Orbital-Optimized Unitary Coupled Cluster for Indirect Nuclear Spin-Spin Coupling Constants within a Quantum Linear Response Framework

TL;DR

This work develops a quantum-linear-response framework within an active-space formalism to compute indirect nuclear spin-spin coupling constants relevant to NMR, using unitary CC and orbital-optimized UCC ansätze. By decomposing the couplings into DSO, PSO, FC, and SD contributions and employing triplet spin-adapted operators within a truncated active space, the authors benchmark UCCSD and ooUCCSD against CASCI/CASSCF and CCSD across five small molecules. They find that truncating to doubles suffices for most cases and, crucially, that orbital optimization dramatically improves robustness and agreement with CCSD, particularly for FC-dominated terms. The results establish ooUCCSD as a promising, quantum-computing-friendly approach for accurate NMR coupling constants and pave the way for assessing noise and scalability in quantum simulations of electronic response properties.

Abstract

We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.

Figures (14)

• Figure 2.1: Breakdown of spin-spin coupling constant of H$_2$ in a 6-31G-J basis into individual contributions. Note that the PSO contribution is zero for all methods and active spaces.
• Figure 2.2: Breakdown of the H-H spin-spin coupling constant of H$_2$O in a 6-31G-J basis into individual contributions.
• Figure 2.3: Breakdown of the O-H spin-spin coupling constant of H$_2$O in a 6-31G-J basis into individual contributions.
• Figure 2.4: Breakdown of the H-H spin-spin coupling constant of NH$_3$ in a 6-31G-J basis into individual contributions.
• Figure 2.5: Breakdown of the N-H spin-spin coupling constant of NH$_3$ in a 6-31G-J basis into individual contributions.