Relativistic unitary coupled cluster method for ground-state molecular properties

TL;DR

This work addresses the challenge of accurately predicting ground-state first-order molecular properties for heavy-element systems by developing a relativistic unitary coupled cluster framework with an expectation-value formalism. It contrasts perturbative UCC3 with a non-perturbative qUCCSD approach, implemented in a four-component relativistic setting, and validates the methods against CCSD Z-vector results and experimental data. The qUCCSD method consistently yields results in close agreement with CCSD Z-vector for properties such as permanent dipole moments, hyperfine structure constants, and electric field gradients, while UCC3 often exhibits sizable deviations due to incomplete relaxation treatment. The findings demonstrate the viability of the Unitry-Coupled-Cluster framework for relativistic first-order properties on classical hardware and suggest directions toward higher-order properties and broader chemical systems.

Abstract

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.

Figures (4)

• Figure 1: (a). Comparison of the total PDM calculated using the four-component relativistic UCC3, qUCCSD, and the Z-vector. (b) Comparison of the relative variation of PDM calculated using the UCC3, qUCCSD, and the Z-vector method from the experimental values.
• Figure 2: Comparision of the (a) $A_{\parallel}$ and (b) $A_{\perp}$ for the UCC3, qUCCSD and the Z-vector methods .
• Figure 3: Comparison of the relative deviation of (a) $A_{\parallel}$ and (b) $A_{\perp}$ for the UCC3, qUCCSD, and the Z-vector method with respect to the experimental values.
• Figure 4: (a) Comparison of the $q_{zz}(\vec{R}_{X})$ values (in a.u.) in FX(X = F, Cl, Br, I, At) molecules using four-component UCC3, qUCCSD and the CCSD Z-vector methods. (b) Relative variation of $q_{zz}(\vec{R}_{X})$ values calculated with UCC3 and qUCCSD methods in position X with respect to the CCSD Z-vector values.