Kramers systems

The singlet (S = 0) state lies about 1000 cm above the ground state triplet (S = 1) in the EPR spectrum of free dioxygen. Transitions associated with triplet oxygen in solution are detectable by EPR at low temperatures, but dioxygen complexes with even electron metal centers (e.g., ferroheme) are not generally observable by this method. Usually, only odd electron systems (Kramers systems) are detectable by magnetic resonance. 

For Kramers (e.g. one-electron) states where the eigenvalue of T2, A = — 1, the metric gAA is antisymmetric, and so relating to symplectic algebras (in relativistic terms to pure torsion rather than to curvature), rather than symmetric as for non-Kramers systems. The joint action of Hermitian conjugation and time reversal (which is not commutative) is summarized with the above results for these individual operations in Table 1. 

Surerus, K. K. Hendrich, M. P. Christie, P. D. Rottgardt, D. Orme-Johnson, W. H. Miinck, E. Mossbauer and integer-spin EPR of the oxidized P-clusters of nitrogenase POX is a non-Kramers system with a nearly degenerate ground doublet. J. Am. Chem. Soc. 1992, 114(22), 8579-8590. 

Half-integer systems with. S > 1 /2 are referred to as Kramers systems. These systems have a degeneracy in the ground state that is relieved through Zeeman interaction. The simplest example to consider is S = 3/2. To make things easier, we will assume an axial system (A/D = 0) in a zero external field (Bo)- Therefore, the total energy is... 

---