Relativistic unitary coupled cluster method for ground-state molecular properties

We propose a relativistic unitary coupled cluster (UCC) expectation value approach for computing first-order properties of heavy-element systems. Both perturbative (UCC3) and non-perturbative (qUCC) commutator-based formulations are applied to evaluate ground-state properties, including the permanent dipole moment (PDM), magnetic hyperfine structure (HFS) constant, and electric field gradient (EFG). The results are compared with available experimental data and those from conventional coupled cluster (CC) calculations. The non-perturbative commutator-based approach truncated at the singles and doubles level (qUCCSD) exhibits markedly better agreement with both CCSD and experiment than the perturbative UCC3 method, likely due to its improved treatment of relaxation effects.

💡 Research Summary

The authors present a relativistic unitary coupled‑cluster (UCC) expectation‑value framework for the accurate prediction of first‑order molecular properties of heavy‑element systems. Starting from a four‑component Dirac–Hartree–Fock (DHF) reference, they construct the wavefunction as |Ψ⟩ = e^{T−T†}|Φ₀⟩, where the excitation operator T is truncated at the singles‑and‑doubles (SD) level. Because the unitary ansatz leads to an infinite Baker‑Campbell‑Hausdorff (BCH) expansion, two truncation strategies are explored: a perturbative MP‑based UCC(n) scheme and a commutator‑based scheme employing Bernoulli numbers. The latter gives rise to the quadratic UCC (qUCC) method, which retains all nested commutators up to a chosen order. In the expectation‑value formalism the property operator D is dressed by a series of commutators, D +