The Coupled Pair Approaches

Let us now turn to the coupled pair methods. The conventional discussion of these approaches starts from the well known exp(T) ansatz for the wave operator. Since this ansatz is reviewed elsewhere, we will choose an alternative route, which is in fact more straightforward. From a practical (or technical) point of view, pair techniques aim at a size-extensive treatment at the computational expense of a Cl calculation with single and double excitations (CI(SD)), which requires including effects of higher excitations in an approximate manner. This goal has been approached in basically three different ways  

The coupled electron-pair approximation (CEPA). This starts from the hierarchy of the full Cl equations. A truncation on the SD level is then achieved by approximating the Hamiltonian matrix elements which couple the singles and doubles with higher terms (triples, quadruples). 

The coupled pair functional (CPF). An alternative route is to begin with the convenient expression for the CI(SD) energy, to analyse its drawbacks (violation of size extensivity) and to remedy these shortcomings by means of appropriate modifications of the energy functional. 

The variational CEPA (CEPA-V). - In this variant one constructs an energy functional which upon variation yields CEPA equations as closely as possible. 

The first of these approaches, the CEPA method of W. Meyer, leads to coupled pair equations of the form (if we concentrate on the doubles in this 

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