Computation of high-energy vibrational eigenstates: Application to C6H5D

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Abstract
In this study, a two loop iteration scheme, similar to one developed recently [Phys. Rev. E 51, 3643 (1995)], is applied to the computation of high energy vibrational eigenstates in 21-mode planar C6H5D. The computational method is based upon the use of a spectral filter to extract a small number of eigenpairs (near the test input energy E) from the interior of the dense energy spectrum. In the outer iteration loop, a very effective filter, the Green function G(E)=(E1−H)−1, is used to drive the Lanczos recursion algorithm through a small number of steps (frequently <10). The result is a small tridiagonal representation of the Green function. The Lanczos algorithm converges quickly because the desired eigenvalues, those near the test energy, are mapped to the extreme edges of the spectrum of the filter. In order to apply the Green function to the current Lanczos vector, a matrix partitioning technique is combined with a perturbation–iteration method in the inner iteration loop. The Green function–Lanczos algorithm, GFLA, was then used to compute eigenstates for 21-mode planar C6H5D near the energy of the v=3 CD overtone (about 6700 cm−1). These computations were done using an active space with the dimension 20 000. The resulting eigenfunctions were then subjected to several types of analysis, including basis state and vibrational mode distributions. It is shown that the energetic distribution of basis functions in the eigenvectors exhibits multifractal scaling (finer features built upon coarser features).