Cluster and Quadratic Configuration Interaction Methods

Coupled Cluster and Quadratic Configuration Interaction Methods 

Exploring Chemistry with Electronic Structure Methods 

Including triply excited configurations is often needed in order to obtain very accurate results with MP4, QCISD or CCSD (see Appendix A for some of the computational details). The following example illustrates this effect. 

The structure of ozone is a well-known pathological case for electronic structure theory. Prior to the QCI and coupled cluster methods, it proved very difficult to model accurately. The following table summarized the results of geometry optimizations of ozone, performed at the MP2, QCISD and QCISD(T) levels using the 6-31G(d) basis set  

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The concomitant advances in theoretical methodologies and algorithms have also played a vital role in increasing computational capabilities for theoretical thermochemistry. These advances include (1) new methods for accurate treatment of electron correlation in molecules and atoms such as coupled cluster and quadratic configuration interaction methods, (2) new basis sets such as the correlation consistent basis sets, and (3) development of model chemistry ... 

Coupled-cluster and quadratic configuration interaction methods... 

Coupled Cluster and Quadratic Configuration Interaction Methods. 117... 

Z. He and D. Cremer, Int. J. Quantum Chem., Quant. Chem. Symp., 25,43 (1991). Analysis of Coupled Cluster and Quadratic Configuration Interaction Theory in Terms of Sixth-Order Perturbation Theory. Z. He and D. Cremer, Theor. Chim. Acta, 85, 305 (1993). Analysis of Coupled Cluster Methods. 11. What Is the Best Way to Account for Triple Excitation in Coupled Cluster Theory. ... 

An extensive quantum-mechanical study that included correlation by second-order Meller-Plesset perturbation and quadratic configuration-interaction methods showed that the cluster species (NH4)2 is bound with respect to 2 NH4 by 7.5 to 9.7 kcal/mol, but unstable with respect to 2 NH3 + H2 by 86 to 89 kcal/mol. The bonding results from the interaction of the 3sai Rydberg orbitals of NH4. A minimum-energy structure of C2h symmetry was predicted. 

CBS extrapolation procedure Coupled cluster methods Exphcitly correlated CCSD(T) computation Configuration interaction methods and quadratic configuration interaction methods Counterpoise-correction procedure... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

One of the most dramatic changes in the standard theoretical model used most widely in quantum chemistry occurred in the early 1990s. Until then, ab initio quantum chemical applications [1] typically used a Hartree-Fock (HF) starting point, followed in many cases by second-order Moller-Plesset perturbation theory. For small molecules requiring more accuracy, additional calculations were performed with coupled-cluster theory, quadratic configuration interaction, or related methods. While these techniques are still used widely, a substantial majority of the papers being published today are based on applications of density functional theory (DFT) [2]. Almost universally, the researchers use a functional due to Becke, whose papers in 1992 and 1993 contributed to this remarkable transformation that changed the entire landscape of quantum chemistry. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

Two approaches to electron correlation that are widely used today for the studies of organic radical cations are Coupled Cluster (CC) calculations or the similar, but not identical, Quadratic Configuration Interaction (QCI) method with single and double excitations, often followed by CCSD(T) or QCISD(T) single point calculations with a larger basis set. These methods suffer to a much lesser extent from... 

C. Hampel, K. A. Peterson, and H.-J. Werner, Chem. Phys. Lett., 190, 1 (1992). A Comparison of the Efficiency and Accuracy of the Quadratic Configuration Interaction (QCISD), Coupled-Cluster (CCSD), and Brueckner Coupled-Cluster (BCCD) Methods. 

Although a wide variety of theoretical methods is available to study weak noncovalent interactions such as hydrogen bonding or dispersion forces between molecules (and/or atoms), this chapter focuses on size consistent electronic structure techniques likely to be employed by researchers new to the field of computational chemistry. Not stuprisingly, the list of popular electronic structure techniques includes the self-consistent field (SCF) Hartree-Fock method as well as popular implementations of density functional theory (DFT). However, correlated wave function theory (WFT) methods are often required to obtain accmate structures and energetics for weakly bound clusters, and the most useful of these WFT techniques tend to be based on many-body perturbation theory (MBPT) (specifically, Moller-Plesset perturbation theory), quadratic configuration interaction (QCI) theory, and coupled-cluster (CC) theory. 

For correlated methods such as truncated configuration interaction (CID or CISD), coupled cluster (CCD or CCSD), quadratic configuration interaction (QCISD) and Brueckner doubles (BD) (see Configuration Interaction and Coupled-cbister Theory), the energy and wavefunction can be written as... 

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