CC2 Ground-State Energy Calculations

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

E_CC = 〈HF| H| CC〉 = 〈HF| H exp(T)| HF〉  , (9.1)

$$\sum_{{iajb}}^{} \Big[ \Big] \Big[ \Big]$$ (9.2)

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

$$\sum_{{ai}}^{}$$ T₁ (9.3)

$${\frac{{1}}{{2}}} \sum_{{aibj}}^{}$$ T₂ (9.4)

(for a closed-shell case; in an open-shell case an additional spin summation has to be included). The cluster amplitudes t_ai and t_aibj are obtained as solution of the CC2 cluster equations [101]:

$$\hat{{H}} \hat{{H}}$$ Ω_μ1 (9.5)

$$\hat{{H}}$$ Ω_μ2 (9.6)

with

$$\hat{{H}}$$ = 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(t_ai, t_aibj) is the so-called vector function. The recommended reference for the CC2 model is ref. [101], the implementation with the resolution-of-the-identity approximation, RI-CC2, was first described in ref. [10].