Coupled pair theory

Primas, H. Separability in many-electron systems. In Modem quantum chemistry. Istanbul lectures. Sinanoglu, O. (ed.). New York Academic Press 1965 s°) Paldus, J., Ctzek, J. Relation of coupled-pair theory, Cl and some other many-body approaches. In Energy, Structure, and Reactivity. Proceedings of the 1972 Boulder Summer Research Conference on Theoretical Chemistry. Smith, D. W., McRae, W. B. (eds.). New York Wiley 1973, pp. 198-212... 

In recent work on gradient evaluations in coupled pair theories, Pulay gave a succinct description of the properties which should ideally be incorporated in a fictitious pair theory ... 

Pulay reconsidered Eq. (56) in his paper on gradient evaluation in coupled pair theories. There he aimed for a thorough variation of (56) and named this approach variational CEPA (CEPA-V). 

The CPF method—and other coupled pair theories developed to date— nowhere accounts for effects of linked triples, quadruples and higher terms. In view of available evidence we expect these terms to increase both R. and Dg, which would reduce discrepancies with experiment. The neglect of linked triples may be the major error source of the CPF method, as has already been mentioned in Section IV.B. 

Although size consistency seems like a modest requirement, all forms of Cl except full Cl, which is of course exact, do not have this property. In this chapter we consider pair and coupled-pair theories, which are size consistent, and in the next chapter we discuss a form of perturbation theory, which also has this property. Ilie price one pays for size consistency is that unlike DCI, pair and perturbation theories are not variational and the total... 

In Section 5.2 we consider how to go beyond the lEPA by incorporating coupling between different pairs of electrons. We will discuss the coupled pair many-electron theory (CPMET) which is also called the coupled-cluster approximation (CCA). We then describe a number of simplifications to this rather sophisticated approach in particular, we consider the coupled electron pair approximation (CEPA). Finally, in Subsection 5.2.4 we present some numerical applications of coupled-pair theories. 

Table 5.2 The formal rdathmshlp between DCI and various coupled-pair theories...

Hurley, A. C., Electron Correlation in Small Molecules, Academic Press, New York, 1976. An advanced monograph containing a detailed discussion of Cl, lEPA, and various forms of coupled-pair theories with numerous literature references. The CCA equations are given in an explicit form. 

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