Coupled cluster single-double excitations

Atomic calculations. Most atomic calculations for the heaviest elements were performed by using Dirac-Fock (DF) and Dirac-Slater (DS) methods [20-24,58] and later by using multiconfiguration Dirac-Fock (MCDF) [64-72] and Dirac-Coulomb-Breit Coupled Cluster Single Double excitations (DCB CCSD) [73-85] methods, with the latter being presently the most accmate one. 

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. 

Comparing the different methods with the experimental data of Kaufman and Radziemski [88], the excitation energies of the U + ion appear to be best described by the XIHFSCCSD scheme (extrapolated Intermediate Hamiltonian Fock-Space Coupled Cluster Singles Doubles excitations), which within the large UBS basis set gives an MAE relative to the experimental data of 1,650 cm without and 651 cm with the Breit interaction. 

Equilibrium Bond Distance and the Harmonic Frequency for N2 from the 2-RDM Method with 2-Positivity (DQG) Conditions Compared with Their Values from Coupled-Cluster Singles-Doubles with Perturbative Triples (CCD(T)), Multireference Second-Order Perturbation Theory (MRPT), Multireference Configuration Interaction with Single-Double Excitations (MRCI), and Full Configuration Interaction (FCI)". 

Kucharski SA, Bartlett RJ (1991) Recursive intermediate factorization and complete computational linearization of the coupled-cluster single, double, triple, and quadruple excitation equations. Theor Chim Acta 80 387 105. 

Kucharski SA, Wloch M, Musial M, Bartlett RJ (2001) Coupled-cluster theory for excited electronic states The full equation-of-motion coupled-cluster single, double, and triple excitation method. J Chem Phys 115 8263-8266. 

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]. 

D. Watts and R.. Bartlett,/. Chem. Phys., 93, 6104 (1990). The Coupled-Cluster Single, Double, and Triple Excitation Model for Open-Shell Single Reference Functions. 

S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta, 80,387 (1991). Recursive Intermediate Factorization and Complete Computational Linearization of the Coupled-Cluster Single, Double, Triples, and Quadruple Excitation Equations. 

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. 

CCSD(T) Coupled Cluster singles, doubles and perturbative triple excitations... 

For high accuracy, we must take into account also the connected triple excitations. Truncating the cluster expansion (13.2.5) at the T3 level, we arrive at the coupled-cluster singles-doubles-and-triples (CCSDT) model [6,7]. Although highly accurate for the description of dynamical correlation, the CCSDT model is computationally very demanding and can be applied only to small systems. 

Koch H, Jensen HJA, Jorgensen P, Helgaker T (1990) Excitation-energies from the coupled cluster singles and doubles linear response function (CCSDLR) - applications to be, CH+, CO, and H2O. J Chem Phys 93 3345... 

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

Christiansen O, Koch H, J0rgensen P (1996) Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies. J Chem Phys 105 1451-1459. 

Shiozaki T, Hirao K, Hirata S (2007) Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states. J Chem Phys 126 244106 (11 pages). 

G. E. Scuseria, A. C. Scheiner, T. J. Lee, J. E. Rice, and H. F. Schaefer, J. Chem. Phys., 86, 2881 (1987). The Closed-Shell Coupled-Cluster Single and Double Excitation (CCSD) Model for the Description of Electron Correlation. A Comparison with Configuration Interaction (CISD) Results. 

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