Theory magnetic dipole transition moment

Deutsche and Moscowitz, a number erf semiempirical models have been proposed to explain features in experimental spectra. Although none has enjoyed any but the most modest successes, experience is gradually accumulating on the limits of applicability. Some of these are reviewed below. It is readily shown that within the Born-Oppenheimer (BO) approximation, the electronic contribution to the magnetic dipole transition moment associated with a vibrational transition of a molecule in its ground electronic state vanishes. A non-BO theory of VCD intensities was independently developed by several groups.2° 2" ... 

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). 

Analogously to UV/ECD, IR and VCD intensities are proportional to the quantities dipole (D) and rotational (R) strengths, respectively, which are calculated using equations (16) and (17), at the same level of theory employed in the optimization step. However, in the case of VCD, the electric (jx) and magnetic (m) dipole transition moment vectors include the wavefunctions of the ground (0) and the first excited vibrational state (1), within the ground electronic state of the molecule. Furthermore, in the harmonic approximation, the dipole strength in the normal mode Qa is proportional to ... 

In group theory, the electric dipole operator transforms according to the operations of translation, and the magnetic dipole operator transforms as a rotation. It is not difficult to show that the individual transition moments are invariably orthogonal as long as the molecular point group contains improper axes of rotation. This rule is often trivialized to... 

The CD strength of a magnetic dipole allowed d-d transition of the chromophore A as defined earlier arises from second-order perturbation theory, and incorporates the two electric moments involving a CT state (referred to as the intermediate state) of the A chromophore to provide the dipole-dipole coupling to the B chromophore system. The CD arising from a particular chelate I at the d-d transition energy has the form (5 )... 

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