Coupled-cluster method CCSDT

Piecuch P, Kucharski SA, Bartlett RJ (1999) Coupled-cluster methods with internal and semiinternal triply and quadruply excited clusters CCSDt and CCSDtq approaches. J Chem Phys 110 6103-6122. 

Watts JD, Bartlett RJ (1996) Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states The EOM-CCSDT-3 and EOM-CCSD(r) methods. Chem Phys Lett 258 581-588. 

J. D. Watts and R. J. Bartlett, Chem. Phys. Lett., 258, 581 (1996). Iterative and Noniterative Triple Excitation Corrections in Coupled-Cluster Methods for Excited Electronic States— The EOM-CCSDT-3 and EOM-CCSD(T) Methods. 

Another major point in which the theoretical methods differ is the quantum chemical approach to solve the operator equation of the Hamilton operator itself. The most important schemes are Hartree-Fock self consistent field (HF-SCF), density functional theory (DFT) and multi-body second order perturbation theory (MP2). Different combinations have been established, so for instance GIAO-SCF, GlAO-DI I, (,IA()-MI>2, or DF I-IGLO. Most precise measurements on small systems were done with coupled cluster methods, as for instance GIAO-CCSDT-n. ... 

M. Rittby and R. J. Bartlett,/. Phys. Chem., 92,3033 (1988). An Open-Shell Spin-Restriaed Coupled Cluster Method Application to Ionization Potentials in N2. (ROHF-CCSD, ROHF-CCSDT-1, QRHF-CCSD.)... 

It is generally accepted that the family of coupled cluster methods, CCSD, CCSD(T) and CCSDT represents the most sophisticated class of single-reference methods that are... 

Abstract The singlet-triplet splittings of the di-radicals methylene, trimethylene-methane, ortha-, meta- and para-benzynes, and cyclobutane-l,2,3,4-tetrone have become test systems for the applications of various multi-reference (MR) coupled-cluster methods. We report results close to the basis set limit computed with double ionization potential (DIP) and double electron attachment (DBA) equation-of-motion coupled-cluster methods. These diradicals share the characteristics of a 2-hole 2-particle MR problem and are commonly used to assess the performance of MR methods, and yet require more careful study unto themselves as benchmarks. Here, using our CCSD(T)/6-311G(2d,2p) optimized geometries, we report DIP/DEA-CC results and single-reference (SR) CCSD, CCSD(T), ACCSD(T) and CCSDT results for comparison. 

Instead of the very demanding CCSDT calculations one often performs CCSD (T) (note the parentheses), in which the contribution of triple excitations is represented in an approximate way (not refined iteratively) this could be called coupled cluster approximate (or perturbative) triples. The quadratic configuration method (QCI) is very similar to the CC method. The most accurate implementation of this in common use is QCISD(T) (quadratic Cl singles, doubles, triples, with triple excitations treated in an approximate, non-iterative way). The CC method, which is usually only moderately slower than QCI (Table 5.6), is apparently better [102]. CCSD(T) calculations are, generally speaking, the current benchmark for practical molecular calculations on molecules of up to moderate size. 

Kowalski, K. Piecuch, P The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches, ... 

This equation is not restricted to the CCSD approximation, however. Since higher excitation cluster operators such as T3 and T4 cannot produce fully contracted terms with the Hamiltonian, their contribution to the coupled cluster energy expression is zero. Therefore, Eq. [134] also holds for more complicated methods such as CCSDT and CCSDTQ. Higher excitation cluster operators can contribute to the energy indirectly, however, through the equations used to determine the amplitudes, and t-h, which are needed in the energy equation above. 

Every term in the coupled cluster amplitude equations that is nonlinear in T may be factored into linear components. As a result, each step of the iterative solution of the CCSD equations scales at worst as ca. 0(X ) (where X is the number of molecular orbitals). The full CCSDT method in which all Tycon-taining terms are included requires an iterative 0(X ) algorithm, whereas the CCSD(T) method, which is designed to approximate CCSDT, requires a noniterative O(X ) algorithm. The inclusion of all T4 clusters in the CCSDTQ method scales as... 

By truncating the cluster operator f after single, double, triple,... replacements the hierarchy of coupled cluster models CCS, CCSD, CCSDT, etc. is obtained. In this series the accuracy of the results - but also the computational costs -converge rapidly to those of Full Configuration Interaction (FCI). This motivated the development of several intermediate methods which are derived from the above standard models by either... 

Perturbation and coupled cluster theories (e.g., MP2 or CCSD) provide correlation corrections. Density functional theory (DPT) appears to offer the best of all worlds, correlation-quality results at single-determinant prices. However, there is always a limit somewhere. The choice today seems to be between correlated methods with large basis sets, such as CCSDT, which systematically approach the "correct" answer at appreciable cost, and DFT, with its relatively economical efficiency, but which cannot be systematically improved (5). 

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