Previous studies on the use of diagrammatic moment methods in the recursive residue generation method lsqb;I. Schek and R. E. Wyatt, J. Chem. Phys.83, 3028, 4650 (1985)rsqb; are extended, with emphasis upon the role played by linked diagrams. Equivalence between the Green function for the source state (which initiates the recursion method) in the zero order and the corresponding tridiagonal (Lanczos) representation is shown. Chain parameters in the tridiagonal representation are constructed by comparing linked diagrams in the two representations and the dynamics of the source state is introduced in terms of the linked moments. The equivalence between Lanczos states and generalized doorway states is shown. Finally, a closed expression for the level shift of the source state (due to its interaction with the rest of the states) is given, using a diagrammatic approach in the tridiagonal representation.
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