  Adapting a veritable many-body method to a system of non-interacting
particles (NIP), while being trivial from a physical point of view, can be of
interest with regard to methodological aspects. In this article we study the
NIP versions of the bi-orthogonal (BCC) and unitary (UCC) coupled-cluster
methods both for the ground state and generalized excitations. The essential
simplification here is that the cluster operator is confined to single (or
$p$-$h$) excitations. For the ground state, specifically the CC amplitude
equations, the NIP versions illustrate the enormous complexity of the UCC
approach as compared to the BCC concept. In the treatment of excitations, on
the other hand, the UCC outperforms the BCC method, as the UCC secular matrix
is block-diagonal with respect to the excitation classes, e.g., $1h$
(one-hole), $2h$-$1p$ (two-hole-one particle), $\dots$ excitations of $N\!-\!1$
particles. Moreover, the UCC basis states are essentially equivalent with the
states used in the ADC/ISR (algebraic-diagrammatic construction/intermediate
state representation) approach, whose NIP version has been discussed in a
recent paper [J. Schirmer, arXiv:2309.15721].
