Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling.

We present a formulation and implementation of the calculation of (orbital-unrelaxed) expectation values at the 4-component relativistic coupled cluster level with spin-orbit coupling included from the start. The Lagrangian-based analytical energy derivative technique constitutes the basic theoretical framework of this work. The key algorithms for single reference relativistic coupled cluster have been implemented using routines for general tensor contractions of up to rank-2 tensors in which the direct product decomposition scheme is employed to benefit from double group symmetry. As a sample application, we study the electric field gradient at the bismuth nucleus in the BiX (X = N, P) series of molecules, where the effect of spin-orbit coupling is substantial. Our results clearly indicate that the current reference value for the nuclear quadrupole moment of Bi needs revision. We also have applied our method to the calculation of the parity violating energy shift of chiral molecules. The latter property is strictly zero in the absence of spin-orbit coupling. For the HX (X = O,S,Se,Te) series of molecules the effect of correlation is found to be quite small.