VIBRATIONAL EIGENSTATES OF 4-ATOM MOLECULES - A PARALLEL STRATEGY EMPLOYING THE IMPLICITLY RESTARTED LANCZOS METHOD

We present an approach for determining the vibrational eigenstates of four-atom molecules. The primary representation of the (six-dimensiona l) eigenstates involves a finite basis or quantum number representatio n, whereas Hamiltonian matrix-vector products are evaluated with the a id of certain grid or discrete variable representations. This approach leads to computational and memory demands that are within acceptable limits. The implicitly restarted Lanczos method, as implemented in the ARPACK suites of codes, is then applied to determine some of the corr esponding vibrational eigenstates. A distributed-memory parallel imple mentation of the method allows very large symmetric matrix eigenvalue problems on the order of N = 2 x 10(6) - to be tackled. The lowest fif ty vibrational states of the HOCO molecule, with zero total angular mo mentum and even parity, are accurately computed on Argonne National La boratory's IBM SP computer. (C) 1998 Published by Elsevier Science B.V .