Recursive residue generation

Such a method was first proposed by Wyatt and co-workers.43 7,56 In their so-called recursive residue generation method (RRGM), both eigenvalues and overlaps are obtained using the Lanczos algorithm, without explicit calculation and storage of eigenvectors. In particular, the residue in Eq. [41] can be expressed as a linear combination of two residues ... 

Phys., 104, 7807 (1996). Calculation of Vibrational (J=0) Excitation Energies and Band Intensities of Formaldehyde Using the Recursive Residue Generation Method. 

Quantum Dynamics The Recursive-Residue-Generation Method. 

Willoughby, Eds., North Holland, Amsterdam, 1986, pp. 67-79. Quantum Dynamics with the Recursive Residue Generation Method Improved Algorithm for Chain Propagation. 

N. M. Poulin, M. J. Bramley, T. Carrington Jr., H. G. Kjaergaard, and B. R. Henry, J. Chem. Phys., 104, 7807 (1996). Calculation of Vibrational (/ = 0) Excitation Energies and Band Intensities of Formaldehyde Using the Recursive Residue Generation Method. 

A. Nauts, R.E. Wyatt, New approach to many-state quantum dynamics—The recursive-residue-generation method, Phys. Rev. Lett. 51 (25) (1983) 2238-2241. 

General aspects of the recursion method. The recursive residue generation method provides a computationally efficient way to compute spectra and survival probabilities in large multistate systems. Before presenting any details, we will first review some of the basic features of the method. In order to make a link between the lineshape function and the term residue, we will rewrite Eq. (6) in Section I.B as... 

RRGM summary. In this section, we have reviewed the recursive residue generation method for the computation of the lineshape function and the transition probabilities. The RRGM aims at computation of the set of residues and eigenvalues ra, Ea. The steps are summarized as follows ... 

H. O. Karlsson and O. Goscinski Perturbed Hydrogenic Manifolds Studied by the Recursive Residue Generation Method J. Phys. B 25, 106 (1992). 

GENERATION AND IMPORTANCE OF LINKED AND IRREDUCIBLE MOMENT DIAGRAMS IN THE RECURSIVE RESIDUE GENERATION METHOD ... 

One can see from eq.(l) that the amount of Informations needed to compute the spectrum Is In fact rather limited only the eigenvalues and the projections < y Fo> of the ket y fo> onto the eigenvectors are needed, and not all their components. These Informations are provided straightforwardly through the Recursive Residue Generation (RRG) method of Wyatt and coworkers 17-8>, which is based on the Lanczos method. 

EOMCC = equation-of-motion coupled-clu.ster FOD = fourth-order differencing MBGF = many-body Green s function RR = resonance Raman RRGM = recursive-residue-generation method SIL = short-time iterative Lanczos SOD = second-order differencing. 

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