In CCSD the ground-state energy is (as for CC2) evaluated as

E_{CC} |
= 〈HF| H| CC〉 = 〈HF| H exp(T)| HF〉 , |
(10.1) |

where the cluster operator

T_{1} |
= t_{ai}τ_{ai} , |
(10.2) |

T_{2} |
= t_{aibj}τ_{aibj} . |
(10.3) |

In difference to CC2, the cluster amplitudes

Ω_{μ1} |
= 〈μ_{1}| + [, T_{2}]| HF〉 = 0 , |
(10.4) |

Ω_{μ2} |
= 〈μ_{2}| + [, T_{2}] + [[, T_{2}], T_{2}]| HF〉 = 0 , |
(10.5) |

where again

and

E_{MP3, tot} = |
E_{HF} + E_{MP2} + E_{MP3} |
(10.6) |

= | 〈HF| + [, T_{2}^{(1)}]| HF〉 + t_{μ2}^{(1)}〈μ_{2}|[, T^{(1)}_{2}]| HF〉 |
(10.7) |

with

〈μ_{1}|[, T_{1}^{(2)}] + [, T^{(1)}_{2}]| HF〉 = |
0 | (10.8) |

〈μ_{2}|[, T_{2}^{(2)}] + [, T^{(1)}_{2}]| HF〉 = |
0 | (10.9) |

〈μ_{3}|[, T_{3}^{(2)}] + [, T^{(1)}_{2}]| HF〉 = |
0 | (10.10) |

From these the fourth-order energy correction is computed as:

E_{MP4} = |
t_{μ2}^{(1)}〈μ_{2}|[, T^{(2)}_{1} + T^{(2)}_{2} + T^{(2)}_{3}] + [[, T^{(1)}_{2}], T^{(1)}_{2}]| HF〉 . |
(10.11) |

Eqs. (10.5) and (10.7) - (10.11) are computational much more complex and demanding than the corresponding doubles equations for the CC2 model. If is a measure for the system size (e.g. the number of atoms), the computational costs (in terms of floating point operations) for CCSD calculations scale as

- Explicitly-correlated CCSD(F12) methods:
- CC calculations with restricted open-shell (ROHF) references:
- Perturbative triples corrections:
- Integral-direct implementation and resolution-of-the-identity approximation:
- Disc space requirements:
- Memory requirements:
- Important options:
- CCSD(T) energy with a second-order correction from the interference-corrected MP2-F12:
- Excitation energies with CCSD: