Full cluster expansion theories

FULL CLUSTER EXPANSION THEORIES IN HILBERT SPACE... 

FULL CLUSTER EXPANSION THEORIES IN FOCK SPACE 7.1 Preliminaries for a Fock Space Approach... 

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]

As explained in Sec.2, the full cluster—expansion theories in Hilbert space are designed to compute wave-functions for the open-shell states that are explicitly size-extensive with respect to the total number of electrons N. The underlying cluster structure of all these developments is what was envisaged by Silverstone and Sinanoglu/48/s... 

Full-scale treatments of correlation effects, found to be necessary to repair some of the known deficiencies of the HF model wavefunction, generally are done by Configuration Interaction theory [l),(5j. With highly developed computer codes it has been found possible to include more than 10s — 10 determinants, either explicitly or implicitly in the wavefunction expansion. Unfortunately, procedures for selecting the most important terms in the Cl expansion have proved to be a source of difficulty, despite successes of Coupled Cluster methods and related schemes (6],[7]. 

The only way to get a wave operator that is symmetric under time-reversal symmetry is to impose the restriction from the beginning. While this fixes the relations between the amplitudes, it also forces the occupied and the unoccupied Kramers components of the open shell to be treated equivalently. This equivalence is what introduces the ambiguity in the treatment of the open shell the open-shell Kramers pair must behave as both a particle and a hole, and the result is that the truncated commutator expansions in the coupled-cluster equations are much longer than in closed-shell theory. The alternative is to use an unrestricted wave operator with the Kramers-restricted spinors. The use of the latter provides some reduction in the work due to the relations between the integrals, but not a full reduction (Visscher et al. 1996). 

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