CCSD coupled-cluster singles, doubles approximations

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CCSD = coupled cluster single double excitations CVC = core-valence correlation ECP = effective core potential DF = density functional GDA = gradient corrected density approximation MCLR = multiconfigurational linear response MP2 = M0ller-Plesset second-order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multiconfigurational self-consistent field TD-SCF = time-dependent self-consistent field. 

There are cases where neither MC-GIAO nor MP2-GIAO is good enough and where more sophisticated treatments of electron correlation must be used. The climax on these lines is CCSD(T)-GIAO (where CCSD(T) = coupled cluster, singles-doubles-approximate triples). The computational cost of these sophisticated treatments is so high that it will probably remain limited to special cases. 

The single-reference coupled cluster (CC) theory [1-5] has become a standard computational tool for studying ground-state molecular properties [6-10]. The basic approximations, such as CCSD (coupled cluster singles and doubles approach) [11-15], and the noniterative CCSD[T] [16,17] and CCSD(T) [18] methods, in which the cleverly designed corrections due to... 

There have been many calculations of a for neon itself at various levels of approximation. Some of these are summarized in Ref. [26] and a basis set analysis has been made in Ref. [25]. Of the electron-correlated results[42]-[47], there appears to be a consensus that the best value using coupled-cluster-single-doubles wavefunctions with a perturbational estimate of connected triplet excitations, CCSD(T), is 2.680-2.690 au[25],[44],[46],[47]. 

In Table 6.3, the values of De for RfCU are compared with those obtained within various approximations using relativistic effective core potentials (RECP) Kramers-restricted Hartree-Fock (KRHF) (Han et al 1999), averaged RECP including second-order M0ller-Plesset perturbation theory (AREP-MP2) for the correlation part (Han et al. 1999), RECP coupled-cluster single double (triple) [CCSD(T)] excitations (Han et al. 1999), and a Dirac-Fock-Breit (DFB) method (Malli and Styszynski 1998). The AREP-MP2 calculation of De gives 20.4 eV, while the RECP-CCSD(T) method with correlation leads to 18.8 eV. Our value of De of 19.5 eV is just between these calculated values. 

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. 

The partitioned equation-of-motion second-order many-body perturbation theory [P-EOM-MBPT(2)] [67] is an approximation to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) [17], which will be fully described in Section 2.4. The EOM-CCSD method diagonalizes the coupled-cluster effective Hamiltonian H = [HeTl+T2) in the singles and doubles space, i.e.,... 

In this section we construct working equations for the coupled cluster singles and doubles (CCSD) method. Beginning from the approximation 7 = 7 + T2, we use algebraic and diagrammatic techniques to obtain programmable... 

In this coupled-cluster singles and doubles (CCSD) approximation, none of the coefficients in the FCI expansion is ignored. Instead, they are approximated by a much smaller set of singles and doubles amplitudes. 

Spin-spin coupling constants were evaluated using the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method in the Cl (configuration interac-tion)-like approximation [52, 53], with all electrons correlated. For these calculations, the Ahlrichs [54] qzp basis set was placed on and F, and the qz2p basis... 

The purpose of the present work is to test the efficiency and performance of the implementation of the explicitly correlated coupled-cluster singles-and-doubles, CCSD(F12), model in the Turbomole package. This model, initially proposed by Fliegl et al. [41], is the approximation to the full CCSD-F12 approach originally given by Noga et al [40]. It has been demonstrated that this method is able to recover quintuple- quality correlation energies with the orbital basis set of the size of triple- [31]. 

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