Kramers Degeneracy / Pair

An electron configuration with an odd number of electrons (f, f, ..., etc.) has a Kramers degeneracy that can be lifted by a magnetic field but not by a crystal field. However, it is possible that the pair of states which lies lowest will not have an EPR signal because the selection rule AJ = 1 will be violated. For example, consider a J = 5/2 term in a purely axial crystal field. This term will be split into three doublets, J, = 1/2, 3/2, 5/2. If the crystal field is such that the = 3/2 or = + 5/2 state is lowest, there will be no EPR transitions allowed. 

Genuine 2m-fold degenerate irreps, where the members of Kramers pairs can be assigned to different rows. An example is Td, which has two real irreps of degeneracy 2 and one of degeneracy 4. 

We can analyze this problem formally by considering a doubly occupied Kramers pair. For simplicity we drop the small component and work with 2-spinor functions in a group that has no degenerate irreps. We also represent the wave function as a simple Hartree product. The extension to a determinantal function, 4-spinor functions, and groups with degeneracies is straightforward, but it would unnecessarily complicate the analysis. We write the wave function as... 

Here, S is the pseudo-spin of the system, and F is the KS Fock operator up to first order in the external field or the nuclear spin magnetic perturbation. LWA is suitable for Kramers doublets. Assuming no spatial degeneracy, a pair of degenerate Kramers orbitals is initially calculated from SO DFT by assigning equal occupations of 0.5 to two frontier orbitals. One then chooses one of them, (p, and constructs from its real and imaginary parts of the spin a and l3 components the Kramers pair d>i, 2 as... 

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