Generation and interpretation of chain parameters in the recursive residue generation method

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Abstract
In the recursive residue generation method [A. Nauts and R. E. Wyatt, Phys. Rev. Lett. 51, 2238 (1983)] molecular multiphoton excitation is treated by first converting the molecule-field Hamiltonian matrix into tridiagonal form, using the Lanczos equations. A procedure is developed here for construction of generating operators for successive recursive basis functions in the chain (tridiagonal) representation. These operators are used to construct the self-energies and the linking terms from successive moments of the Hamiltonian with respect to a source vector. These self-energies and linking terms are interpreted in terms of masses and stiffness of members of a mechanical chain and the chain dynamics is explained. The self-energies and coupling terms are expressed in terms of linked diagrams and explicit connections to the Hamiltonian moments are developed.