CCSD energy, defined

The idea of renormalizing the CCSD(T) method via the MMCC formalism, as described above, can be easily extended to the CCSD(TQ) case. The resulting CR-CCSD(TQ) approaches are examples of the MMCC(2,4) scheme, defined by Eq. (44), in which we improve the results of the CCSD calculations by adding the non-iterative corrections Sq(2, 4), defined in terms of moments 9Jt fc(2) and 0Jll lcd(2), to the CCSD energies. Two variants of the CR-CCSD(TQ) method, labeled by the extra letters a and b , are particularly useful. The CR-CCSD(TQ),a and CR-CCSD(TQ),b energies are calculated in the following manner [11-14,24,33,34] ... 

The coefficients entering Eqs. (13) and (14) are the hole-particle de-excitation amplitudes that in the exact expansion of the correlation energy in terms of the generalized moments of the CCSD equations, which produces the full Cl energy, define the three-body component of the left ground eigenstate (l of the similarity-transformed Hamiltonian obtained by diagonalizing ff(ccso) jjj gj,tire... 

CCSD energy, given by Eq. (13) and defining the CR-CC(2,3), CCSD(T), and other non-iterative triples CC approximations, can be rewritten as sums of contributions associated with the individual occupied spin-orbitals. The CCSD correlation energy A (ccsD) is a sum of the contributions defined by Eq. (11), whereas the... 

We performed the benchmark calculations of DFT+ALL methods in order to assess applicability. We used the CCst, GCst, and GGst proposed in JSCH-benchmark sets [34], where the most accurate computations were performed with approximated CCSD(T)/CBS-limit level of theory. We compared these references with the results of DFT+ALL methods in several basis sets. Pople-type basis sets (6-31G,6-31G(d,p),6-31++G(d,p),6-311+G(d,p),6-311++G(df,pd) were used for this benchmark. We estimated the stacking energy between C (or G) and C (or G). By means of in the conventional DFT, HF, and MP2 methods, we estimated the stacking energy defined as... 

The starting point for our discussion is equation (13.2.30) for the CCSD energy and equations (13.2.40) and (13.2.41) for the CCSD amplitudes. Omitting from these equations all terms containing commutators that are quadratic or higher in f and from (13.2.41) also the term containing [[H, f i], til we arrive at the equations that define the ( CISD model ... 

Another standard for quality/price is defined within the coupled cluster approach. In particular, the CCSD(T) method [42] is nowadays generally accepted as the most accurate method which can be applied systematically for systems of a reasonable size. One must nevertheless be aware of the high computational cost of the method, which is often used only for energy calculations on geometries optimized with other computational methods. 

For sake of comparison, in all studied cases, we run calculations for those geometries and basis sets with a FCI (or near FCI) available. The methods we deal with are CCSD, CAS-SDCI, (SC)2CAS-SDCI and ec-CCSD corrected from both CAS-SDCI and (SC) CAS-SDCI. The performance of the methods is examined from two aspects the total energy and the quality of the potential energy surface (PES), being this quality measured by the so-called non-parallelity error (NPE). For a given set of calculations in a dissociative curve, the NPE is defined as the difference between the maximal and minimal deviation from the exact FCI PES. 

CC/EOMCC equations corresponding to the approximate method A, as defined by Eq. (48). In particular, if we want to recover the full Cl energies E from the CCSD/EOMCCSD energies (the niA = 2 case), we... 

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