Theoretical Model Chemistry and Its Relevance to the Open-Shell Formalisms

THEORETICAL MODEL CHEMISTRY AND ITS RELEVANCE TO THE OPEN-SHELL FORMALISMS 

Before describing the unifying theme, which will classify the various theoretical developments in the cluster expansion formalisms, it is pertinent to summarize first certain essential criteria that an 

A Theoretical Model Chemistry /18,24/ has an underlying approximation scheme which is of potentially uniform precision for all the phenomena it wants to describe, so that the viability of the model can be tested by an appeal to the experimental results. The criteria that a theoretical model should satisfy are the following  

We may recall that the desirability of ensuring size-extensivity for a closed-shell state was one of the principal motivations behind the formulation of the MBPT for the closed-shells. The linked cluster theorem of Bruckner/25/, Goldstone/26/ and Hubbard/27/, proving that each term in the perturbation series for energy can be represented by a linked (connected) diagram directly reflects the size-extensivity of the theory. Hubbard/27/ and Coester/30/ even pointed out immediately after the inception of MBPT/25,26/, that the size-extensivity is intimately related to a cluster expansion structure of the associated wave-operator that is not just confined only to perturbative theory. The corresponding non-perturbative scheme for the closed-shells was first described by Coester and Kummel/30,31/ in nuclear physics and this was transcribed to quantum chemistry 

As Bartlett/18/ has pointed out, for a closed shell single determinant Hartree-Fock (HF) function as the starting point for MBPT or CC theory, separability into neutral fragments is not automatically guaranteed, since sometimes the UHF rather than the RHF dissociates properly. When the criteria (a) and (d) above are both satisfied, the model may be called 

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