Magnetic-dipole transition strength

They are called, respectively, electric-dipole transition strength (Z>ns), magnetic-dipole transition strength (M ), and rotational strength (R ). Then, the total transition strength is given as + Afjjj 2Rj ). This indicates that the effects for left- and right-circularly... 

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)... 

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

The ellipticity, or the intensity of the circular dichroism (CD) spectrum, is fundamentally characterized by the rotatory strength R, which is given by the imaginary part of the inner product between the electronic and magnetic dipole transition moment vectors ... 

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) ... 

Stephens PJ (1987) Gauge dependence of vibrational magnetic dipole transition moments and rotational strengths. J Phys Chem 91 1712-1715... 

The oscillator strengths were calculated from the observed spectra using Equation 1. For the two cases in which the magnetic-dipole transition intensity is appreciable, the — fi3/2 transition of Er and the... 

The s are the intensity parameters. The line strength for the magnetic dipole transitions is given by... 

Here E(PJ) - E(j8 J ) = AE 0, the operators in general are defined by (4.12) and (4.13), AE and submatrix elements are presented in atomic units. Then WEk is in s-1. Let us recall that the oscillator strengths are dimensionless quantities. The relevant expressions for magnetic dipole transitions are given by formulas (27.8) and (27.9), respectively. 

It is important to realize that the dipole strength for MD fransifions are five orders of magnifude smaller than for fhe allowed ED fransifions. However, fhe induced electric dipole transitions in lanthanides are of fhe same magnifude as fhe magnetic dipole transitions. 

In general, transitions have partial magnetic dipole and partial induced electric dipole character. The total experimental dipole strength then contains contributions of both electric dipole and magnetic dipole transitions ... 

The magnetic dipole transitions (A/ = 1) are, as previously stated in the introduction, insensitive to the surroundings of the ion, and may therefore be used as a standard for comparison of other transition strengths. 

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