CCSD coupled-cluster singles, doubles triples, quadruples

B-CC = Brueckner CC CCD = coupled-cluster doubles CCSD = coupled-cluster singles and doubles CCSDT = coupled-cluster singles, doubles, and triples CCSDTQ = coupled-cluster singles, doubles, triples, and quadruples Cl = configuration interaction EOM = equation-on-motion FCI = full-configuration interaction. 

Unlike the CCSD model, the CCSDT and higher models - such as the coupled-cluster singles-doubles-triples-and-quadruples (CCSDTQ) model [8] - are therefore not treated in detail in this chapter. Fortunately, accurate coupled-cluster models have been developed that include the effects of the connected triples in an approximate fashion. We defer the discussion of such approximate CCSDT treatments to Chapter 14. 

For a more accurate treatment of electron correlation, coupled-cluster (CC) approaches [23] enter into play. While the full CC singles, doubles, triples (CCSDT) model [24] and augmented CCSDT approaches that feature corrections for quadruple and even higher excitations [25, 26] are currently too expensive, CC singles and doubles (CCSD) approximation [27] and CCSD augmented by a perturbative treatment of triple excitations, CCSD(T) [28], are more feasible and rather widely adopted. 

A second purpose of the present work is to assess the performance of the explicitly correlated coupled-cluster model CCSD(F12) that we have recently implemented in the TuR-BOMOLE program package [68, 69]. This model has the potential to yield electronic molecular energies at the level of coupled-cluster theory with single and double excitations (CCSD [37, 70]) at the limit of a complete one-particle basis set. In conjunction with corrections for higher excitations (connected triples and connected quadruples) it should be possible to compute the barrier height for the above reaction with an accuracy of about 1-2 kJ mol that is, with an error of about 0.5-1.0%. 

Couple cluster methods differ from perturbation theory in that they include specific corrections to the wavefunction for a particular type to an infinite order. Couple cluster theory therefore must be truncated. The exponential series of functions that operate on the wavefunction can be written in terms of single, double and triple excited states in the determinantl " . The lowest level of truncation is usually at double excitations since the single excitations do not extend the HF solution. The addition of singles along with doubles improves the solution (CCSD). Expansion out to the quadruple excitations has been performed but only for very small systems. Couple cluster theory can improve the accuracy for thermochemical calculations to within 1 kcal/mol. They scale, however, with increases in the number of basis functions (or electrons) as N . This makes calculations on anything over 10 atoms or transition-metal clusters prohibitive. 

CCSD(TQ) Coupled-cluster calculations with single and double substitutions with inclusion of noniterative triple and quadruple excitations ACCSD(T)) CCSD(T) correction term DFT Density functional theory... 

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