Eliminating gauge invariances in projected coupled cluster theory

Develop a fully satisfactory method to eliminate gauge invariances in projected coupled cluster theory, particularly in PCCSD when the disentangled cluster operator W is truncated, to ensure uniqueness of the projected coupled cluster solutions.

Background

Gauge invariances in projected coupled cluster arise from numerical invariances that persist when symmetry projection is combined with truncated excitation operators, leading to non-unique solutions in PCCSD.

While partial remedies have been proposed in the literature, the authors state that no fully satisfactory approach currently exists, highlighting a concrete methodological gap that impacts robustness and reproducibility.