Kramers conjugate states

In the discussion of the Kramer s doublets we have dealt entirely with the properties of the atomic orbitals of the heme iron. In a different approach the electronic states are expressed in terms of molecular orbitals. This is particularly interesting for aromatic radicals because the unpaired electron spreads out over the entire conjugated system of -orbitals. 

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. 

Sirringhaus, H., Tessler, N., Thomas, D.S., Brown, P.J. and Friend, R.H., High-mobility conjugated polymer field-effect transistors. In Advances in Solid State Physics, Vol. 39, ed. B. Kramer Vieweg, Braunschweig, Germany, 1999, 101-110. 

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