CCSD energies

The CCSD energy is given by the general CC equation (4.53), and amplitude equations are derived by multiplying (4.50) with a singly excited determinant and integrating (analogously to eq. (4.54)). 

CCSD Energy Second Derivatives. The number in the parenthesis is CCSD with orbital relaxation. 

Here, Ti and T2 are the singly and doubly excited clusters obtained by solving the CCSD equations, is the CCSD energy, and... 

Let us now examine the contents of the QMMCC theory, in a somewhat greater detail, by discussing the QMMCC equations for the special case, where the QMMCC corrections are added to the CCSD energy (7 = Ti + T2) and Z is... 

CCSD) energy functional. unitary CCSD energy functional. 

Note tliat compared to the R12 benchmark energies, the CCSD energies with individual basis sets are quite slowly convergent. Even with the staggeringly large cc-pV6Z basis set, the mean unsigned error over the seven molecules remains 4.2 mEi,. The extrapolated values... 

As an example, consider the CCSD energy equation derived earlier in Eq. [134] using Wick s theorem. Each term of the general expression... 

Recognition of this relationship between coupled cluster theory and MBPT has inspired research efforts to construct perturbation-based corrections to the CCSD energy to account for higher excitation contributions. Undoubtedly, the most successful and popular of these is the (T) correction first described for closed-shell molecular systems by Raghavachari et al. " In the next section, we will describe the structure of this correction using diagrammatic techniques. 

As pointed out in the preceding section, the CCSD energy contains contributions identical to those of the MBPT(2) and MBPT(3) energy, but lacks triple-excitation contributions necessary for MBPT(4). Thus, a natural approach to the triples problem is to correct the CCSD energy for the missing MBPT(4) terms,using the CCSDT similarity-transformed Hamiltonian,... 

Note the appearance of the T3 operator through the use of Hccsdt- Since we wish to construct a correction to the CCSD energy, which already contains the contributions from the Tj and T2 terms, we need to construct only the component of Eq. [216], which may be represented diagrammatically as... 

The ROHF-CCSD energy is indeed completely spin-projected, as discussed in Refs. 35,27, and 37, but is still different from that computed using a spin-adapted coupled cluster wavefunction. 

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