd within the electric-dipole approximation. Some pseudoscalars that arise at order n are tabulated below. 

In the ligand polarization mechanism for optical activity, the potential of the electric hexadecapole component, Hxy(x>-y>), produces a determinate correlation of the induced electric dipole moment in each ligand group which does not lie in an octahedral symmetry plane of the [Co Ng] chromophore (Fig. 8). The resultant first-order electric dipole transition moment has a non-vanishing component collinear with the zero-order magnetic moment of the dxy dxj yj transition in chiral complexes, and the scalar product of these two moments affords the z-component of the rotational strength, RJg, of the Aj -> Ti octahedral excitation. 

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