Completely renormalized

The isomerization process interconverting the three isomers depicted in Figure 4, with and without ammonia ligands, has been studied recently,54 58 using the completely renormalized coupled cluster level of theory, including... 

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... 

Nevertheless, it must be noted that in this way, we do not obtain a completely renormalized theory for all values of the space dimension d. In the regularized theory, the contributions of the diagrams remain meromorphic functions of d. Moreover, poles appear for physical values of d, in particular for d = 3. 

Examination of the terms to O(k ) in the SL expansion for the free energy show that the convergence is extremely slow for a RPM 2-2 electrolyte in aqueous solution at room temperature. Nevertheless, the series can be summed using a Pade approximant similar to that for dipolar fluids which gives results that are comparable in accuracy to the MS approximation as shown in figure A2.3.19(a). However, unlike the DHLL + i 2 approximation, neither of these approximations produces the negative deviations in the osmotic and activity coefficients from the DHLL observed for higher valence electrolytes at low concentrations. This can be traced to the absence of the complete renormalized second virial coefficient in these theories it is present... 

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... 

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