If we truncate our equations at the CCSD level, it corresponds to performing a transformation of the Hamiltonian matrix of the following type for a six particle problem (with a two-body Hamiltonian):
| \( 0p-0h \) | \( 1p-1h \) | \( 2p-2h \) | \( 3p-3h \) | \( 4p-4h \) | \( 5p-5h \) | \( 6p-6h \) | |
| \( 0p-0h \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | 0 | 0 | 0 | 0 |
| \( 1p-1h \) | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | 0 | 0 | 0 |
| \( 2p-2h \) | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | 0 | 0 |
| \( 3p-3h \) | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | 0 |
| \( 4p-4h \) | 0 | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) |
| \( 5p-5h \) | 0 | 0 | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) |
| \( 6p-6h \) | 0 | 0 | 0 | 0 | \( \tilde{x} \) | \( \tilde{x} \) | \( \tilde{x} \) |