Relativistic unitary coupled-cluster method for ground-state molecular properties

We propose a relativistic unitary coupled-cluster expectation-value approach for computing first-order properties of heavy-element systems. Both perturbative and non-perturbative commutator-based formulations are applied to evaluate ground-state properties, including the permanent dipole moment, magnetic hyperfine structure constant, and electric field gradient. The results are compared with available experimental data and with those obtained using conventional coupled-cluster calculations. The non-perturbative commutator-based approach truncated at the singles and doubles level exhibits markedly better agreement with both the coupled-cluster Z-vector method and experimental values than the perturbative variant, likely due to its improved treatment of relaxation effects.