Articles you may be interested in Description of spin-orbit coupling in excited states with two-component methods based on approximate coupled-cluster theory An ab initio two-component relativistic method including spin-orbit coupling using the regular approximation 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 209 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 H 2 X 2 (X = O,S,Se,Te) series of molecules the effect of correlation is found to be quite small. Published by AIP Publishing. [http://dx.