By Dirac

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**Example text**

Ground-state potential energy curves of the N2 molecule as described by the STO-3G basis set. The QECCSD, ECCSD, QECCSD(TQ), and ECCSD(TQ) calculations were performed using the ECC theory of Arponen and Bishop. the QECCSD(TQ) potential energy curve for the DZ N2 molecule is located above the full CI curve and the QECCSD(TQ) approach completely eliminates the unphysical humps on the CR-CCSD(T) and CR-CCSD(TQ) curves, obtained with the CCSD values of T1 and T2 . , CR-CC) calculations. All of this is very encouraging, since the QECCSD(TQ) method is a relatively inexpensive singlereference approach employing the spin-adapted RHF reference.

As in the case of the MBS S4 model, we examined the quality of the T1 and T2 clusters obtained in the CCSD and various ECC calculations for N2 by computing the expectation values of the Hamiltonian, designated by X , where X = CCSD, BECCSD, QECCSD, and ECCSD, with the normalized CCSD-like wave functions (X) Ψ0(X) = N (X) eT1 (X) +T2 |Φ , X = CCSD, BECCSD, QECCSD, ECCSD, (62) where T1(X) and T2(X) (X = CCSD, BECCSD, QECCSD, ECCSD) are the T1 and T2 cluster components obtained with the CCSD, BECCSD, QECCSD, and complete ECCSD meth(X) † (X) † (X) (X) ods, respectively, and N (X) = Φ|e(T1 ) +(T2 ) eT1 +T2 |Φ −1/2 are the corresponding normalization factors (see Table 3).

Thus, in order to develop practical methods based on the MMCC theory defined by equation (72), we must first truncate the manybody expansions for corrections δ0(A) or δ0(CCSD) at some, preferably low, excitation level mB satisfying mA < mB < N . This leads to the MMCC(mA , mB ) schemes, in which we calculate the energy as follows [11–13,30–32,74,75]: (MMCC) E0 (A) where E0 (A) (mA , mB ) = E0 + δ0 (mA , mB ), (82) is the energy obtained with the standard CC method A and mB n δ0 (mA , mB ) = n=mA +1 k=mA +1 Ψ0 |Cn−k (mA )Mk (mA )|Φ Ψ0 |eT (A) |Φ (83) is the relevant MMCC correction.