Operator representations in Kramers bases

Using the time-reversal symmetry operations, we introduce the time-reversal adapted Kramers basis operators Xpq± which are the natural expansion set for any relativistic Hermitian or anti-Hermitian one-electron operator and thus replace the spin-adapted basis operators of non-relativistic quantum mechanics. Depending on the time-reversal symmetry or Hermiticity of the one-electron operator, either X+ or X−, but never both of them, appear in the expansion, thus causing the symmetry blocking that is important for computational saving in relativistic electronic structure calculations. We determine the combinations of X operators that become irreducible tensor operators in the non-relativistic limit and we use the particle-hole expansion case to offer an interpretation of the new basis as operators that describe simultaneous excitation and deexcitation of particle-hole states with opposite spin-polarization in the non-relativistic limit.