Coupled-cluster doubles method

QCISD(T) = quadratic Cl including single, double, and triple excitations, UCCD(ST) = coupled-cluster doubles method based on the unrestricted Hartree-Fock method and corrected for single and triple replacements, MC SCF = multiconfiguration SCF, MRD Cl = multireference singles and doubles Cl, MBPT= many-body perturbation theory, SD Cl = singles and doubles Cl. 

Results. Calculations were carried out at two internuclear separations, the equilibrium Re = 2.0844 A as in Ref. [89], and 2.1 A, for comparison with Ref. [127]. The relativistic coupled cluster (RCC) method [130, 131] with only single (RCC-S) or with single and double (RCC-SD) cluster amplitudes is used (for review of different coupled cluster approaches see also [132, 133] and references). The RCC-S calculations with the spin-dependent GRECP operator take into account effects of the spin-orbit interaction at the level of the one-configurational SCF-type method. The RCC-SD calculations include, in addition, the most important electron correlation effects. 

Bachrach, S. M., Chiles, R. A., and Dykstra, C. E., Application of an approximate double substitution coupled cluster (ACCD) method to the potential curves of CO and NeHe Higher order correlation effects in chemically and weakly bonded molecules, J. Chem. Phys. 75, 2270-2275 (1981). 

Besler, B. H., Scuseria, G. E., Scheiner, A. C., and Schaefer, FI. F., A systematic theoretical study of harmonic vibrational frequencies The single and double excitation coupled cluster (CCSD) method, J. Chem. Phys, 89, 360-366 (1988). 

In spite of the method s present utility and popularity, the quantum chemical community was slow to accept coupled cluster theory, perhaps because the earliest researchers in the field used elegant but unfamiliar mathematical tools such as Feynman-like diagrams and second quantization to derive working equations. Nearly 10 years after the essential contributions of Paldus and Cizek, Hurley presented a re-derivation of the coupled cluster doubles (CCD) equa-... 

The Coupled-clusters (CC) method[7] based on the cluster expansion of the wavefunction has been established as a highly reliable method for calculations of ground state properties of small molecules with the spectroscopic accuracy. When this method is used together with a flexible basis set it recovers the dominant part of the electron correlation. Typically, CC variant explicitly considering single and double excitations (CCSD) is used. In order to save computer time the contributions from triple excitations are often calculated at the perturbation theory level (notation CCSD(T) is used in this case). CCSD(T) method can be routinely used only for systems with about 10 atoms at present. Therefore, it cannot be used directly in zeolite modeling, however, results obtained at CCSD(T) level for small model systems can serve as an important benchmark when discussing the reliability of more approximate methods. 

B. H. Besler, G. E. Scuseria, A. C. Scheiner, and H. E Schaefer III,/. Chem. Phys., 89,. 350 (1988). A Systematic Theoretical Study of Harmonic Vibrational Frequencies The Single and Double Excitation Coupled Cluster (CCSD) Method. 

Inclusion of only J2 gives an approximate CC approach called the coupled-cluster doubles (CCD) method. Since = + T2 + lf + , the wave function i ccd contains determinants with double substitutions, quadruple substitutions, hextuple substitutions, and so on. Recall (Section 15.17) that quadruple substitutions are next in importance after double substitutions in a Cl wave function. The treatment of quadruple substitutions in the CCD method is only approximate. The CCD quadruple excitations are produced by the operator tl, and so the coefficients of the quadruply substituted determinants are determined as products of the coefficients of the doubly substituted determinants [see Eq. (15.92)], rather than being determined independently, as in the CI-SDTQ method The CCD approximation of the coefficients of the quadruply substituted determinants turns out to be pretty accurate. 

In the following, the theory of Kutzelnigg s linear R12 functions shall be presented and analyzed in the framework of the coupled-cluster doubles (CCD) method, To illustrate the ideas and approximations employed in the linear R12 methods, it is sufficient to consider the CCD model, as the corresponding CCD-R12 theory exhibits all properties of the R12 theories. It is a relatively simple matter to include singles (CCSD) or even triples (for example in the CCSD(T) method), and CI-R12-type wave functions or MPn-R12 energies require essentially the same computational procedures as the CCD-R12 approach. 

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