  In this Communication, we provide numerical evidence indicating that the
standard single-reference coupled-cluster (CC) energies can be calculated
alternatively to its copybook definition. We demonstrate that the CC energies
can be reconstructed by diagonalizing the effective Hamiltonians describing
correlated sub-systems of the many-body system. In the extreme case, we provide
numerical evidence that the CC energy can be reproduced through the
diagonalization of the effective Hamiltonian describing sub-system composed of
a single electron. These properties of CC formalism can be exploited to design
protocols to define effective interactions in sub-systems used as a probe to
calculate the energy of the entire system and introduce a new type of
self-consistency for approximate CC approaches.
