Finite element method for two-dimensional vibrational wave functions: Theory and application to van der Waals molecules

A variational formulation finite element method is developed for calculatio n of vibrational wave functions in a domain spanned by close-coupled, or Ja cobi, coordinates R and gamma. C-1 tensor-product basis functions, which al low straightforward separation of kinetic and overlap integrals into produc ts of one-dimensional integrals, are used. Furthermore, representation of t he potential energy surface in terms of the same tensor-product basis funct ions used to represent the wave functions allows the potential energy integ rals to also be written as a sum of products of one-dimensional integrals. Factorization of the integrals, together with expression of one-dimensional integrals in analytic or rapidly convergent power series form, reduces the computational effort of calculation of all matrix elements to a small, and arguably insignificant, level. It is shown that the theoretical error in e igenvalue, i.e., O(h(6)) for bicubic Hermite functions, is achieved for a n umber of rare gas van der Waals triatomics for which surfaces have been pre viously published. We also present illustrative calculations on NeHCl and ( 2)A(') and (2)A(') NeHCl+, which have not been previously studied, for surf aces calculated at the CCSD(T)/cc-pVTZ level. (C) 2001 American Institute o f Physics.