Enhanced method for determining rovibrational eigenstates of van der Waals molecules

The discrete variable representation (DVR) method has been modified in three major ways to produce a more efficient scheme for calculating the rotational-vibrational energies of van der Waals molecules. First, the implicitly restarted Lanczos method (IRLM) of Sorensen (SIAM J. Matrix Anal. Appl. 1992, 13, 357) is used to determine the eigenpairs of interest. Second, Chebychev polynomial preconditioning is applied to make it easier to project out unwanted eigenfunctions and thus speed up the convergence of the IRLM. Finally, a very efficient matrix-vector algorithm is introduced that makes maximum use of the underlying sparsity of the DVR Hamiltonian. Calculations for a protypical system Ar-HCl are reported. For the 20 lowest Ar-HCl eigensolutions corresponding to angular momentum J = 1 and using only a single processor of a Gray YMP, the modified DVR approach is about 6 times faster than the original DVR method and 14 times faster than the collocation method of Feet and Yang (J. Chem. Phys. 1989, 91, 6598). As the total angular momentum is increased, the relative performance of the modified DVR approach improves dramatically. For instance, with J = 5 the modified method is about 45 times faster than the original DVR and 100 times faster than the collocation method on a single processor of a Gray YMP. This modified DVR approach also runs significantly faster on a range of workstations such as DEC Alpha and the IBM RS/6000. Application of this method is also shown to be effective in obtaining an improved interaction potential for the A(2) Sigma(+) state of Ar-HO.