Size extensive formulations incomplete model space

SIZE-EXTENSIVE FORMULATIONS WITH INCOMPLETE MODEL SPACE (IMS)... 

There are mainly two inter-related reasons why on would like to formulate a size-extensive theory involving incomplete model spaces (i) to bypass intruders, (ii) for calculating the low-lying EE s of a closed-shell ground state, one feels that a set of hole-particle determinants would suffice as a choice for a reasonable model space, which involves valence holes as well as valence particles. This is an IMS. 

Incomplete model spaces generate disconnected diagrams not only for the h used by Hose and Kaldor, but for other perturbative and CC formulations [20, 45, 46]. The effects of such diagrams on the size extensivity of the calculated energies depend both on the particular h and on the kind of model space used [21, 47-52]. Most of the recent work on... 

Coupled Cluster based size-extensive intermediate hamiltonian formalisms were developed by our group [33-35] by way of transcribing a size-extensive CC formulation in an incomplete model space in the framework of intermediate hamiltonians. In this method, there are cluster operators correlating the main model space. There are no cluster operators for the intermediate space. This formulation thus is conceptually closer to the perturbative version of Kirtman... 

There have been several attempts to avoid the CAS restriction and achieve size extensivity for an incomplete model space (see, for example. Refs. [69,70]). The methods based on abandoning the intermediate normalization condition resulted in an excessively complex formalism and as far as we know were actually never implemented. Only recently this problem has been attacked successfully by Li and Paldus, who introduced so called C-conditions for the amplitudes of internal excitations [15,42,43,71]. When these conditions are incorporated into the MRCC amplitude equations of the Jeziorski-Monkhorst method, the solutions with a general incomplete model space become also exactly size extensive. The C-conditions are, however, not limited to the original Jeziorski-Monkhorst formulation [36], but rather they apply to any Hilbert-space MRCC... 

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