Kramers double-replacement

The formalism can be straightforwardly extended to two-electron operators with the introduction of Kramers double replacement operators [81]. However, the multitude of terms arising in subsequent derivations finally leads to a rather cumbersome formalism. In the author s opinion it is better to derive general formulas and then consider the structure due to time reversal symmetry after the derivation. 

Using these auxiliary operators, it is easy to define Kramers double-replacement operators in an analogous manner ... 

In principle, all four-component molecular electronic structure codes work like their nonrelativistic relatives. This is, of course, due to the formal similarity of the theories where one-electron Schrbdinger operators are replaced by four-component Dirac operators enforcing a four-component spinor basis. Obviously, the spin symmetry must be treated in a different way, i.e. it is replaced by the time-reversal symmetry being the basis of Kramers theorem. Point group symmetry is replaced by the theory of double groups, since spatial and spin coordinates cannot be treated separately. 

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