Spin-orbit couphng

Danovich, D., Shaik, S., 1997, Spin-Orbit Couphng in the Oxidative Activation of H-H by FeO+. Selection Rules and Reactivity Effects , J. Am. Chem. Soc., 119, 1773. 

The various mechanisms which affect the Ti-<- Sq intensity and thus the radiative lifetime have been discussed earlier. For the class of aromatic hydrocarbons spin-orbit couphng is small and a t5q3ical value of about 30 sec for Tr seems appropriate However, the observed phosphorescence lifetimes vary greatly, demonstrating in most cases a dominating influence of the radiationless contribution. Siebrand and Williams > have noticed a very interesting correlation (Fig. 27) between the radiationless deactivation rate = 1 /rri and the triplet... 

It is worthy of note that in the complexes with Csv symmetry such as [CuBr(Meetren)]Br (47, 42) (Fig. 10) the spectra still have two d—d bands and have much the same appearance as those of Dsh chromophores (Fig. 14). In the above compound the two bands, when resolved into Gaussian components, are found at 10.3 (e 450, P = 5.4-10 3) and 13.5 kK (e 180, P=1.4-10 3) ( ). Their separation of 3.2 kK is in this case too large to be attributed solely to spin-orbit couphng and the two bands are therefore assigned as - 2 (1) and - 2 (2) (8). This spectrum is very similar to that of the chromium(II) analog (d< configuration). 

The only term depending upon % is the last on the left hand side and this is just the spin-orbit couphng. If this term is dropped x-independent solutions, corresponding to zero spin-orbit couphng, are obtained. However, the large relativistic shifts, the mass velocity and Darwin terms are retained. In Fig. 3, for example, the relativistic levels remain in place but each of the spin-orbit split pairs is replaced by the average energy level... 

The second contribution to the temperature-dependent MCD from spin-orbit couphng involves the perturbation of the transition dipoles to give... 

Spin-orbit coupling The interaction of the electron spin magnetic moment with the magnetic moment due to the orbital motion of the electron. One consequence of spin-orbit couphng is the mixing of zero-order states of different multiplicity. This effect may result in fine structure called spin-orbit splitting. 

It has been shown that the spin-Hall effect may arise from various spin-orbit couphngs, such as a spin-orbit (SO) interaction induced by the electron-impurity scattering potential,a Rashba SO conphng in two-dimensional systems, etc. Murakami et al. also predicted a nonvanishing spin-Hall cnrrent (AHC) in a perfect Luttinger bnlk p -type semiconductors (no impurities or defects)." Experimental observations of the spin-Hall effect have been reported recently in a n -type bnlk semiconductor and in a two-dimensional heavy-hole system. ... 

For definitions of the mass-velocity, Darwin, and spin-orbit couphng terms, see ... 

The spin-orbit couphng constant / used to be reduced in magnitude by the amount k as compared to the free-ion value The Zeeman operator can be expressed with the help of the relationship... 

We continued by considering an improved electronic model [251,252,254] that includes spin-orbit couphng of the zero phonon E and T2 excited states. The presence of spin-orbit coupling provides a mechanism for incorporating spin-allowed character into the E —> A2 transition and contributes to an increase in fg. The extent of spin-orbit coupling depends on the spin-orbit coupling constant Vs(, ... 

We note that the coefficient of %+ in (or the coefficient of 5 in ( i) has an absolute value close to unity so that the lowest Kramers doublet closely resembles the -orbital. The departure from exact correspondence or the reason for the appearance of the terms in vj and is due to spin-orbit coupling. Thus the main effect of spin-orbit couphng... 

The interpretation of the cesr signals in terms of particle size has not been attempted. All the authors notice Cuxie-Weiss behavior, which is indicative of quantum-sized particles [87,89]. One is tempted to locate these particles in the supercages. The maximum diameter is then aroimd 1.2 nm, which corresponds to 630 li, 252 Na, 88 K, 71 Rb or 48 Cs atoms in a closed packed spherical arrangement. The Hne width, increasing with the size of the atom, is qualitatively explained by this decrease of the number of atoms per cluster. The g values are equal to or somewhat lower than the free electron values. The deviation is explained by spin-orbit coupHng effects and thus is more pronounced for the heavier elements (Table 6). 

Relativistic effects, such as mass-velocity, Darwin and spin-orbit couphng perturbative corrections, or more sophisticated relativistic treatments. Obviously, these corrections become important even at the chemical accuracy level if elements from the lower part of the periodic table are considered. 

Keywords Configuration interaction (Cl) Full Cl Multireference single- and double-excitation Cl (MRD-CI) Condon rules Slater determinants Table Cl Direct Cl Spin-orbit couphng... 

---