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CC2 Ground-State Energy Calculations

The CC2 ground-state energy is--similarly to other coupled-cluster energies--obtained from the expression

ECC = 〈HF| H| CC〉 = 〈HF| H exp(T)| HF〉  , (9.1)
  = ESCF + $\displaystyle \sum_{{iajb}}^{}$$\displaystyle \Big[$tabij + taitbj$\displaystyle \Big]$$\displaystyle \Big[$2(ia| jb) - (ja| ib)$\displaystyle \Big]$, (9.2)

where the cluster operator T is expanded as T = T1 + T2 with

T1 = $\displaystyle \sum_{{ai}}^{}$taiτai (9.3)
T2 = $\displaystyle {\frac{{1}}{{2}}}$$\displaystyle \sum_{{aibj}}^{}$taibjτaibj (9.4)

(for a closed-shell case; in an open-shell case an additional spin summation has to be included). The cluster amplitudes tai and taibj are obtained as solution of the CC2 cluster equations [109]:

Ωμ1 = 〈μ1|$\displaystyle \hat{{H}}$ + [$\displaystyle \hat{{H}}$, T2]| HF〉 = 0  , (9.5)
Ωμ2 = 〈μ2|$\displaystyle \hat{{H}}$ + [F, T2]| HF〉 = 0  , (9.6)

with

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

where μ1 and μ2 denote, respectively, the sets of all singly and doubly excited determinants.

The residual of the cluster equations Ω(tai, taibj) 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].



Subsections
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