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10.1. CC2 GROUND-STATE ENERGY CALCULATIONS
187
• for the auxiliary def2-basis sets from Rb to Rn the reference is:
A. Hellweg, C. Hättig, S. Höfener, and W. Klopper, Theor. Chem. Acc.
117 (2007) 587–597.
• for the auxiliary cc-pVXZ-PP, aug-cc-pVXZ-PP, cc-pwCVXZ-PP, and
aug-cc-pwCVXZ-PP basis sets for Ga–Kr, In–Xe, and Tl–Rn:
C. Hättig, G. Schmitz, J. Koßmann, Phys. Chem. Chem. Phys. 14 (2012)
6549–6555.
(For more details on the references for the basis sets included in the basis set
libraries of the TURBOMOLE distribution see Sec. 1.3 and the library files.)
10.1
CC2 Ground-State Energy Calculations
The CC2 ground-state energy is—similarly to other coupled-cluster energies—obtained from the expression
ECC = hHF|H|CCi = hHF|H exp(T )|HFi ,
ih
i
X h ij
= ESCF +
tab + tia tjb 2(ia|jb) − (ja|ib) ,
(10.1)
(10.2)
iajb
where the cluster operator T is expanded as T = T1 + T2 with
X
T1 =
tia τai
(10.3)
ai
T2 =
1 X ij
tab τaibj
2
(10.4)
aibj
(for a closed-shell case; in an open-shell case an additional spin summation has to
be included). The cluster amplitudes tia and tij
ab are obtained as solution of the CC2
cluster equations [124]:
Ωµ1 = hµ1 |Ĥ + [Ĥ, T2 ]|HFi = 0 ,
(10.5)
Ωµ2 = hµ2 |Ĥ + [F, T2 ]|HFi = 0 ,
(10.6)
with
Ĥ = 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. [124], the implementation with the
resolution-of-the-identity approximation, RI-CC2, was first described in ref. [10].