Abstract
In this paper we analyse the relevant role played by the third-order correlation terms in the contracted Schrodinger equation (CSE) methodology. The quality of the approximations used when evaluating these terms influence significantly both the convergence of the iterative procedure and the accuracy of the final energy value obtained. But where the performance of these approximating algorithms for the third-order terms becomes crucial is in the study of those states whose description, at first-order, needs more than one Slater determinant. This is still an unsolved problem, which is analysed here. Two possible ways for approximately solving this problem are outlined here.
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