In explicitly-correlated CCSD calculations the double excitations
into products of virtual orbitals, described by
*T*_{2} = *t*_{aibj}*τ*_{aibj},
are augmented with double excitations into the explicitly-correlated
pairfunctions (geminals) which are described in Sec. 8.5:

T |
= T_{1} + T_{2} + T_{2'} |
(10.6) |

T_{2'} |
= c^{kl}_{ij}τ_{kilj} |
(10.7) |

where

Ω_{μ1} |
= 〈μ_{1}| + [, T_{2} + T_{2'}]| HF〉 = 0 , |
(10.8) |

Ω_{μ2} |
= 〈μ_{2}| + [, T_{2} + T_{2'}] + [[, T_{2} +2T_{2'}], T_{2}]| HF〉 = 0 , |
(10.9) |

Ω_{μ2'} |
= 〈μ_{2'}|[, T_{2'}] + + [, T_{2}]| HF〉 = 0 . |
(10.10) |

Similar as for MP2-F12, also for CCSD(F12) the coefficients for the doubles excitations into the geminals,

E_{CCSD(F12)-SP} |
= L_{CCSD(F12)} = 〈HF| H| CC〉 + c_{μ2'}Ω_{μ2'} |
(10.11) |

This is the recommended approach which is used by default if not any other approch has been chosen with the

`examp`

option
in `examp noinv`

option should not be combined with CCSD calculations).
CCSD(F12)-SP calculations are computationally somewhat less expensive
that CCSD(F12) calculations which solve Eq. (10.10),
while the boths approaches are approximately similar accurate for
energy differences.
The CPU time for a CCSD(F12) calculation is approximately the sum of the
CPU time for an MP2-F12 calculation with the same basis sets plus that
of a conventional CCSD calculation multiplied by
(1 + *N*_{CABS}/*N*), where
*N* is the number of basis and *N*_{CABS} the number of
complementary auxiliary basis (CABS)
functions (typically
*N*_{CABS} 2 - 3*N*).
If the geminal coefficients are determined by solving Eq. (10.10)
instead of using fixed amplitudes, the costs per CCSD(F12) iteration
increase to
(1 + 2*N*_{CABS}/*N*) the costs for conventional CCSD iteration.
Irrespective how the geminal coefficients are determined, the disc space
for CCSD(F12) calculations are approximated a factor of
(1 + 2*N*_{CABS}/*N*)
larger than the disc space required for a conventional CCSD calculation.
Note that this increase in the computational costs is by far outweighted
by the enhanced basis set convergence.