Coupled-cluster theory closed shell

The SAC/SAC-CI method is a correlated electronic-structure theory for the ground and excited states in various spin multiplicities. The SAC method belongs to the coupled-cluster theory [30, 31]. In the case of a closed-shell singlet state, the SAC wave function is written as... 

The developments of the cluster expansion theories appear to have reached a stage where a clear perspective is beginning to emerge, although no comprehensive review of the various facets of the approach and a critical evaluation of the seemingly disparate formalisms put forward is available in the literature. There are, however, several reviews on closed-shell coupled cluster theories where the open-shell cluster expansion theories are also touched upon/18,19,21,22/. A few reviews on the open-shell MBPT describe in broad terms the cluster expansion techniques in so far as they relate to MBPT /20,23/. A concise survey of what we shall call full cluster expansion theories appears in a recent article by Lindgren and Mukherjee/94[Pg.293]

Recognition of this relationship between coupled cluster theory and MBPT has inspired research efforts to construct perturbation-based corrections to the CCSD energy to account for higher excitation contributions. Undoubtedly, the most successful and popular of these is the (T) correction first described for closed-shell molecular systems by Raghavachari et al. " In the next section, we will describe the structure of this correction using diagrammatic techniques. 

M.. O. Deegan and P.. Knowles, Chem. Phys. Lett., 117, 321 (1994). Perturbative Corrections to Account for Triple Excitations in Closed- and Open-Shell Coupled-Cluster Theories. 

Nonadditive effects in open-shell clusters have been investigated only recently and relatively little information is available on their importance and physical origin. From the theoretical point of view, open-shell systems are more difficult to study since the conventional, size-consistent computational tools of the theory of intermolecular forces, like the Mpller-Plesset perturbation theory, coupled cluster theory, or SAPT, are less suitable or less developed for applications to open-shell systems than to closed-shell ones. Moreover, there are many types of qualitatively different open-shell states, exhibiting different behavior and requiring different theoretical treatments. 

Most of the effort in coupled-cluster theory has concentrated on systems which are essentially of closed shell type, where the wave function is dominated by a single Slater determinant, such that the wave function can be expanded around this and good convergence is expected. 

At first, aU these methods were developed for closed-shell systems only. Later research in this area was directed towards local methods for open-shell systems and excited states, local triples corrections beyond (T) (triples included in coupled cluster iterations), [138], local energy gradients for geometry optimizations of large molecules [139], combination of the local correlation method with explicitly correlated wavefunctions. It is evident from the discussion that these local 0 N) methods open the applications of coupled-cluster theory to entirely new classes of molecules, which were far ont-of-scope for such an accurate treatment before. Possible applications lie, for example, in the determination of the thermochemistry of reactions involving... 

Except for the closed-shell CCSD theory of Section 13.7, the theory presented in this chapter has been that of spin-unrestricted coupled-cluster theory. Spin-unrestricted coupled-cluster theory has the advantage of conceptual simplicity and general applicability and is widely used for open-shell systems. Still, there are considerable disadvantages associated with the spin-unrestricted approach, making it worthwhile to look for an alternative approach for open-shell systems. First, spin-unrestricted coupled-cluster theory suffers from spin contamination, which may adversely affect the calculation of excitation processes and spin-dependent (magnetic) properties. Second, spin-unrestricted theory is expensive since, in the spin-orbital basis, we work with separate sets of orbitals for the alpha and beta spins. 

In the closed-shell theory of Section 13.7, we developed a spin-restricted theory in which both of these problems are solved. Thus, for closed-shell systems, we may calculate a singlet coupled-cluster wave function at a fraction of the cost of the corresponding spin-unrestricted wave function. Unfortunately, for open-shell systems, the problems are more complicated and it is no longer obvious how we should best satisfy the Schrbdinger and spin equations in coupled-cluster theory. 

For the treatment of electron correlation, Cizek uses classical techniques as well as techniques based on mathematical methods of quantum field theory, namely, a coupled-cluster approach. A rapid development and deployment of these methods during the past decade was stimulated by the realization of the importance of size consistency or size extensivity in the studies of reactive chemical processes. Although truly remarkable accuracy and development have been achieved for ground states of closed-shell systems, an extension to quasidegenerate and general open-shell systems is most challenging. Cizek also works on the exploitation of these approaches to study the electronic structure of extended systems (molecular crystals, polymers107). His many interests in-... 

The present contribution considers general electronic states of solvated molecules and is not limited to closed shell molecular compounds. For closed shell molecular systems, methods utilizing closed shell coupled-cluster electronic structure and closed shell density density functional theory for the electronic structure of the solvated system have appeared in the literature [54-67],... 

Koch H, Jdrgen H, Jensen A, Jorgensen P, Helgaker T, Scuseria GE, Schaefer III HF (1990) Coupled cluster energy derivatives. Analytic Hessian for the closed-shell coupled cluster singles and doubles wave function Theory and applications. J Chem Phys 92 4924-4940... 

H. Koch, H. J. Aa. Jensen, P. j0rgensen, T. Helgaker, G. E. Scuseria, and H. F. Schaefer, /. Chem. Phys., 92, 4924 (1990). Coupled-Cluster Energy Derivatives. Analytic Hessian for the Closed-Shell Coupled-Cluster Singles and Doubles Wave Functions Theory and Applications. 

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