Characteristics of the Implementation and Computational Demands

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 = T₁ + T₂ consist of linear combination of single and double excitations:

$$\sum_{{ai}}^{}$$ T₁ (10.2)

$${\frac{{1}}{{2}}} \sum_{{aibj}}^{}$$ T₂ (10.3)

In difference to CC2, the cluster amplitudes t_ai and t_aibj are determined from equations which contain no further approximations apart from the restriction of T to single and double excitations:

$$\hat{{\tilde{H}}} \hat{{\tilde{H}}}$$ Ω_μ1 (10.4)

$$\hat{{\tilde{H}}} \hat{{\tilde{H}}} \hat{{H}}$$ Ω_μ2 (10.5)

where again

$$\hat{{\tilde{H}}}$$ = exp(- T₁)$$\hat{{H}}$$exp(T₁),

and μ₁ and μ₂ are, respectively, the sets of all singly and doubly excited determinants. Eq. (10.5) is computational much more complex and demanding than the corresponding doubles equations for the CC2 model. If $\cal {N}$ 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 $\cal {O}$($\cal {N}$⁶). If for the same molecule the number of one-electron basis functions N is increased the costs scale with $\cal {O}$($\cal {N}$⁴). (For RI-MP2 and RI-CC2 the costs scale with the system size as $\cal {O}$($\cal {N}$⁵) and with the number of basis functions as $\cal {O}$($\cal {N}$³).)