E_{CC} |
= 〈HF| H| CC〉 = 〈HF| H exp(T)| HF〉 , |
(9.1) |

= E_{SCF} + t^{ab}_{ij} + t^{a}_{i}t^{b}_{j}2(ia| jb) - (ja| ib), |
(9.2) |

where the cluster operator

T_{1} |
= t_{ai}τ_{ai} |
(9.3) |

T_{2} |
= t_{aibj}τ_{aibj} |
(9.4) |

(for a closed-shell case; in an open-shell case an additional spin summation has to be included). The cluster amplitudes

with

= exp(- *T*_{1})*H* exp(*T*_{1}),

where

The residual of the cluster equations
*Ω*(*t*_{ai}, *t*_{aibj})
is the
so-called vector function.
The recommended reference for the CC2 model is ref. [109],
the implementation with the resolution-of-the-identity approximation, RI-CC2,
was first described in ref. [10].