Natural expansion of vibrational wave functions: RRGM with residue algebra

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Abstract
The natural expansion (NE) of vibrational eigenstates is useful for identifying the optimum local coordinates for any vibrational energy and it provides a positive test for regular (nonstochastic) behavior. In previous NE analyses, both eigenvalues and eigenvectors of the Hamiltonian matrix were required. However, through use of the recursive residue generation method (RRGM), we will illustrate how to perform the NE analysis without the need to compute eigenvectors of the N×N Hamiltonian matrix. In addition, a new computational method to obtain all transition amplitudes among a set of states is developed. The method, based upon residue algebra, reduces the CPU requirement by a factor of N/2. To illustrate these procedures, the A1 symmetry eigenfunctions in the classically chaotic regime (where the modes are strongly coupled) of a 2D model Hamiltonian are analyzed with the modified RRGM.