Coupled cluster single-double excitations CCSD

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. 

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. 

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]. 

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

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)... 

Instead, practical methods involve a subset of possible Slater determinants, especially those in which two electrons are moved from the orbitals they occupy in the HF wavefunction into empty orbitals. These doubly excited determinants provide a description of the physical effect missing in HF theory, correlation between the motions of different electrons. Single and triple excitations are also included in some correlated ab initio methods. Different methods use different techniques to decide which determinants to include, and all these methods are computationally more expensive than HF theory, in some cases considerably more. Single-reference correlated methods start from the HF wavefunction and include various excited determinants. Important methods in inorganic chemistry include Mpller-Plesset perturbation theory (MP2), coupled cluster theory with single and double excitations (CCSD), and a modified form of CCSD that also accounts approximately for triple excitations, CCSD(T). 

A different study provides some further information coneeming the effects of electron correlation upon calculated intensities. In addition to SCF and MPn type methods, these authors considered also the coupled-cluster model which is an infinite-order generalization of MR Coupled-cluster, limited to single and double excitations (CCSD), was considered, as well as CCSD + T which includes the effects of connected triple excitations. The doubleharmonic approximation was made, consistent with most calculations of H-bonded systems. The [5s3pld/3slp] basis set is of the polarized double- variety, within reach of most workers. 

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. 

As has been demonstrated by numerous studies, the accuracy of properties calculated using the GGA DFT methods is, in most cases, comparable to or better than those from ab initio MP2 (Mpller-Plesset second-order perturbation) or CISD (configuration interaction with single and double excitations) methods. In fact, the accuracy of the DFT results in some instances matches those obtained from the much more costly (but, in principle, more exact) CCSD(T) (coupled cluster singles and doubles with a perturbative inclusion of connected triple excitations) method (29) and the ab initio G1 procedure (30). 

---