Investigating the robustness of the fixed-point iteration in local-correlation Coupled-Cluster algorithms.

Coupled-cluster (CC) theory is a widely used, high-accuracy method in electronic-structure calculations, with the CCSD(T) variant often regarded as the “gold standard” of quantum chemistry. However, the steep polynomial scaling of CC methods in the canonical molecular-orbital (MO) basis limits their direct application to relatively small systems. This motivated the development of local-correlation (LC) approaches that employ unitary transformations away from the MO basis to reduce computational cost while retaining accuracy.

The CC equations in MO basis, are commonly solved through a simple fixed-point (FP) iteration involving orbital-energy denominators. The validity of this procedure follows from the diagonal form of the Fock operator in the MO basis and its perturbative correspondence with the zeroth-order Hamiltonian. When orbital transformations are introduced to enhance locality or enable screening, however, this perturbative partitioning is disrupted, and the canonical FP map is no longer guaranteed to converge.

We show that gauge transformations yield canonical FP iteration spectral radii above unity, leading to guaranteed divergences for realistic molecules. We assess a gauge-robust solver that is effective across different orbital gauges, demonstrating that it reliably restores convergence in localized CC calculations, which elucidate the gauge dependence of iterative solver performance in CC theory and provide a practical route toward more stable LC-CC algorithms.