Coupled-cluster theory open-shell

M. Urban, P. Neogrady, and I. Hubac, Spin Adaptation in the Open-Shell Coupled-Cluster Theory with a Single Determinant Restricted Hartree-Fock Reference. In R. J. Bartlett (Ed.) Recent Advances in Coupled-Cluster Methods. Recent Advances in Computational Chemistry, Vol. 3. (World Scientific, Singapore, 1997), pp. 275-306. 

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]

Coupled Cluster Theory for Open-Shell Molecules... 

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. 

P.. Knowles, C. Hampel, and H.-. Werner,/. Chem. Phys., 99, 5219 (1993). Coupled-Cluster Theory for High-Spin, Open-Shell Reference Wave Functions. 

P. Neogrady, M. Urban, and I. Hubac, /. Chem. Phys., 100, 3706 (1994). Spin Adapted Restricted Hartree-Fock Reference Coupled-Cluster Theory for Open-Shell Systems. 

X. Li and J. Paldus,/. Chem. Phys., 101, 8812 (1994). Automation of the Implementation of Spin-Adapted Open-Shell Coupled-Cluster Theories Relying on the Unitary Group Formalism. 

M. Nooijen and R. J. Bartlett,/. Chem. Phys., 104,2652 (1996). General Spin Adaptation of Open-Shell Coupled Cluster Theory. 

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. 

C., and Werner, H.-J. (1993) Coupled cluster theory for high spin, open shell reference wave functions. J. Chem. Phys., 99, 5219 5227 (d) Watts, ).D., Gauss,... 

For open-shell molecules, spin contamination can be a problem, as mentioned earlier. DFT and coupled-cluster theory are resistant to spin contamination and may be helpful. One may also choose spin-restricted open-shell HF (ROHF) as a starting point, instead of UHF, unless dissociation behavior is important. ROHF has no spin contamination. 

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... 

Open-shell coupled-cluster theory can be formulated in terms of the one-particle spinor or spin-orbital basis. However, spin-restricted or Kramers-restricted open-shell theories are complicated by the ambiguous role of the open-shell orbital or Kramers pair. We develop here the basic outline of open-shell Kramers-restricted coupled-cluster theory. 

Well-defined variational (Cl-type see Configuration Interaction), perturbational (MPn see M0ller-Plesset Perturbation Theory), and coupled cluster (CC see Coupled-cluster Theory) techniques have all been employed to determine anharmonic force fields. Important conclusions of these studies include (1) Near equilibrium, the correlation energy is a low-order function of the bond distances,even a linear approximation is meaningful(2) For open-shell species, spin contamination can significantly deteriorate results if a... 

High-spin open-shell coupled-cluster theory... 

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. 

Lindsren I, Mukheriee D. On the connectivity criteria in the open-shell coupled-cluster theory. PhysRep. 1987 151 93. 

Chapter 13 discusses coupled-cluster theory. Important concepts such as connected and disconnected clusters, the exponential ansatz, and size-extensivity are discussed the Unked and unlinked equations of coupled-clustCT theory are compared and the optimization of the wave function is described. Brueckner theory and orbital-optimized coupled-cluster theory are also discussed, as are the coupled-cluster variational Lagrangian and the equation-of-motion coupled-cluster model. A large section is devoted to the coupled-cluster singles-and-doubles (CCSD) model, whose working equations are derived in detail. A discussion of a spin-restricted open-shell formalism concludes the chapter. 

---