Spin-orbit energies/splittings

Spin-orbit interaction splits the components so that the energy level after interaction is shifted by... 

The first excited CFT 2 g is well separated from the ground 2T2g by the energy A0 = 10Dq. The spin-orbit coupling splits the ground term into / (ground) and / 7 multiplets separated by S0/hc = 237 cm 1, which results from the calculations in the complete d1 space spanned by ten functions (Table 70). 

In the octahedral case, spin orbit coupling splits the ground level yielding a Kramers doublet of lowest energy6-1. When lower symmetry components are operative it is very important to know the relative energy order of the three orbital split states. Since the parent state can be considered to a good approximation to originate from the t g... 

With the basis functions of Table 8.46 and the one-electron matrix elements of equation (8.103), it is a simple matter to calculate the crystal field energies. We present in Table 8.48 the complete crystal-field and spin-orbit energy matrices of f1 in D3h the splitting of the 2F of f1 configuration under spin-orbit interaction and further in D3h crystalline field is shown in Fig. 8.44. 

The most widely-used source is the photoemission GaAs source (Gar-win, Pierce and Siegmann, 1974 Pierce et al, 1980), the principle of which is shown in fig. 2.11. The spin—orbit interaction splits the P-valence band at the r point (fe = 0 in the plot of one-electron energy E vs momentum k) into fourfold degenerate P3/2 and twofold degenerate Pl/2 bands with a separation of 0.34 eV. 

The presence of these three electronic states, as well as the sizable spin-orbit (SO) splitting in the F and Cl atoms (1.15 kcaEmol for F and 2.52 kcaEmol for Cl [25]) raises two important questions (1) what is the reactivity of the excited spin-orbit state relative to that of the ground state and (2) how well is the dynamics of the reaction described by calculations on a single, electronically adiabatic potential energy surface (PES). If the reaction were to proceed adiabatically on a single PES, as would be predicted by the Bom-Oppenheimer (BO) approximation, then the excited SO state should not react.[26, 27]... 

Hexafluorocobaltate(III) ion is a high-spin complex. Draw the orbital-energy splitting diagram for its d orbitals. 

Figure 12.6 The splitting of atomic energy levels. The Russell-Saunders ftee ion term (left) becomes more complex when the spin and orbital contributions couple (centre). In a magnetic field each spin-orbit level splits into a further (2J + 1) equally spaced levels (right)...

The results obtained by Glurdzhidze et al. (1978) by reflection spectra in the phonon energy range 0.06-2.3 eV have permitted the observation, for the first time, of the fine structure of the absorption and reflection spectra associated with the splitting of the initial and final electron states. The authors conclude that the spin-orbit interactions splits the 4f ( Hj), 4f ( Fj) and 5d t2g states. Moreover, there is an energy gap of 0.15 eV between the valence and conduction bands. 

Spin-orbit coupling splits free-ion terms into states of different energies. The term therefore splits into states of three different energies, and the energy level diagram for the carbon atom is as follows ... 

Each energy level of a multiplet with A 0 is doubly degenerate, corresponding to the two values for M. Thus a A term has six different wave functions [Eqs. (13.87), (13.89), (11.57) to (11.59)] and therefore six different molecular electronic states. Spin-orbit interaction splits the A term into three levels, each doubly degenerate. The double degeneracy of the levels is removed by the A-type doubling mentioned previously. 

---