Spin-orbit mixing

Fig. 29. Group-theoretical predictions of the polarizations of the vibronic transitions, allowed to second order, from the individual zero-field levels of the lowest triplet state of 2,3-dichIoro-quinoxaline to vibrational levels of the ground electronic state. Solid line transitions gain intensity by spin-orbit mixing between states which differ in the electronic type of one electron e.g., S n and T . The dashed line transitions require the mixing to occur between states of the same electronic type (e.g., S and T n ) and is expected to be weaker. The dash-dotted transition could involve the favorable mixing between states that differ in the electronic type of one electron, but a spin-vibronic perturbation is needed. (From Tinti and El-Sayed, Ref. ))...

In those calculations, the contributions from electronic orbital motion (induced by spin-orbit mixing) were estimated from crystal field theory (for the copper atom) or were neglected (for the nitrogen and hydrogen atoms). Here I discuss for the first time direct calculations of these contributions to the copper and nitrogen hyperfine tensors, as well as to the molecular -tensor. 

The luminescence of Bi " is quite diverse and depends strongly on the host lattice (Boulon 1987 Blasse and Grabmaier 1994 Blasse et al 1994). For the heavy Bi " the transitions between the ground state and the Pi state becomes additionally allowed by spin-orbit mixing of the Pi and Pi states. After excitation at low temperature, the system relaxes to the lowest excited state. Consequently, the emission at low temperatures can be ascribed to the forbidden transition Pq- Sq and has a long decay time. Nevertheless, both Pi and Po are emitting levels and they are very close so that at higher temperatures the luminescence from the Pi level may appear with a similar spectrum, but shorter decay (Fig. 5.49). 

C/° 2 Intensity parameter of a C term caused by spin-orbit mixing of... 

If accurate electronic wave functions are available, Aa> and Aa> can be estimated from equations (7.109) and (7.120) respectively. All nearby electronic states which contribute by spin-orbit mixing to A(2) must be included if the result is to be reliable. 

It is defined to operate within the ground vibronic state by (9.104), but the second-order part of the parameter X, (9.100), arises from spin orbit mixing of excited states with A equal to 0, 1 and AS = 0, 1. In molecules containing an atom beyond the first row of the periodic table, the second-order contribution to X (i.e. X(2)) is far larger than the first-order part, 7(1). 

Finally we note that it was possible to determine the value of the fourth-order spin spin splitting constant 0 the value of this parameter depends upon the spin-orbit mixing of excited electronic states with the ground state. 

The effect of suUur participation on the orbital g -shifts in the EPR spectra, illustrated in Pig. 20, accounts for the qualitatively different spectra observed for tyrosyl phenoxyl and Tyr-Cys phenoxyl radicals (Gerfen et al., 1996). The rhombicity of the simple tyrosyl radical EPR spectrum is a consequence of the splitting between gx and gy principal g -values. These g -shifts deviate from the free electron g--value ge = 2.00023) as a result of orbital angular momentum contributions. While a nondegenerate electronic state (such as the A" ground state for ere) contains no hrst-order unquenched orbital momentum, second-order spin-orbit mixing between close-lying a and a" functions results... 

Fig. 20. Spin-orbit mixing mechanism for orbital g-shifts in substituted phenoxyl radicals. The electronic g-tensor is perturbed by spin-orbit effects which can be viewed as orbital rotation elements. The perturbation of theg t term arises from mixing perpendicularly oriented valence orbitals on the same atom under the G orbital operator and summing these individual contributions over all atoms to produce the resultant molecular g-shift.

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