Extended coupled cluster theory

Improving the T and Ti Components by the Extended Coupled-Cluster Theory... 

Improving the quality of the quasi-degenerate electronic wave functions and the description of bond breaking by the extended coupled-cluster theory... 

THE EXTENDED COUPLED-CLUSTER THEORY OF PIECUCH AND BARTLETT... 

Feller, D. and Dixon, D.A. (2001) Extended benchmark studies of coupled cluster theory through triple excitations. J. Chem. Phys., 115, 3484-3496. 

The convergence of the quantum chemical calculations can be studied in terms of two types of hierarchies. First, the quality of the calculations depends on the flexibility of the MO space the AOs that are used to expand the MOs may be extended in a well-defined and systematic manner, thereby establishing a one-electron hierarchy. Second, we can increase the excitation level in coupled-cluster theory or the order of perturbation expansion, thus setting up an n-electron hierarchy of approximate electronic wave functions. In Fig. 5, the roles of the one-electron and the ra-electron hierarchies are illustrated. 

Couple cluster methods differ from perturbation theory in that they include specific corrections to the wavefunction for a particular type to an infinite order. Couple cluster theory therefore must be truncated. The exponential series of functions that operate on the wavefunction can be written in terms of single, double and triple excited states in the determinantl " . The lowest level of truncation is usually at double excitations since the single excitations do not extend the HF solution. The addition of singles along with doubles improves the solution (CCSD). Expansion out to the quadruple excitations has been performed but only for very small systems. Couple cluster theory can improve the accuracy for thermochemical calculations to within 1 kcal/mol. They scale, however, with increases in the number of basis functions (or electrons) as N . This makes calculations on anything over 10 atoms or transition-metal clusters prohibitive. 

NEW ALTERNATIVES FOR ELECTRONIC STRUCTURE CALCULATIONS RENORMALIZED, EXTENDED, AND GENERALIZED COUPLED-CLUSTER THEORIES... 

New alternatives for electronic structure calculations Renormalized, extended, and generalized coupled-cluster theories 119... 

Extended articles on the most common electron correlation methods such as limited configuration interaction (Cl see Configuration Interaction), M0ller-Plesset many-body perturbation theory (MBPT see M0ller Plesset Perturbation Theory), variation-perturbation methods (such as PCILO see Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) and Configuration Interaction), and coupled cluster theory (CC see Coupled-cluster Theory), as well as on explicitly ri2-dependent wave functions (see rxi Dependent Wave functions), can be found elsewhere. 

More recent investigations with the RPH employ standard correlation-corrected methods such as M0ller-Plesset (MP) perturbation theory (see M0ller-Plesset Perturbation Theory) at second or fourth order (MP2, MP4) or coupled cluster (CC) methods (see Coupled-cluster Theory) in connection with DZP or TZP basis sets. The repertoire of methods has recently been extended by applying density functional theory (DFT) (see Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field) and some convincing results have been published (see Section 3). 

Extended coupled cluster (ECC) theory (76,77) is a powerful existing framework for going beyond the standard coupled cluster energy ansatz, (3) In ECC theory (limited to double excitations, here), the energy is obtained by minimizing the following functional with respect to the bra (A2) and ket (T2) amplitudes ... 

The coupled-cluster model represents a significant improvement on the truncated Cl model in that it provides a description of the electronic structure that is both size-extensive and noore compact. On the other hand, it has proved difficult to extend the application of coupled-cluster theory to... 

In the RISM-SCF theory, the statistical solvent distribution around the solute is determined by the electronic structure of the solute, whereas the electronic strucmre of the solute is influenced by the surrounding solvent distribution. Therefore, the ab initio MO calculation and the RISM equation must be solved in a self-consistent manner. It is noted that SCF (self-consistent field) applies not only to the electronic structure calculation but to the whole system, e.g., a self-consistent treatment of electronic structure and solvent distribution. The MO part of the method can be readily extended to the more sophisticated levels beyond Hartree-Fock (HF), such as configuration interaction (Cl) and coupled cluster (CC). 

If affordable, there is a range of very accurate coupled-cluster and symmetry-adapted perturbation theories available which can approach spectroscopic accuracy [57, 200, 201]. However, these are only applicable to the smallest alcohol cluster systems using currently available computational resources. Near-linear scaling algorithms [192] and explicit correlation methods [57] promise to extend the applicability range considerably. Furthermore, benchmark results for small systems can guide both experimentalists and theoreticians in the characterization of larger molecular assemblies. 

The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

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