Electric dipole transition moment, determination

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. 

Theoretical calculation can also be used to determine the direction of electric dipole transition moments of a chromophore within a complex system (e.g., for the use of exciton chirality method). Although TDDFT calculations could be used for this purpose," the DeVoe polarizability model has also been applied for various compounds, including supramolecular systems. ... 

We mentioned in previous pages that (IIlB-22) was not the most efficient for use with electric-dipole-allowed transitions. The reason for this is that electric-dipole transition moments can be obtained experimentally from spectra they do not have to be estimated from wave functions pertaining to a hypothetical, completely isolated group. Therefore, it is wise to write our equations in a way which makes the best use of the experimentally determined transition moments and frequencies. 

In conventional photokinetic studies, radiation effects an electronic transition from the ground state of the molecule to some electronically excited state. Coupled with the electronic transition there are changes in the vibrational and rotational state of the molecule. For a transition to occur the Bohr frequency condition, Ae = hv = HcqIX, must be obeyed. Absorption at a specific wavelength is determined by the molar absorption coefficient which, for photochemically interesting problems, is proportional to the square of the electric dipole transition moment... 

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) ... 

Transition intensities are determined by the wavefunctions of the initial and final states as described in the last sections. In many systems there are some pairs of states for which the transition moment integral vanishes while for other pairs it does not vanish. The term selection rule refers to a summary of the conditions for non-vanishing transition moment integrals—hence observable transitions—or vanishing integrals so no observable transitions. We discuss some of these rules briefly in this section. Again, we concentrate on electric dipole transitions. 

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