Spin-orbit coupling direct

When spin-orbit coupling is introduced the symmetry states in the double group CJ are found from the direct products of the orbital and spin components. Linear combinations of the C"V eigenfunctions are then taken which transform correctly in C when spin is explicitly included, and the space-spin combinations are formed according to Ballhausen (39) so as to be diagonal under the rotation operation Cf. For an odd-electron system the Kramers doublets transform as e ( /2)a, n =1, 3, 5,... whilst for even electron systems the degenerate levels transform as e na, n = 1, 2, 3,. For d1 systems the first term in H naturally vanishes and the orbital functions are at once invested with spin to construct the C functions. 

Here, L is the angular momentum operator, ge is the g value for the free electron (ge = 2.0023), and X is the spin-orbit coupling constant. Considering only the z direction, this equation becomes... 

Phosphorescence excitation spectroscopy also allows us to observe the transitions starting at 389 nm to the second triplet state, which is of (n,n ) nature. Direct spin-orbit coupling (mechanism I) to a Sn n,n ) state introduces strong in-plane, long-axis polarization. Indeed, in-plane polarization is preferred over out-of-plane polarization by 3 1, and long-axis polarization is about four times stronger than the short-axis contribution. 

The basic mechanism of spin-orbit coupling is magnetic induction. It is therefore a truly relativistic effect, as will be discussed shortly. The potentials of a moving charge can be found from Maxwell s equations, as direct solutions or from Lorentz transformations of potentials of a static charge to a moving frame. Maxwell s equations can be divided into the homogeneous parr... 

The crystal field interacts directly only with the orbital motion of the unpaired electrons and it has an effect on the electronic spins only through the spin orbit coupling. The strongest spin-lattice interaction will therefore occur for ions with ground states having an appreciable orbital character. 

The difference between Es and ET is about constant for the helicenes with five to nine rings (Table 22), while the kisc increase by a factor of about 3 I25). This may suggest the participation of a quasi degenerate triplet state in the intersystem crossing. This most likely will be the 3Lb state since a direct spin-orbit coupling between Lb and 3Lb is allowed in the helicenes because of their C2-symmetry. It is proposed 125) that the increase in kisc reflects the departure from coplanarity when the amount of benzene rings increases. 

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