Coupled-cluster ansatz

R. J. Bartlett, S. A. Kucharski, and J. Noga, Alternative coupled-cluster ansatz. II. The unitary coupled-cluster method. Chem. Phys. Lett. 155, 133-140 (1989). 

J. M. Cullen and M. C. Zerner,/. Chem. Rhys., 77, 4088 (1982). The Linked Singles and Doubles Model An Approximate Theory of Electron Correlation Ba.sed on the Coupled-Cluster Ansatz. 

Another important development was the reahzation of the importance of the size-consistency and size-extensivity in the studies of associative or dissociative chemical processes by Primas [67], as well as his clear delineation of the relationship between the configuration interaction and the exponential coupled-cluster Ansatze. 

Although the approach described above is presented in its most general form, using a multiple coupled-cluster Ansatz for the SS-MRCC formalism, suitable approxi-mants to it such as the state-specific multi-reference perturbation theory (SS-MRPT) or state-specific multi-reference CEPA (SS-MRCEPA) can be generated by straightforward approximations. Since the new closed component of the wave operator for IMS appear first at the quadratic power, it is evident that the expressions we have derived in this and the earlier papers for the CAS will remain valid if the quadratic powers of are ignored in the approximants to SS-MRCC for IMS. This implies that all the SS-MRPT... 

The k coefficients in the RSPT expansion can be obtained from the coupled-cluster ansatz through iteration of the T equations. For instance, the first iteration of the T2 equation gives K2 that is,... 

In principle, the coupled-cluster ansatz for the wave function is exact if the excitation operator in Eq. (8.234) is not truncated. But this defines an FQ approach, which is unfeasible in actual calculations on general many-electron systems. A truncation of the CC expansion at a predefined order in the excitation operator T is necessary from the point of view of computational practice. Truncation after the single and double excitations, for instance, defines the CCSD scheme. However, in contrast with the linear Cl ansatz, a truncated CC wave function is still size consistent, because all disconnected cluster amplitudes which can be constructed from a truncated set of connected ones are kept [407]. The maximum excitation in T determines the maximum connected... 

Let us summarize the spin-restricted coupled-cluster ansatz for high-spin open-shell systems [34]. The reference wave function is an RHF state and the projection manifold consists of determinants of the same spin projection as the reference state - for example, all states obtained from the reference state by single and double spin-orbital replacements. The spin-restricted coupled-cluster energy is calculated in the usual manner... 

MBPT/CCM can be developed from the coupled-cluster ansatz, 3... 

Also in the recently very active field of multireference coupled-cluster theory, first FI 2-extensions have been reported. Demel et al. reported such an development for the case of Mukherjee s state-specific multireference coupled-cluster ansatz (Mk-MRCC), while Liu et al. applied F12 theory to internally contracted multireference theory. 

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