Approximate-coupled-clusters-doubles

Coupled—Pair Functional (ACPF) and Coupled Electron Pair Approximation (CEPA). The simplest form of CEPA, CEPA-0, is also known as Linear Coupled Cluster Doubles (LCCD). 

Christiansen O, Koch H, Jorgensen P (1995) The second-order approximate coupled cluster singles and doubles model CC2. Chem Phys Lett 243 409 t 18... 

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

O. Christiansen, H. Koch, and P. Jorgensen, Chem. Phys. Lett., 243, 409 (1995). The Second-Order Approximate Coupled Cluster Singles and Doubles Model CC2. 

Various approximations of Eq. (6), the exact wave function in the coupled-cluster formalism, have been discussed in the chemical literature. In particular, Cizek s coupled-pair many-electron theory (CPMET),5 also referred to as coupled-cluster doubles (CCD) by Bartlett,8 has re-... 

CCDPPA coupled-cluster doubles polarization propagator approximation (Section VII. E),... 

The ab initio HF calculations reported below have been performed with the GAUSSIAN 76 [26] program package. The atomic basis sets applied are a minimal (STO-3G [26]) one, a split valence (6-31G [26]) one, a split-valence one plus a set of five d-functions on carbon (6-31G [26]), and one with an additional set of p-functions on hydrogen (6-31G [26]). The correlation energy has been computed using Mpller-Plesset many body perturbation theory of second order (MP2) [27], the linear approximation of Coupled Cluster Doubles theory (L-CCD)... 

Approximate Coupled Cluster Methods Combined Reduced Multireference and Almost-Linear Coupled Cluster Methods with Singles and Doubles ... 

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. 

Pedersen, T. B., Sanchez de Meras, A. M.and Koch, H. (2004). Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions, /. Chem. Phys. 120, pp. 8887-8897, doiilO.1063/1. 1705575. 

Photoisomerization of gas-phase azobenzene was theoretically calculated by A-self-consistent-field (ASCF) density-functional theory (DFT), time-dependent DFT (TD-DFT), and approximate coupled cluster singles and doubles (R1-CC2) methods and discussed ... 

Refs. [44, 46, 49, 51], the second- and third-order approximate coupled cluster (CC2 and CC3) calculations of Ref. [50], the equation of motion coupled cluster with single, double and perturbative triple excitations calculations of Ref. [45], the symmetry adapted cluster configuration interaction calculations of Ref. [48] and the time-dependent density functional theory calculations using the B3LYP functional of Ref. [39]. 

Order Approximate Coupled Cluster Singles and Doubles Model CC2. 

Christiansen, O., Koch, H., and Jprgensen, P. (19956). The second-order approximate coupled cluster singles and doubles model CC2. Chem. Phys. Lett., 243, 409-418. Christiansen, O., Koch, H., and Jprgensen, P. (1996). Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies. J. Chem. Phys., 105, 1451-1459. 

The currently available dispersion corrections including effects of intramolecular correlation are E, / = 1, 2. These corrections typically account for about 20% of dispersion energy. Recently a coupled-cluster doubles (CCD) approximation to the dispersion energy has been developed including singles and triples contributions calculated with the converged double excitation amplitudes. For the systems investigated so far the total effect beyond was small so that the... 

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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