Xg. Wang et T. Carrington, The utility of constraining basis function indices when using the lanczos algorithm to calculate vibrational energy levels, J PHYS CH A, 105(12), 2001, pp. 2575-2581
Direct product basis sets are frequently used to calculate vibrational ener
gy levels of small polyatomic molecules. They have the important advantage
of simplicity. However, they have the important disadvantage that a very la
rge number of direct product functions is necessary to obtain converged ene
rgy levels. By using an iterative, rather than an explicit, method to calcu
late eigenvalues of the Hamiltonian matrix, it is possible to calculate ene
rgy levels despite the huge size of the direct product basis. Nonetheless,
it is natural to attempt to reduce the size of the direct product basis by
excluding functions that do not contribute to the wave functions associated
with the energy levels of interest. In this paper we present a variational
basis representation (VBR) example and a discrete variable representation
(DVR) example demonstrating that it is possible to use the Lanczos method a
nd exclude direct product basis functions by restricting basis function ind
ices while maintaining the favorable n(f+1) scaling relation for the cost o
f direct product basis matrix-vector products.