Orbital interaction nondegenerate

Figure 3.5. Orbital interaction diagrams a) nondegenerate case (b) degenerate case.

Consider a dn configuration present in a crystal field that leaves the ground state nondegenerate except for spin. The ground state then consists of (25+ l)-spin states and the effect of the spin-orbit interaction plus the magnetic field can be computed using first- and second-order perturbation theory. If we take as the perturbation operator... 

It is of interest to compare the nature of the HOMOs in 10-electron systems Nj and CO. The HOMO 2o of N3 shown in Figure is stabilized by d eneiate orbital interaction but destabilized via nondegenerate interaction (see 6.4). If the non-degenerate contribution is larger than the degenerate one then this orbital too can... 

In relativistic calculations, the spinors are not necessarily so well separated, due to the spin-orbit interaction. As an example of the effect of spin-orbit interaction, we choose the atoms of group 14—C, Si, Ge, Sn, Pb—which in a nonrelativistic picture have the valence configuration np, and the ground state is np i P) in LS coupling. In a relativistic model the np manifold splits into the nondegenerate sets of npi/2 and np3/2 spinors. If we apply a simple Aufbau principle, we would end up with the state 2p i22py2 J = 0) for the relativistic ground state of C. If we expand the 2p /2 spinor into spin-orbitals, we find that this state is % and / 2p ( S), which we know... 

In a nondegenerate orbital interaction, the magnitude of the interaction energy is inversely proportional to the energy difference between the interacting orbitals. 

In both degenerate and nondegenerate orbital interaction cases, a two-orbital-two-electron interaction is stabilizing, while a two-orbital-four-electron interaction is destabilizing. 

As mentioned in Chapter 3, these MOs yr, and xj/j can undergo further orbital interactions with other MOs via nondegenerate perturbations. 

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