Single-reference coupled-cluster

Recent years have witnessed a considerable activity towards extending the standard single-reference coupled-cluster (CC) methods (1-9) to potential energy surfaces (PESs) involving bond breaking without invoking a multireference description (see, e.g., refs 9-31). Undoubtedly, it would be very useful if we could routinely calculate large portions of molecular PESs with the ease-... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Perturbative analyses have yielded many insights into single-reference coupled-cluster theory. Although we generally are using the canonical transformation... 

In addition to the encouraging numerical results, the canonical transformation theory has a number of appealing formal features. It is based on a unitary exponential and is therefore a Hermitian theory it is size-consistent and it has a cost comparable to that of single-reference coupled-cluster theory. Cumulants are used in two places in the theory to close the commutator expansion of the unitary exponential, and to decouple the complexity of the multireference wave-function from the treatment of dynamic correlation. 

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... 

M. Head-Gordon and T. J. Lee, in Recent Advances in Coupled-Cluster Methods, R. J. Bartlett, Ed., World Scientific Publishing, Singapore, 1997, pp. 221-253. Single Reference Coupled Cluster and Perturbation Theories of Electronic Excitation Energies. 

P. G. Szalay, M. Nooijen, and R. J. Bartlett,/. Chem. Phys., 103, 281 (1995). Alternative Ansatze in Single Reference Coupled-Cluster Theory. III. A Critical Analysis of Different Methods. 

For nondegenerate systems, single reference coupled cluster (CC) methods have proven to be quite successful in their description of the electron correlation problem (1-3). This is primarily due to their (size) extensivity and ability to efficiently incorporate higher-order correlation effects—CC models including triple excitation effects are generally within 1-2 kcal mol 1 of full Cl (3). 

B. Datta, D. Mukherjee, Treatment of quasi-degeneracy in single-reference coupled-cluster theory. Separation of dynamical and nondynamical correlation effects, Chem. Phys. Lett. 235 (1995) 31. 

Cluster expansion representation of a wave-function built from a single determinant reference function [1] has been eminently successful in treating electron correlation effects with high accuracy for closed shell atoms and molecules. The cluster expansion approach provides size-extensive energies and is thus the method of choice for large systems. The two principal modes of cluster expansion developments in Quantum Chemistry have been the use of single reference many-body perturbation theory (SR-MBPT) [2] and the non-perturbative single reference Coupled Cluster (SRCC) theory [3,4]. While the former is computationally economical for the first few orders of the perturbation expansion... 

It is now well established by numerous and extensive applications that the single reference (SR) based many-body methods, viz. many-body perturbation theory (PT) [1], coupled cluster (CC) theory [2], coupled electron-pair approximations (CEPA) [3], etc. provide rather accurate descriptions of the energy in and around the equilibrium geometry of the closed-shell states. In particular, the single reference coupled cluster (SRCC)... 

Keywords Coupled-cluster theory Local correlation methods Cluster-inmolecule formalism Linear scaling algorithms Single-reference coupled-cluster methods CCSD approach CCSD(T) approach Completely renormalized coupled-cluster approaches CR-CC(2,3) approach Large molecular systems Bond breaking Normal alkanes Water clusters... 

The first term in Equation 6.2 is a direct term similar to the matrix elements of similarity-transformed Hamiltonians in single reference coupled cluster theory, while the second term is a coupling term that describes the coupling between model functions. It has been shown that the structme of the coupling term is crucial for ensuring that the theory is both size-extensive and intruder-free. 

Let us now return to the Rayleigh-Schrodinger formalism which is used in developing the standard coupled cluster formalism. The single-reference coupled cluster expansion can be developed by first of all writing the Schrodinger equation for the non-degenerate case as... 

The use of the exponential ansatz in formulating a quantum mechanical many-body theory was briefly described in Chapter 3, Section 3.3.2. This approach was first realized in nuclear physics by Coester and Ktimmel [81,82] and its introduction into quantum chemistry is usually attributed to Click. [76]. A recent overview of this method has been given by Paldus [73]. The single-reference coupled cluster approach has been described [83] as... 

MR-MBPT multi-reference many-body perturbation theory MR-MPPT multi-reference Mpller-Plesset perturbation theory CCSD single-reference coupled cluster with single and double replacements... 

Brillouin-Wigner single-reference coupled cluster with single and double replacements... 

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