Completely renormalized methods

It has been demonstrated in several benchmark calculations that the CR-CCSD(T) (completely renormalized CCSD(T)) and CR-CCSD(TQ) (completely renormalized CCSD(TQ)) methods provide an excellent description of entire PESs involving single and double bond dissociation (P, 13, 15, 17-19, 21, 111), highly-excited vibrational term values near dissociation 17, 18, 21, 111), and... 

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... 

In this work, in addition to the CCSD approximation, we examine two different ways of correcting the CCSD energy for the effects of the connected triply excited clusters, namely, the CCSD(T) method and its completely renormalized CR-CC(2,3) extension. Since the CCSD(T) approach can be obtained as a natural approximation to CR-CC(2,3) [24, 25], we begin our brief description of both methods with the key equations of CR-CC(2,3). 

In this chapter, we have reviewed our recent effort toward the extension of the linear scaling local correlation approach of Li and coworkers [38 0], abbreviated as CIM, to the standard CCSD approach and two CC methods with a non-iterative treatment of connected triply excited clusters, including the conventional CCSD(T) method and its completely renormalized CR-CC(2,3) analog [102] (see, also, W. Li and P. Piecuch, unpublished work). The local correlation formulation of the latter method based on the CIM formalism is particularly useful, since it enables one to obtain an accurate description of single bond breaking and biradicals, where CCSD(T) fails, with an ease of a black-box calculation of the CCSD(T) type [24-26, 109-117]. At the same time, CR-CC(2,3) is as accurate as CCSD(T) in applications involving closed-shell molecules near their equilibrium geometries. 

Oono (1983) has applied the method of renormalization group transformations for hydrodynamic quantities in the whole crossover region. In this ca.se, the complete renormalization group equation 17 should be considered, with its general solution of the form... 

New noniterative coupled-cluster methods for bond breaking the method of moments of coupled-cluster equations and its quadratic variant and the renormalized and completely renormalized coupled-cluster approaches... 

As mentioned in the Introduction, the renormalized (R) and completely renormalized (CR) CC approaches, which represent new classes of noniterative single-reference CC methods that are capable of removing the failing of the standard CCSD(T) and similar methods at larger internuclear separations, are based on the formalism of the method of moments of CC equations (MMCC) [11-13, 30-32,36, 75, 76]. Thus, we begin our description of the R-CC and CR-CC methods and their quadratic MMCC (QMMCC) extension for multiple bond breaking with a synopsis of the general MMCC theory. 

This leads to the so-called MMCC(my, ttib) schemes. The renormalized and completely renormalized CCSD(T) and CCSD(TQ) methods discussed in... 

The renormalized and completely renorm,alized CCSD(T) and CCSD(TQ) methods... 

The completely renormalized CCSD(T) method (the CR-CCSD(T) approach) is an MMCC(2,3) scheme, in which the wave function o) is replaced by the very simple, MBPT(2)[SDT]-like, expression. 

Although calculations of entire molecular PESs involving single bond breaking require using CR-CCSD[T] and CR-CCSD(T) methods rather than their simplified renormalized versions [11-13,30,31,33,35,37], these R-CCSD[T] and R-CCSD(T) approaches allow us to understand the relationship between the standard and completely renormalized CC approaches. 

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