CC theory is a high-accuracy method in electronic-structure calculations, but its steep scaling has motivated local correlation (LC) methods relying on unitary transformations away from the MO basis, where cluster amplitudes are commonly updated with fixed-point (FP) iteration using orbital-energy denominators, an approach supported by the diagonal Fock operator and its perturbative relation to the 0th-order Hamiltonian. Transformed orbitals enhance locality or screening, but perturbative partitioning is disrupted and the canonical FP map is not guaranteed to converge. We show that under such gauge transformations the FP iteration can acquire spectral radius greater than unity and diverge for realistic molecules. We assess a gauge-robust solver effective across gauges, and demonstrate that it reliably restores convergence in LCCC calculations. Our results clarify the gauge dependence of solver performance in CC theory and provide a practical path toward stable, efficient LC algorithms.

Chanaka Mapa is a third-year Ph.D. student in the RPI Department of Mathematical Sciences, supervised by professor Fabian Falustich. He develop scalable algorithms for quantum many-body problems.

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