Coupled cluster (CC) methods are among the most accurate methods in quantum chemistry. However, the standard CC linear response formulation is not gauge invariant, resulting in errors when modelling properties like optical rotation and electron circular dichroism. Including an explicit unitary orbital rotation in the CC Lagrangian makes the linear response function gauge invariant, but the resulting models are not equivalent to full configuration interaction (FCI) in the untruncated limit. In this contribution, such methods are briefly discussed and it is demonstrated that methods using a nonorthogonal orbital transformation, such as nonorthogonal orbital optimized CC, can converge to FCI in the untruncated limit. This has been disputed in the literature.