Spin-orbit coupling constant interaction

The spin—orbit coupling constants f4f and fsd, which represent the relativistic spin—orbit interaction in the 4f and 5d shells, also determined by means of the radial wave functions Rrd of the 4f and 5d Kohn—Sham orbitals of the lanthanide ions.23... 

Spin-orbit interactions mix states with the same J but different L 8 by second (or higher) order perturbations, such perturbations become important when the separation between the levels is small. The spin-orbit coupling constants ( 4/) increase more rapidly through the rare earth series with increasing number of /-electrons than do the F s. This results in the breakdown of L 8 coupling even more near the middle of the rare earth series, because of the greater population of the upper... 

The operator//so = S llisi ofthe spin-orbit coupling interaction of [Fe(CN)6] is represented within the t2g ( , rj, t,)a and Q, rj, spin-orbital basis in (11) (the spin-orbit coupling constant (is defined as positive for Fe ) see Sect. 3.1 for its further use. 

The energies of the magnetic interaction of orbital and spin angular momenta are —A and +A/2 in the atomic ion, while they are —A/2, 0, and +A/2 in the molecular ion. Here, A is a spin-orbit coupling constant in the ground state of atomic ion. An additional off-diagonal matrix element arises in the molecular ion from the microscopic spin-orbit operator... 

Effantin, et al., (1982), Amiot and Islami (1986), and Wada and Kanamori (1999), in their analysis of CO a3n a 3E+ perturbations, found it necessary to include in their Heff fit model, in addition to the spin-orbit ( o) and L-uncoupling (/ o) off-diagonal interaction parameters, a direct spin-spin interaction parameter (e) as well as a second-order Hso x HROT interaction term (p3). The p3 parameter is not a centrifugal correction to either o or (3o. It is a cross term between the implicit iZ-dependence of the spin-orbit coupling constant of the c3n state and the explicit iZ-dependence of the B(R)J-h perturbation operator. 

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